Hydrodynamical Aspects of the Eutrophication Modelling in the Case of Lake Balaton

NOT F O R QUOTATION W I T H O U T P E R M I S S I O N O F T H E AUTHOR

HYDRODYNAMICAL A S P E C T S O F T H E E U T R O P H I C A T I O N M O D E L L I N G I N T H E C A S E O F LAKE BALATON

L . S o m l y o d y

F e b r u a r y 1 9 7 9 C P - 7 9 - 1

C o Z Z a b o r a t i v e Papers r e p o r t w o r k w h i c h h a s n o t been p e r f o r m e d s o l e l y a t t h e I n t e r n a t i o n a l I n s t i t u t e f o r A p p l i e d S y s t e m s A n a l y s i s and w h i c h h a s received o n l y l i m i t e d r e v i e w . V i e w s o r o p i n i o n s e x p r e s s e d h e r e i n do n o t n e c e s s a r i l y r e p r e s e n t t h o s e of t h e I n s t i t u t e , i t s N a t i o n a l M e m b e r O r g a n i z a t i o n s , o r o t h e r o r g a n i - z a t i o n s s u p p o r t i n g t h e w o r k .

I N T E R N A T I O N A L I N S T I T U T E F O R A P P L I E D S Y S T E M S A N A L Y S I S A - 2 3 6 1 L a x e n b u r g , A u s t r i a

L. Somlyody i s w i t h t h e R e s e a r c h C e n t e r f o r Water R e s o u r c e s Development, B u d a p e s t , Hungary.

PREFACE

S i n c e A p r i l 1978 a c o l l a b o r a t i v e sk.udy h a s b e e n underway between IIASA and t h e C o o r d i n a t i o n C o u n c i l f o r t h e E n v i r o n m e n t a l R e s e a r c h on Lake B a l a t o n o f t h e H u n g a r i a n Academy o f S c i e n c e s . T h i s s t u d y i s aimed a t t h e d e v e l o p m e n t and i n v e s t i g a t i o n of t h e t h r e a t o f t h e l a k e ' s i n c r e a s i n g e u t r o p h i c a t i o n . P r i n c i p a l e l e m e n t s o f t h e s t u d y a r e t h e i d e n t i f i c a t i o n o f t h e dominant n u t r i e n t s o u r c e s , t h e i n v e s t i g a t i o n o f t h e d o m i n a n t modes o f n u t r i e n t t r a n s p o r t f r o m t h e w a t e r s h e d t o t h e l a k e , and t h e

s t u d y of t h e e f f e c t s o f t h e n u t r i e n t i n p u t s on t h e w a t e r q u a l i t y o f t h e l a k e s w i t h t h e h e l p o f w a t e r q u a l i t y m o d e l s .

T h i s c o l l a b o r a t i v e p a p e r d e a l s w i t h t h e m o d e l l i n g o f w a t e r movement a s p a r t of t h e w a t e r q u a l i t y m o d e l l i n g e l e m e n t of t h e p r o j e c t . The p a p e r summarizes t h e s p e c i a l h y d r o d y n a m i c a l f e a t u r e s o f t h e l a k e , a n a l y z e s t h e r e l e v a n c e i n c o n n e c t i o n w i t h e u t r o p h i - c a t i o n and s e t s o u t s c e n a r i o s f o r f u r t h e r work on t h o s e hydro- d y n a m i c a l a s p e c t s t h a t a r e i m p o r t a n t f o r a b e t t e r u n d e r s t a n d i n g of t h e l a k e ' s q u a l i t y d e v e l o p m e n t .

The work r e p o r t e d i n t h i s p a p e r was p r e p a r e d by t h e a u t h o r d u r i n g a s h o r t s t a y a t IIASA. I t i s r e c o g n i z e d t h a t i t c o n s t i t u t e s o n l y t h e f i r s t s t e p i n a c o n t i n u i n g e f f o r t . W e would t h e r e f o r e a p p r e c i a t e a n y comments, r e m a r k s , o r s u g g e s t i o n s by o u r r e a d e r s t h a t c o u l d h e l p t o b e t t e r s h a p e f u t u r e a c t i v i t i e s i n t h i s f i e l d .

HYDRODYNMIICAL ASPECTS OF TIE EUTROPIIICATION b1ODELLING IN CASE OF

LAKE M L A T O N

Contents

1. Introduction

2. Origin of Information Available

3.

Characterization of the Motion of Air, Vater and Sediment

4. Applicability of a Hydrodynamic-Transport Model for Lake Balaton

5 . Recommendations

References

Figures, Tables

1. INTRODUCTION

Most of t h e e u t r o p h i c a t i o n models assume t h a t t h e r e i s a s p a t i a l homogeneity i n s p a c e and o n l y tlie change o f t h e p r o c e s s w i t h t i m e h a s t o be c o n s i d e r e d . The e q u a t i o n s a r e o r d i n a r y d i f f e r e n t i a l ones ( g e n e r a l l y n o n - l i n e a r ) b u t

i n v o l v e nany u n c e r t a i n t i e s because of t h e u n s a t i s f a c t o r y knowledge on tlie b i o l o g i c a l p r o c e s s e s and l a c k of c o n s i s t e n t d a t a .

I n s p i t e of t h e s e d i f f i c u l t i e s o f t e n t h e s p a t i a l v a r i a - t i o n s may n o t be n e g l e c t e d and t r a n s p o r t p r o c e s s e s (mainly i n p r e s e n c e of l a r g e r p o l l u t a n t s o u r c e s ) h a s t o b e t a k e n i n t o c o n s i d e r a t i o n ( s e e e.g. Halfon and Lam, 1978, 1978; Lam and J a q u e t , 1976; P a r k e r , 1978; George and Iseaney, 1978). S p a t i a l changes may be c a u s e d n o t o n l y by t r a n s p o r t p r o c e s s e s i n s i d e w a t e r . The e n t r a i n m e n t ( o r s e t t l i n g ) and v a r i a t i o n of e x t i n c - t i o n due t o wind a c t i o n may p l a y an i m p o r t a n t r o l e , t o o .

These f a c t o r s i n f l u e n c e t h e f o r m a t i o n o f e u t r o p h i c a t i o n p r o c e s s i n s p a c e , however t h e y p r o b a b l y c a u s e changes mainly w i t h time.

Taking i n t o a c c o u n t t h e a f o r e m e n t i o n e d a s p e c t s t h e i n - f l u e n c e of wind a c t i o n , flow p a t t e r n , t r a n s p o r t p r o c e s s e s , e n t r a i n m e n t , e x t i n c t i o n , e t c . o f t e n h a s t o be i n v o l v e d i n t o an e c o l o g i c a l model on a more p r e c i s e manner t h a n i t i s u s u a l . The whole model w i l l become n a t u r a l l y more c o m p l i c a t e d . How- e v e r t h e h i g h e r c o m p l e x i t y d o e s n o t n e c e s s a r i l y r e q u i r e a b e t t e r u n d e r s t a n d i n g and d e s c r i p t i o n of t h e b i o l o g i c a l and

chemical p r o c e s s e s . Ifhen u s i n g some t y p e of g r i d s i n t h e c o u r s e of t h e n u m e r i c a l s o l u t i o n of t h e more d i m e n s i o n a l problem,

t h e k i n e t i c e q u a t i o n s w i l l remain t h e same s e p a r a t e l y f o r a l l t h e boxes ( g r i d elements).

Whether i t i s w o r t h ~ i h i l e t o u s e a more complex model it depends on t h e s p e c i a l problem t r e a t e d . The p u r p o s e of t h i s r e p o r t i s t o d i s c u s s t h i s q u e s t i o n f o r Lake B a l a t o n .

I n t h e n e s t two c h a p t e r s t h e knowledge a v a i l a b l e a b o u t a i r , w a t e r and s e d i m e n t motion w i l l be p r e s e n t e d . The f o u r t h

chapter considers the possibilities of modelling in the light of the results available. The question of the use of three-dimensional hydrodynamical model available at IIASA will be discussed here, too. The last chapter includes recommendations concerning future work on this field.

2. ORIGIN OF INFORMATION AVAILABLE

In the last 10-15 years with the setting up of a measure- ment network system for the whole lake intensive examinations were elaborated. These measurements involved the following

(~ig. 1, Muszkalay and Starosolszky, 1964; PIuszkalay, 1973;

Hamvas, 1967).

2.1 WIND FIEAS-NTS

The wind data (hourly or three times a day) are registered at seven stations:

Sidfok Szemes

Szemes, middle-point in the cross section Akali

~ ~ r i a f

iirdo"X

~ e m e s v i t a ~ Keszthely 2.2 WATER MOTION

2.2.1 Water Level Measurements (hourly data1 The stations are as follows:

Kenese Sidfok Als6iSrs

Tihany

x

Irregular measurements.

Szemes

Szemes, middle-point Aka1

i

~ony6d Badacsony Keszthely

Miiriaf i i r d ~ ~

~ a l a t onber6nP

Mouth of river zalaX

~~6 rij kX szigligetX

2.2.2 Wave Measurements (three times daily, having five minutes duration)

Si6fok Tihany Szemes

2.2.3 Velocity Measurements

~ i 6 f okx

Tihany (four points in a vertical, regularly) Szemes , middle-pointx

Mouth of river 2alaX9=

2 . 2 . 4

Examination on a Combined Air-Water Physical Model

(~yorke, 1975)

The area of Lake Balaton realized on model is illustrated on Fig. 1.a. The scales are the following:

Continental area h

=

1000 , undistorted Lake (~roude model) l h

=

1000 , horizontally

\

=

50 , vertically.

Irregular measurements.

,W

The measurements do not characterize the lake relations.

The a i r motion i n t h e model w a s produced by 18 f a n s c a p a b l e of r e g u l a t i n g t h e wind parameters both i n space and time ( t h e range of a i r v e l o c i t y was 7-13 ma-'). Only t h e w e s t e r n p a r t of t h e l a k e w a s b u i l t up i n t h e model d e f i n i n g t h e r i g h t s i d e boundary by t h e nodal zone of t h e l o n g i t u d i n a l seichex.

Examining t h e wind d a t a of more y e a r s s i x b a s i c wind t y p e s were determined. A y e a r l o n g run on t h e model c o n s i s t e d of p u t t i n g t o g e t h e r t h e s e b a s i c winds having d i f f e r e n t d u r a t i o n s and f r e q u e n c i e s b u t r e s u l t i n g t h e t o t a l y e a r l y energy i n p u t by t h e a i r ,

2.2.5 Sediment hlotion

a) E r o s i o n measurements were performed i n 9 c r o s s s e c t i o n s (Fig. l e d , y e a r l y data a r e a v a i l a b l e ) .

b) The movement of t r a c e d bottom sediment were examined on 6 p l a c e s ( s p e c i a l measurements).

c ) D a i l y suspended s o l i d s measurements5 were made i n some of t h e c r o s s s e c t i o n s mentioned i n p o i n t a),

d) Combined bottom sediment and suspended s o l i d s neasure- ments were e l a b o r a t e d i n 14 p o i n t s (see t h e a r e a i n Fig. 1.d)

between 1969-71 ^XXX ( ~ y o r k e , 1975). The purpose of t h e s e measurements w a s t o examine i n n a t u r e t h e e f f e c t of wind on sediment motion. Thus i n each occasion t h r e e measurements were made

I. b e f o r e s e t t i n g up t h e wind (background l e v e l i n w a t e r and sediment);

11. d u r i n g storm (W = 20-30 knh-l);

111. 1 2 hours a f t e r a b a t i n g t h e storm.

Four samples were t a k e n from each v e r t i c a l from t h e water.

e ) Sediment motion w a s s t u d i e d a l s o on t h e p h y s i c a l model.

X V a l i d i t y of open boundary c o n d i t i o n i s not e x a c t l y proved.

Furthermore some u n c e r t a i n t i e s e x i s t i n s c a l i n g r u l e s as w e l l .

XX

-

Not c o n t i n u e d Y e a r l y 1-2 measurements, a t p r e s e n t .

3 . CELULICTERIZJITION OF TLIE M O T I O N OF A I R , VATLY Ah3 SZDI?.fESI'

3.1 V I X D COX.ITIONS ALONG TLlE LAKE

I n t h e c a s e of Lake Dalaton t h e f r o n t a l winds a r e t h e most important having a d u r a t i o n of 12-36 h o u r s , and an average d i r e c t i o n N , NNlg. The mountains .surrounding t h e n o r t h e r n s h o r e of t h e l a k e i n f l u e n c e v e r y e x p r e s s i v e l y t h e wind c o n d i t i o n s ( s e e l a t e r ) . From t h e p o i n t of view of s e d i - ment (and probably w a t e r ) motion, a i r ~uovements having a

v e l o c i t y l a r g e r t h a n 10 1un h-' p l a y a r o l e . A s an average t h e number of days h a v i n g such t y p e of wind i s 100 i n a y e a r (wind d i r e c t i o n between IJNIf and ENE).

When c h a r a c t e r i z i n g a wind t h e most important parameters a r e tlie a b s o l u t e v a l u e (V) and d i r e c t i o n ^(q) of t h e wind, t h e d u r a t i o n ( t ) and f e t c h (F). Approximately t h e energy of wave motion induced by t h e wind

and s i m i l a r l y t h e s h e a r s t r e s s a t t h e f r e e s u r f a c e

However, from t h e p o i n t of view of e r o s i o n and entrainment from t h e bottom t h e d u r a t i o n i s a l s o important. Thus i t was found by Gyorke (1975), t h a t t h e parameter

i s d e c i s i v e e x When c o n s i d e r i n g a c e r t a i n time p e r i o d ( e . 6 . a y e a r ) , one can sum t h e v a l u e s

v2 .

t i n each d i r e c t i o n

--

% o r t h e c h a r a c t e r i z a t i o n of entrainment p r o c e s s t h e product W 2 .t.F could be a l s o a p p l i e d i n v o l v i n g t h e r o l e of f e t c h . Another u s u a l parameter i s W e t .

and form a r e s u l t a n t

R

given by

I ^fl

a n d s x R .

Without going i n t o d e t a i l e d d i s c u s s i o n s t h e f o l l o w i n g y e a r l y averaged v a l u e s w i l l be p r e s e n t e d f o r s i x s t a t i o n s

a able

1, s e e F i g , 1 and a more d e t a i l e d map) ( ~ y o r k e , 1975). C o n s i d e r i n g t h e data t h r e e p r o p e r t i e s have t o be underlined:

a)

1 R \

h a s a d e c r e a s i n g tendencf from ~ i 6 f o k t o Keszt- h e l y showing t h e o r i g i n of s i l t i n g t h e K e s z t h e l y Bay (see l a t e r ) ;

b)

IR 1

i s small on t h e n o r t h e r n p a r t of t h e l a k e ( ~ k a l i ,

~ z i g l i g e t ) because of t h e s p e c i a l c o n f i g u r a t i o n s of t h e t e r r a i n ;

c) due t o t h e p r e s e n c e of t h e mountains t h e r e i s an ex- tremely l a r g e change i n oC ( o r d e r of magnitude 20

-

^50').

Conclusions

a) t h e p r e v a i l i n g wind d i r e c t i o n i s N , NW; however t h e s p a t i a l v a r i a t i o n above t h e l a k e i s l a r g e ;

b) e r o s i o n w i l l t a k e p l a c e n e a r t h e s o u t h e r n s h o r e ; c) t h e danger of s i l t i n g i s t h e l a r g e s t i n Bay Keszt-

3.2 WATER MOTIONS

The g l o b a l motion (flow, waves, s e i c h e s , e t c . ) i n t h e l a k e i s i n f l u e n c e d mainly by t h e f o l l o w i n g f a c t o r s :

t h e d i r e c t i o n of t h e wind i s approximately p e r p e n d i c u l a r t o t h e l o n g i t u d i n a l axis of t h e l a k e ;

i r r e g u l a r mountains;

X I n s i d e W*

.

^{t 5-t w a s} approximately c o n s t a n t a l o n g t h e l a k e .

p r e s e n c e of p e n i n s u l a Tiliany;

non-steady wind c o n d i t i o n s ;

l a r g e wave h e i g h t as compared t o t h e w a t e r d e p t h . 3.2.1 R e s u l t s Gained from S i t e Measurements

Some t y p i c a l d a t a a r e as f o l l o w s :

a) m a x i m u m l o n g i t u d i n a l d i f f e r e n c e i n w a t e r l e v e l 1.0 m;

b) m a x i m u m t r a n s v e r s a l d i f f e r e n c e i n w a t e r l e v e l a t Sze- mes 0.4 m ( t h e f r e e s u r f a c e i s curved);

c ) maximum v e l o c i t y a t Tihany 1.4 m s o l

d) r a n g e of t h e v e l o c i t y a t Tihany 0.2 to-0.4 msw1 ( n e g a t i v e v a l u e i n d i c a t e s flow towards ~ e s z t h e l y ) ;

e ) r a n g e of t h e v e l o c i t y i n s i d e K e s z t h e l y Bay 0.1 t o 0.2 mso1)

f ) d u r a t i o n of s e i c h e 0.2

-

2 4 . 0 ~ ; as an a v e r a g e v a l u e 5 e 5 h can be g i v e n i n l o n g i t u d i n a l , w h i l e 0.9 h i n t r a n s v e r s a l d i r e c t i o n f o r t h e w e s t e r n b a s i n .

Analyzing t h e d a t a of f i v e y e a r s Muszkalay (1966) g o t t h e f o l l o w i n g r e l a t i o n s h i p s f o r t h e l o n g i t u d i n a l s l o p e

( d e f i n e d on t h e b a s i s of m a x i m u m w a t e r l e v e l d i f f e r e n c e between Kenese and ~ e s z t h e l ~ )

where Wr = Y

.

^{c o s A} t h c l o n g i t u d i n a l component of t h e wind v e l o c i t y v e c t o r (Y

<

^22.5') [ m s -1- J , and t , t h e d u r a t i o n of wind [h]; t

<

^12h.

( X ? 22.5' ( n e a r e r t o t r a n s v e r s a l wind d i r e c t i o n ) ,

No close correlation exists between wind data and transversal slope, but the latter one may be three or four times larger than the longitudinal slope.

The velocity at Tihany is defined by the longitudinal slope between Alsdors and Szemes, and approximately the

estimation can be given (>luszkalay, 1973, 11-1). According to the measurements the flow has the same direction along the whole depth (showing towards Keszthely or ~enese) and the water is often streaming opposite to the wind.

Considering seiche motions, slopes and waves in most of the cases the longitudinal slope is quite small while the transversal one is much larger. Longitudinal seiches are important to which transversal seiches will be superimposed.

The wave motion is of shallow water in character. The height of the wave depends on the parameters of the wind

(??,A,

t, F ) , on turbulence, deptli and interferences, All these

effects may sometimes cause the water level to be 1.5

m

higher than the static one.

The square mean value of wave height was approximated by Pluszlcalay (1973) by the equation

where "aw depends o n x , F, h a

=

0.05 - 0.12; wa[ms-'j is an hourly average value previous to the occurrence of

The formula is valid in the vicinity of Szemes.

Some extreme examples about the global variation of water level are given in Fig. 2-6. (~uszkalay and Starosolszlcy, 1964.)

- ----

*1.0 m below the free surface

3.2.2 R e s u l t s of t h e P h y s i c a l Model ( ~ ~ o r k e , 1975)

Here mainly tlie mixing of f r e s h Zala w a t e r i n t h e l a k c w i l l be c o n s i d e r e d .

a) I f no wind i s a c t i n g t h e l a r g e s t p a r t of f r e s h Z a l a w a t e r remains i n t h e b a y ( ~ i ~ . 7 ) ~ . D u r i n g o u t f l o w i n t h e

~ i 6 c a n a l an i n t e n s i v e motion can be observed t o ~ i a r d s Szig- l i g e t .

b) I n c a s e o f s t e a d y s t a t e wind c o n d i t i o n s (Fig. 8) a c o m p l i c a t e d t h r e e - d i m e n s i o n a l flow p a t t e r n w i l l be gained.

The motion of t h e l a y e r n e a r t o t h e f r e e s u r f a c e c o r r e s p o n d s t o t h e wind d i r e c t i o n . However, t h e l a r g e s t p a r t of f r e s h

Zala w a t e r w i l l be t r a n s p o r t e d i n t h e lower l a y e r i n an o p p o s i t e d i r e c t i o n . T h i s motion i s induced by waves and t r a n s v e r s a l

s l o p e , and c a u s e s sediment ( o r i g i n a t e d mainly from r i v e r ~ a l a ) motion i n t h e same d i r e c t i o n . The motion n e a r t h e bottom i s

d i r e c t e d towards North. The mixing between t h e two b a y s ( ~ e s z t h e l y and ~ z i g l i g e t ) i s small.

c) During i n c r e a s i n g winds a n i n f l o w can b e observed i n t o Bay K e s z t h e l y w h i l e t h e e f f e c t o f d e c a y i n g wind i s j u s t

o p p o s i t e . However, d u e t o t h e q u i c k e r damping of waves i n Bay K e s z t h e l y t h e o u t f l o w i s s m a l l e r ( s e e Fig. 9, t r a n s i e n t condi-

t i o n s ) .

C o n c l u s i o n s

a) Due t o t h e c o m p l i c a t e d g e o m e t r i c a l , t o p o g r a p h i c a l and wind c o n d i t i o n s t h e f l o w i s e x p r e s s i v e l y of t h r e e - d i m e n s i o n a l i n c h a r a c t e r ;

b) I n t h e c r o s s s e c t i o n Tihany t h e flow i s a l o n g i t u d i n a l one h a v i n g h i g h v e l o c i t i e s . The p e n i n s u l a Tihany d i v i d e s t h e l a k e i n t o two a r e a s ;

c ) A c o m p l i c a t e d mixed s e i c h e motion i s formed i n t h e X ~ a t u r a l l y t h e o u t f l o w from t h e bay i s e q u a l t o tlie i n f l o w .

lalre. The t r a n s v e r s a l s l o p e of t h e f r e e s u r f a c e i s g e n e r a l l y much l a r g e r t h a n t h e l o n g i t u d i n a l one. The h e i g h t of waves i s v e r y l a r g e compared t o t h e w a t e r depth. This f a c t c a u s e s e r o s i o n (and probably i n t e n s i v e entrainment from t h e bottom) i n t h e southelm p a r t of t h e lake.

d) D i f f e r e n t zones a r e formed i n t h e lalce having more o r l e s s independent c i r c u l a t i o n s . The two bays ( ~ e s z t h e l ~ and s z i g l i g e t ) belong t o t h i s c a t e g o r y , a l s o . The l a r g e s t p o r t i o n of f r e s h Zala w a t e r (and t h e suspended s o l i d s and n u t r i e n t s connected t o i t ) remains i n Bay K e s z t h e l y (incomplete mixing).

3.3 SEDIMENT FfOTIONS

Sediment t r a n s p o r t i s mainly a f f e c t e d by t h e motion of a i r and water. I t s g e n e r a l f e a t u r e s correspond t o t h e

expected ones on t h e b a s i s of t h e p r e v i o u s c h a p t e r s . 3.3.1 R e s u l t s of I n S i t u Measurements

Analyzing t h e w a t e r balance of Lake Balaton S z e s z t a y (1969) e s t i m a t e d t h e r a t e of s i l t i n g as 0.54 mm/year. However t h e l a r g e s t p a r t of t h e l a k e seems t o be i n e q u i l i b r i u m from t h i s p o i n t of view and f i r s t of a l l Bay K e s z t h e l y i s endangered.

Here t h e s p e c i a l c o n d i t i o n s o f t h e bay and t h e sediment

q u a n t i t y t r a n s p o r t e d from o t h e r s e c t i o n s of t h e l a k e p l a y a n important r o l e .

E r o s i o n and e n t r a i n m e n t a r e i n t e n s i v e n e a r t h e s o u t h e r n s h o r e l i n e . T h i s i s i l l u s t r a t e d on Fig. 10, where t h e y e a r l y development of e r o s i o n and t h e change d u r i n g f o u r months long o b s e r v a t i o n p e r i o d i s a l s o given. The f i g u r e i n v o l v e s wind and suspended s o l i d s (SS) c o n c e n t r a t i o n d a t a , too. Due t o wind a c t i o n t h e suspended s o l i d s c o n c e n t r a t i o n may i n c r e a s e _-

from 20

-

^{30 gmo3 t o 200 gmW3} ( i n extreme c a s e s t o 4-500 .g.~-~).

As the figure shows a correlation exists between wind and SS data. The direction of wind has an important role, the largest entrainment rates can be found in the case of winds normal to the southern shore line.

The special measurements mentioned in 2.2.5.d, served an interesting picture about the entrainment and sediment motion.

The

SS

concentration distribution was uniform along verticals in all the cases. The background value and the concentration belonging to period I11 (section 2.2.5) varied between 20 and 40

gm-3.

During storm (period 11) values between 100-200 grno3 were observed near the southern shore line and in the middle part of lake. In the vicinity of northern shore line only negligible variations could be found compared to the

background level. This fact illustrates clearly the variation of entrainment from the bottom sediment (being influenced by the change in fetch, wave heights, turbulence, etc.).

The particle size distribution was also determined for

SS

and bottom sediment. The pattern is the expected one on the southern shore having coarser fraction

and

a larger mean

particle size in the bottom sediment (150 - ^{200 and} 20 -30/wn, resp.). However on the northern part of the lake the bottom sediment contains smaller particles (mean size 5-10

urn)

than

the water (20-30

urn).

/

/

This fact illustrates that there is a sediment transport associated with water in northern direction.

The bottom sediment motion (see 2.2.5.b) shows a similarly unfavorable picture from the point of view of 13ay Iceszthely, the motion is directed in most of the cases towards the bay (~ig. 11).

3.3.2 Results of the Physical Model

The transport of suspended solids generally follows the

w a t e r motion ( s e e 5.2.3). Thus t h e w a t e r w i l l become "over- s a t u r a t e d t t i n Gay ICcszthely which l e a d s l a t e r t o d e p o s i t i o n and s i l t i n g . The d u r a t i o n of winds h a v i n g d i r e c t i o n s d i f f e - r e n t from t h e p r e v a i l i n g one i s r e l a t i v e l y s h o r t t h u s t h e s e d i m e n t c a n n o t l e a v e t h e bay. S h o r t l y s p e a k i n g , t h e b a y i s w o r k i n g as a t r a p .

The clcposi1;ion p a t t e r n of Z a l a s e d i m e n t a f t e r two y e a r s l o n g s i m u l a t i o n p e r i o d m a j r b e s e e n on F i g . 12. I i o r t h ~ i h i l e t o mention t h a t i n t h e v i c i n i t y of Zala mouth no d e p o s i t i o n t a k e s p l a c e due t o wave n o t i o n and i n t e n s i v e f l o w s .

A c c o r d i n g l y t h e model r e s u l t s s e d i m e n t c a n be t r a n s p o r t e d a l s o from Bay S z i g l i g e t i n t o I3ay K e s z t h e l y .

C o n c l u s i o n s

a) Near t h e s o u t h e r n s h o r e l i n e an i n t e n s i v e e n t r a i n - ment t a k e s p l a c e ;

b) The e n t r a i n e d s e d i m e n t i s t r a n s p o r t e d t o w a r d s t h e n o r t h e r n s h o r e v h e r e l a t e r d e p o s i t i o n w i l l o c c u r ;

c) The b a y i s w o r k i n g as a t r a p ;

d) No d e p o s i t i o n c a n b e o b s e r v e d n e a r t h e Zala mouth due t o wave and f l o w a c t i o n s ,

4 ⁰ APPLICABILITY OF A HYDRODM-JMIIC-TTWPJSPORT

MODEL FOR LAICE BILATOIJ

From t h e p r e v i o u s c h a p t e r s one c a n r e a l i z e t h a t t h e

f l o w p a t t e r n , s e i c h e s , waves, s e d i m e n t motions and wind condi- t i o n s a r e of v e r y c o m p l i c a t e d n a t u r e i n Lake B a l a t o n . Concern- i n g m o d e l l i n g a c t i v i t y b o t h a s p e c t s mentioned i n C h a p t e r 1-- t r a n s p o r t p r o c e s s e s and exchange a t t h e bottom l a y e r

--

^{p l a y}

an i m p o r t a n t r o l e ( s e e Harleman and V a s i l i e v , 1978, t o o ) . The r e s u l t s p r e s e n t e d h e r e showed t h a t t h e f r e s h w a t e r o f

Zala river (containing sediments, nutrients, etc.) would not be mixed completely inside the lake. Due to this fact and the special properties of Bay Keszthely transport

processes may influence strongly the degree of eutrophi- cation (which shows a decreasing tendency in East-Yest direction, Iiarleman and Vasiliev, 1978). The importance of entrainment from the bottom was discussed in Section 3.3.1 and illustrated on Figs. 11 and 12. Though the results were gained for bottom sediments and suspended solids a similar effect may be expected concerning particulate phosphorus.

Due to wind action interstitial water may be stirred up, too.

In this way the soluble phosphorus will also be influenced.

Consequently neither the second aspects of hydrodynamical modelling may be neglected.

In the light of the aforementioned aspects the modelling of the effect of wind induced flows can be classified accord- ing to Fig. 13. Here distinction has to be made whether the model serves for simulation of real situations or for better understanding of the process considered.

4.1 INFLUENCE OF

\KIND

INDUCED F'LOWS ON

THZ

TXi"SP0ItT PROCESS (MODEL ~1

4.1.1 Basically here a combined hydrodynamic-transport model has to be used consisting of boxes (e.g. grid elements). In

the transport model the kinetic equations of nutrients, algae, etc. has to be built in (~alfon and Lam, 1978, 1978), thus the total model will have more boxes and compartments. This type of model can be classified according to Table 2 depending on the number of spatial dimensions and assumptions made on time dependence.

From the table it appears that for Lake Balaton (for purpose A) only the application of model types 111, V and VI

seems to be feasible. nowever the use of models V and VI re-

quires large and fast computers.The execution time is in oase VI

a t b e s t r e a l t i n e / j 0

am,

1973, p e r s o n a l c o m w i i c a t i o n ) and enormous q u a n t i t y of d a t a h a s t o be h a ~ i l l e d when a p p l y i n 3 t h e model f o r r e a l s i t u a t i o n s . These models h e l p i n b e t t e r u n d e r s t a n d i n g of t h e p r o c e s s . On t h i s f i e l d t h e a p p l i c a t i o n of models a l r e a d y e x i s t i n g i s proposed ( ~ a s i l i e v and Kvon, 1977; H a l f o n and Lam, 1978; Durl~am and B u t l e r , 1976).

Because of t h e s h a l l o w c h a r a c t e r of t h e l a k e complete mixing may be a s s u n e d a l o n g v e r t i c a l s . Thus t h e three-dimen- s i o n a l t r e a t m e n t of t h e problem would be r e q u i r e d m a i n l y because of t h e t h r e e - d i m e n s i o n a l p a t t e r n of t h e f l o w , n o t d i r e c t l y b e c a u s e of t h e t r a n s p o r t p r o c e s s . T h i s means i f one h a s t h e c o r r e c t flow p a t t e r n and u s e s a two-dimensional

h o r i z o n t a l t r a n s p o r t n o d e l i n c l u d i n g d e p t h i n t e g r a t e d v a l u e s q u i t e f e a s i b l e r e s u l t s may be g a i n e d ( s e e T a b l e 2 ; n a t u r a l l y t h e appearance o f d i s p e r s i o n X may c a u s e u n c e r t a i n t i e s . Bow- e v e r , i t s e f f e c t i s n o t l a r g e i f t h e c o n c e n t r a t i o n i s

e q u a l i z e d s u f f i c i e n t l y a l o n g d e p t h ) .

Thus f o r p r a c t i c a l p u r p o s e s model t y p e I11

a able

^{2) may}

be proposed ( i n v o l v i n g a second model f o r t h e e s t i m a t i o n of exchange i n bottom l a y e r , s e e l a t e r ) . I t s a p p l i c a b i l i t y w i l l depend mainly on t h e f a c t how c o r r e c t i s HDbI 2

a able

²⁾

c o n c e r n i n g t h e d e p t h a v e r a g e d v e l o c i t i e s . I n t h e c o u r s e of s e l e c t i n g t h e s o l u t i o n t e c h n i q u e o r model t y p e a v a i l a b l e p r i m a r y a t t e n t i o n h a s t o be p a i d t o t h e s t r o n g v a r i a t i o n of wind v e l o c i t y i n s p a c e and s h o r t e x e c u t i o n time of t h e computer program.

F o r i l l u s t r a t i n g t h e p o s s i b l e e f f e c t of change i n wind d i r e c t i o n s e e F i g s . 14 and 1 5 ( ~ u r h a m and B u t l e r , 19761, which show s o l u t i o n s f o r Lake E r i e a t 40 f t d e p t h below t h e

s u r f a c e , f o r two d i f f e r e n t wind d i r e c t i o n s , h a v i n g a d e v i a t i o n

X I t h a s t o be emphasized t h a t d i s p e r s i o n i n c l u d e s h e r e t h e c o n t r i b u t i o n of n o n - u n i f o r m i t i e s a l o n g a v e r t i c a l ( b u t n o t on t h e whole c r o s s s e c t i o n ) t o t h e t r a n s p o r t , only.

0

. a d = 22.5

.

The o r d e r of magnitude of ..qlx i s t h e same o r

l a r g e r f o r Lake Balaton. The two c a s e s n a t u r a l l y may not be compared c o r r e c t l y because along Lake Balaton v a r i a b l e

d e v i a t i o n s can be found among d i f f e r e n t p o i n t s i n space a t t h e same time i n f l u e n c i n g t h e c i r c u l a t i o n p a t t e r n .

N a t u r a l l y i t i s p o s s i b l e t h a t t h e model w i l l n o t produce s a t i s f a c t o r y r e s u l t s because of n e g l e c t i n g v e r t i c a l c i r c u l a - t i o n s and c o n s e q u e n t l y t h e t r a n s p o r t of Zala w a t e r w i l l be fundamentally d i f f e r e n t from t h e r e a l one ( ~ i g , 8, keep i n mind t h a t t h e s u r f a c e w a t e r l a y e r moves a c c o r d i n g t o t h e wind d i r e c t i o n , b u t t h e f r e s h w a t e r of Zala i n c l u d i n g s e d i - ments, n u t r i e n t s , e t c , i n t h e o p p o s i t e one). I t i s proposed t o adopt

an

e x i s t i n g model o r t o develop a low e f f o r t f i r s t o r d e r approach i n o r d e r n o t t o waste time w i t h a f u l l and comprehensive development s i n c e t h e s t a r t i n g assumption may n o t be c o r r e c t , The a t t e m p t has t o be followed by t e s t i n g

simple s i t u a t i o n s f o r Lake Balaton,

I n p o s s e s s i o n of encouraging r e s u l t s d e t a i l e d v e r i f i c a - t i o n may be based on w a t e r l e v e l and w a t e r q u a l i t y d a t a , r e s u l t s of t h e p h y s i c a l model and on f u t u r e measurements ( v e l o c i t y , n u t r i e n t s , e t c , ) , A s a f i r s t s t e p t h e k i n e t i c sub- model can be c a l i b r a t e d by assuming s p a t i a l homogeneity

a able

^{2 ,} I , Lam and J a q u e t , 1976).

From many p o i n t s of view i t might become d e s i r e d t o d i v i d e t h e whole l a k e i n t o s u b r e g i o n s ( s a v i n g computer time, e t c . ) , I t h a s t o be emphasized t h a t t h e two bays ( ~ e s z t h e l ~ and ~ z i g l i g e t ) must n o t be s e p a r a t e d w i t h r e s p e c t t o hydro-

dynamical a s p e c t s , Boundaries of f u r t h e r s u b r e g i o n s can be l o c a t e d e , g , at Szemes and Tihany.

I f o n l y a g i v e n a r e a of t h e l a k e w i l l be c o n s i d e r e d an open boundary c o n d i t i o n h a s t o be d e f i n e d . The s t r u c t u r e of t h e hydrodynamic81 model h a s t o g u a r a n t e e some f l e x i b i l i t i e s i n t h i s r e s p e c t (e,g, i t h a s t o a l l o w t h e d e s c r i p t i o n of w a t e r

l e v e l a l o n g t h e open boundary. O t h e r p o s s i b i l i t i e s a r e o f t e n v e r y u n c e r t a i n , s e e IIorwood and Bedwell, 1978).

4.1.2 P o s s i b i l i t y f o r Use of Three-Dimensional S t e a d y S t a t e H y d r o d y n m i c a l Model A v a i l a b l e a t IIASA

The node1 w a s developed and a p p l i e d f o r Lake E r i e by Durham and B u t l e r , 1976. B a s i c a l l y t h e mixed a n a l y t i c a l - -numerical method of Gedney (1971) w a s used i n t h e frame of which f i r s t t h e i n t e g r a t e d s t r e a m f u n c t i o n w i l l be computed

from a two-dimensional P o i s s o n e q u a t i o n u s i n g over-relaxa- t i o n t e c h n i q u e f o l l o w e d by t h e d e r i v a t i o n of t h e d e p t h

i n t e g r a t e d v e l o c i t i e s , The t h i r d v e l o c i t y component t o g e t h e r w i t h t h e v e r t i c a l d i s t r i b u t i o n s o f h o r i z o n t a l components and p r e s s u r e w i l l be g a i n e d a f t e r w a r d s from a n a l y t i c a l e x p r e s s i o n s . Although a p p l i c a t i o n of t h e model m i g h t c a u s e some s m a l l e r

d i f f i c u l t i e s i n t h e c a s e of Lake B a l a t o n ( i . e . d e f i n i t i o n of open boundary c o n d i t i o n i f n o t t h e whole l a k e i s c o n s i d e r - ed; t h e s h a l l o w n e s s of l a k e ; t h e assumption of c o n s t a n t wind d i r e c t i o n s ; t h e n e g l e c t i o n of w a t e r l e v e l change due t o wind a c t i o n i n some p l a c e s i n t h e c o u r s e of t h e d e r i v a t i o n of g o v e r n i n g e q u a t i o n s , s e e Gedney, 1971, e t c . ) i t would s e r v e some v e r y u s e f u l r e s u l t s f o r b e t t e r u n d e r s t a n d i n g of flow p a t t e r n a t l e a s t u n d e r s t e a d y s t a t e c o n d i t i o n s .

However u n f o r t u n a t e l y t h e program may n o t b e used a t p r e s e n t a t ILISA. The r e a s o n s a r e as f o l l o w s .

a ) Very l a r g e one-, and two-dimensional b l o c k s a r e d e f i n e d . . i c c o r d i n g l y a computer h a v i n g a t l e a s t 300 Kbyte nemorie i s r e q u i r e d (rough e s t i m a t i o n ) , Thus t h e model may n o t be a p p l i e d on PDPll computer a v a i l a b l e a t IUSA.

b) The program i s n o t f l e x i b l e , i t w a s f i t t e d t o t h e s p e c i a l problem of Lake E r i e . Thus t h e number of g r i d p o i n t s i s f i s e d c a u s i n g t h e l a r g e mcmorie r e q u i r e m e n t n e n t i o n e d . A l l t h e "DOtt c y c l e s c o r r e s p o n d t o t h e number of p o i n t s u s e d

(122 and 40 r e ~ ~ e c t i v c l y ) .

c ) Some s m a l l e r p a r t s of t h e progr'm r e s t r i c t a l s o t h e g e n e r a l a p p l i c a t i o n ( s p e c i f i c c o n s t a n t v a l u e s b u i l t i n t h e program, e t c . ) .

d ) A c t u a l l y t h e program was n o t a c c e s s i b l e on computer d u r i n g t h e v i s i t .

C o n s i d e r i n g t h e whole q u e s t i o n t h e f o l l o w i n g p r o p o s i - t i o n s can b e given.

a) E f f o r t s have t o be made t o a p p l y a l a r g e r computer (e.g. IE1 a t ~ i s a ) . IIowever r e o r g a n i z a t i o n , g e n e r a l i z a t i o n and a d o p t a t i o n worlr have t o be performed i n t h i s c a s e , as w e l l .

b) An a t t e m p t h a s t o be t a k e n t o d e c r e a s e d r a s t i c a l l y t h e number of g r i d p o i n t s and t o a d o p t t h e model on PDP11.

The main a d v a n t a g e i n u s e of t h e program would l i e i n t h e comparison of t h e r e s u l t s of a t h r e e - and a two-dimen- s i o n a l model and would s e r v e f o r j u d g i n g t h e a p p l i c a b i l i t y of t h e second one a t l e a s t under s t e a d y s t a t e c o n d i t i o n s .

4.2 INFLULICE OF IfIND LWUCZD FLOTfS ON T I E INTERACTION AT TI3E BOTTOFI LAYER (Nodel B, F i g . 13)

The e f f e c t of t h i s t y p e of exchange due t o p h y s i c a l ac- t i o n i s many-sided ( s e e e a r l i e r , too):

a) S e d i n e n t s and p a r t i c u l a t e phosphorous w i l l b e r e -

e n t r a i n e d from t h e bottom l a y e r (at a d i f f e r e n t r a t e i n space) and l a t e r d e p o s i t e d a g a i n on o t h e r p a r t s of t h e l a k e ;

b) S o l u b l e phosphorous c o n t e n t of t h e i n t e r s t i t i a l w a t e r w i l l be a l s o removed;

c) - t i n c t i o n w i l l vary.

T h e

importance of these effects are different, e.g., if tlie soluble reactive phosphorous plays the decisive role, if the particulate phosphorous is stable enough

and

if the

soluble phosphorous content of interstitial water precipitates quickly after resuspension, the change in extiction will be the capital issue, A decision in this field can only be made after some basic and in situ experiments suggested already on the Tillany meeting, These aspects will influence the question whether it is necessary to apply a more detailed transport equation for the bottom layer or not.

From the point of view of interaction the following parameters are the most important:

a) wind data (absolute value, direction, fetch, duration, time dependence);

b) bottom friction and kinetic energy available at bottom layer (IIar1ema.n and Vasiliev, 1978);

c) density difference between water

and

sediment;

d) type of sediment and suspended solids (particle distribution, shape of particles, cohesive or non- cohesive properties, etc,);

e) the way how phosphorous fractions are bound to the sediment.

Connected to point b), the origin of kinetic energy or bottom shear is important. Thus turbulence, seiches and wave motions may play different roles (in the latter case the bottom orbital velocity has to be taken into consideration, see Lam and

Jaquet, 1976). This fact causes differences in modelling of the interaction process.

Suggestions for modelling are as follo~is.

a) One can use the parameter estimation technique (see

J o l h k a i and Szollbsi-Nagy, 1978). This method does not give

an

insight concerning the nature of the process but it is a useful tool in practice.

b) Regression models can be applied for estinction and entrainment on the basis of wind (absolute value and direc- tion), water level, suspended solids and phosphorous (soluble and particulate) time series belonging to different locations.

Additional measurements are needed, however the data presented on Figs. 10 and 11 can be used for

a

first guess at present.

c) The shear stress, kinetic energy, wave motion, the

2 2

parameters !J

.

^t,

^W .

^{t, W}

.

^t

. ^F

(see Section 3.1) may be involved into the process.

d) Model type

IV able

2) can be used by fitting to measured data.

e) A special simplified model can be developed for esti- mating the effect of waves

a am

and Jaquet, 1976), or the available turbulent kinetic energy at the interface (see for stratified flow, Hansen,

1978).

5.

REC OrnENDATIONS

On the basis of previous chapters and discussions

continued in IIASA the following recommendations may be given for future work on the problem discussed in the report,

5.1 MEASURPlENTS

a) It is proposed to perform some quality measurements (eeg. phosphorous) to get

a

better guess on the importance of spatial variations (within bays; water and bottom sedi- ments have to be involved).

b) lleasurements are required for the estimation of extinc- tion and entrainment (see Section 4.2). At least daily but

during some storms more frequent samples are needed (both on suspended solids and pliosphorous fractions, water and bottom sediment).

c) Velocity measurements would help

a

lot.

d) The conduction of some basic experiments (or collec- tion of results available) is proposed connected to the inter- actions at the bottom, to the phosphorous resuspension, pre- cipitation, etc,

5 . 2 IIODELLLNG ACTIVITY

a)

A

horizontally two-dimensional unsteady hydrodynamical model coupled to

a

transport (diffusion-advection) model in- volving sinks, sources and kinetic equations of different compartments is recommended for practical application. The model has to be capable of taking into consideration the

variation of wind in space and tine furthermore for definition of open boundary conditions.

b) For judzing quiclcly the applicability of such type of model there is

an

urgcnt need to compare at least the results of

a

steady state three- _and two-dimensional hydrodynamical model available for Lc&e Balaton, Concerning tlie three-dimen- sional model

an

effort has to be made for reorganizing ruld adopting the model of Durhan <and Butler, e.g. in Pisa, or by reducing the number of grid points on PDP11.

c) For better understanding of the process attempts have to be made for usage of

an

unsteady three-dimensional hydrodynamical model available elsewhere (node1 of Vasiliev and I{von, or Simon's model used e. g, by Halfon and L ~ I U ) .

d)

A

separate model has to be dcvelopecl for estimation of interactioil processes at tlle bottom. Here the use of para-

meter e s t i m a t i o n t e c h n i q u e , r e g r e s s i o n models, v e r t i c a l l y two-dimensional hydrodynamical model o r o t h e r s p e c i a l models seems t o be f e a s i b l e . This model w i l l s e r v e a s a submodel f o r t h e model mentioned i n p o i n t a).

e) I t i s proposed t o use a computer which allows a v e r y dense a c c e s s i b i l i t y .

f ) Recommended, t o o , t o j o i n t o g e t h e r a l l t h e a s p e c t s mentioned i n t h e r e p o r t as c l o s e l y as p o s s i b l e .

g) I n t e n s i v e work i s r e q u i r e d f o r t h e p r e p a r a t i o n of i n p u t d a t a (bottom c o n f i g u r a t i o n , wind, etc.) t a k i n g i n t o account t h e a c t u a l s i t u a t i o n s .

ACKNOWLEDGMENTS

The w r i t e r e x p r e s s e s h i s g r a t e f u l thanks t o G e r r i t van S t r a t e n f o r v a l u a b l e d i s c u s s i o n s and o t h e r a s s i s t a n c e .

Durham, L.D., B u t l e r , L .9. (1976), Lake E r i e I n t e r n a t i o n a l J e t p o r t liodel F e a s i b i l i t y I n v e s t i g a t i o n , Miscellaneous Paper H-76-3, H y d r a u l i c s Laboratory U.S. Army Engineer Waterways Zxperiment S t a t i o n , Vicksburg, Report 17-7.

Gedney, R.T. (1971), Numberical C a l c u l a t i o n s of t h e Wind-

-Driven C u r r e n t s i n Lake E r i e , NASA Technical Memorandllm, NASA TEE-52985.

George, D.G., Heaney, S.I. (1978), F a c t o r s I n f l u e n c i n g t h e

S p a t i a l D i s t r i b u t i o n of Phytoplankton i n a Small Productive Lake, J o u n i a l of Ecology,

66,

133-155.

Gyorke, 0. (1975), Water and Sediment Motion i n t h e South- - S a s t e n i Area of Lake Balaton C h a r a c t e r i z i n g I3ed Forma- t i o n ( i n ~ u n g a r i a n ) , VITUKI Report.

B a l f o n , E., Lam, D,C.L. (1978), The E f f e c t s of Advection- - 3 i f f u s i o n P r o c c s s e s on t h e E u t r o p h i c a t i o n of L a r g e

L a k e s , a H y p o t h e t i c a l Example: Lake S u p e r i o r ; E c o l o g i c a l M o d e l l i n g , 4 , 119-151.

H a l f o n , E., Lam, D O C .Lo (1978), ?lode1 of P r i m a r y P r o d u c t i o n , I n c l u d i n g C i r c u l a t i o n I n f l u e n c e s , i n Lake S u p e r i o r , A p p l i e d M a t h e m a t i c a l I i o d e l l i n g , Vol. 2 , 30-40.

Hamvas, F. (1967), E x a m i n a t i o n of E r o s i o n on Lake B a l a t o n ( i n I l u n g a r i a n ) , I l i d r o l 6 g i a i Kozlony, 1 2 , 560-563.

IIansen, N.E.O. (1978), ) f i x i n g P r o c e s s e s i n Lakes, N o r d i c Hydrology, 9 , 570; 4.

Harleman, D.R.F., V a s i l i e v , O.F. (1978, Sumnary of C o n c l u s i o n s on H y d r o p h y s i c a l M o d e l l i n g and Data Needs, Lalce B a l n t o n Workshop, Tihany.

Honlrood, J . W . , Bedrvell, J.A. (1978), R e s u l t s from a Hydro-

dynamical P i a t h e m a t i c a l Plodel of t h e I r i s h S e a , E c o l o g i c a l M o d e l l i n g , 4 , 327-357.

~ o l g n k a i , G., S z o l l b s i - N a g y , A. (1978), A S i m p l e E u t r o p h i c a t i o n Model f o r t h e Bay o f K e s z t h e l y , Lalce B a l a t o n , I n t e r -

n a t i o n a l Symposium on M o d e l l i n g t h e ' d a t e r Q u a l i t y of t h e H y d r o l o g i c a l C y c l e , Baden.

Lam, D O C .L o , J a q u e t , J.11. (1976), Computations of P h y s i c a l T r a n s p o r t and R e g e n e r a t i o n of P h o s p h o r o u s i n Lake E r i e , F a l l 1970, J o u r n a l F i s h e r i e s R e s e a r c h Board Canada, Vol.

33, N r . 3, 550-563.

bluszkalay, L. (1966), L o n g i t u d i n a l and T r a n s v e r s a l S e i c l i e s of Lake B a l a t o n ( i n ~ u n g a r i a n ) , ~ i d r o l 6 g i a i Kozlony, 11, 505-508

Fluszkalay, L. (1973), C h a r a c t e r i s t i c Water Motions i n Lake

. B a l a t o n ( i n ~ u n g a r i a n ) , VITUKI I i e p o r t .

Piuszkalay, L., S t a r o s o l s z k y , 0. (1964), Wind I n d u c e d FIoti ons i n Lake B a l a t o n ( i n ~ ~ u n g a r i a n ) , I I i d r o l 6 g i a i Kozl6ny, 4 4 , 8 , 337-3430

Parker, R . A . , S p a t i a l Patterns i n a Nutrient-Plankton Model, E c o l o g i c a l N o d e l l i n g , 4 , 361-370.

S z e s z t a y , I<. (19691, The Water Balance o f Lake Balaton ( i n

~ u n ~ a r i a n ) , VITUKI Report.

V a s i l i e v , O.F., Kvon, V.I. (1977), Numerical Modelling of Flows and Heat Exchange i n Cooling Ponds, 17th Congress o f t h e ZAIIR, Baden-Baden.

FIGmES X i D

TABLES

Figure 1. Fleasurement network on Lake Dalaton.

Figure 2. Longitudinal oscillations (~luszkala~ and Staro- solszky, 1964).

Figure 3. Transversal oscillations (~fuszlralay and Starosolszky, 1964).

Figure

4,

Superimposed motions (~.iuszkalay and Starosolszky, 1964),

Figure

5.

Short term oscillation (~uszkalay _and Starosolszky, 1964).

Figure

6.

Wave picture (Nuszkalay and Starosolszky, 1364).

Figure

7.

1-lotion of fresh Zala water,

W

= 0.

Figure 8. Wind induced flows; I?= 51 lim h-l, direction NNE at ~ g r i af iirdo".

Figure

9.

Effect of transient wind conditions.

Figure 10. Erosion, suspended solids concentrations and wind data (IImvas, 1967).

Figure 11, Suspended solids concentrations and wind data.

Motion of traced bottom sediment (~amvas, 1967).

Figure 12. Dcposition of Zala sediment after two years long siuulation period,

Figure 13. Classification of modelling activity (hyrlrod3mamical aspects).

Figure 14, Velocity pattern for Lake Erie, wind direction _M?.

Figure 15, Velocity pattern for Lalre Erie, wind direction W \ J . Table 1. Average values characterizing wind conditions for 1970.

Table 2, Classification of combined hydrodynamic-transport model s.

Note: IIDPI indicates hydrodynamical model 1 indicates transport model including kinetic processes, sinks and sources.

NUPIf3E.R OF DIMENSIONS 0 I I1 IIDP~ 1

+

n1 1

-

ID11 2

+

mi 2 I11 (~lorizontall~) IIDII 2 (+ TI1 2) IV

(vertically)

r~1.1 3 (+ ml 2 or 3) ~1 3 (+ n1 2 or 3)" & Table 2. Classification of combined hydl-i!,: r. t~r~c-transport models, T IPE DEPENDENT? YES YES YES YES NO YES

There is no transport in space, homogeneity is assumed. In-and outflows of cells will be gained. Because of the co~nplexity of tlie present problem, riot applic- able. Vertical currents neglected. Possible way for application, I llorizontal currents neglectecl. Proposed to be used for purpose B. 14ainly for better uliderstanding. Steady state wind conditions. Plainly for better understanding.

a., Wind data

on the physical model realized area

'p b.,Water level observations

~lsdor s Szigliget

P ;[

b?

d., Erosion and sediment

solids measurements

Fig .I. Measurement network on LAKE BALATON

Fig . 2 . Longitudinal oscillations

(~uszkalay and Starasolszky, 1964)

100

7 E

& .go

-

U ⁸⁰

>

w 80

w 70 80

0

70

I N

n sy

5 z30

2 .=

20

5

^{g z 1 0}

,"LO

~7 1

towards Kenese

5 7 - 0 8 _ 2 q

0 ' 5 c

1

towords Keszlhely

3 g . p

> t

5.10.1963

Fig. 3. Transversal osci llatios

(~uszkalay and Starasolszky, 1964 )

towards towards

Kenese Keszt helv

Fig. 4. Superimposed motions

( ~ u s z k a l a ~ and Starasolszky, 1964)

Fig .5. Short term oscillation

(~uszkalay and Starasolszky ^, 1964)

Fig. 6. Wave picture

( ~ u s z k a l a ~ and Storosolszky, 1964)

KESZTHELY

BAY

River Zala

Fg.7. Motion of fresh Zala water, W

^a

0

- ^flow

near the surface

- ---

flow inside the water body local increasing in water level

SZlGLlGET BAY

- 1

Fig .8. Wind induced flows; W= 31 km h direction

NNE at Mariafurdo

- increasing wind

- - - decreasing wind

River Zala

Fig .9. Effect of transient wind conditions

///I/// change during the observation pericd Relative transverse distance [m]

F g .lo. Erosion suspended solids concentrations and wind data ( Homvas, 1967)

SZEMES

troced bottom sediment ot the beginning of the experiments

two months loter

Longitudinaldistance Windpath

Fig .ll. Suspended solids concentrations and wind data.

Motion of traced bottom sediment ( ~ a m v a s ,1967)

KESZTHELY BAY

River

Fig .l2. Deposition of Zalo - sediment after two

years long simulation period

BETTER UNDERSTANDING OF THE PROCESS

PURPOSE of modelling

1

I ^{USE FOR REAL}

A

SITUATIONS

8

Fig .13. Classification of modelling activity ( hydrodynamical aspects )

COMPUTATION OF THE

^.

INFLUENCE OF WIND

INDUCED FLOW ON THE TRANSPORT OF NUTRIENTS, ALGAE

etc

ESTIMATION OF NUTRIENTS EXCHANGE AT BOTTOM, VARIATION OF EXTINCTION

etc.

DUE TO WIND ACTION

I

17 MPH - NW

HORIZONTAL VELOCITIES AT A DEPTH FROM SURFACE L0.0 FT VECTOR LENGiH = 1 FOOT/ SEC =

Fig .I&. Velocity pattern for Lake Erie, wind direction NW (Durham and Butler, 1976 )