Origin and propagation of ISWs

The temperature data from the three campaigns indicate several events with two consec-utive and abrupt descents of the thermocline in Lake ¨Uberlingen at station G (Fig. 5.2a, arrows). Similar events have been observed previously by Appt et al. [2004] at a

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Front ISW

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Figure 5.2: Progressive surges before and after reflection together with ISWs measured at station G / S1 during (A) autumn 2010 and (B) summer 2009. The white arrow indicates the time, at which the reflected parts of ISW1 should pass.

lar location and were interpreted as the consequence of a steepened surge. According to Appt et al. [2004] the first deepening of the thermocline in the center of Lake ¨Uberlingen

is caused by the passage of the surge propagating from the Sill of Mainau towards the western end of Lake ¨Uberlingen (incoming surge), whereas the reflected surge propagating in the opposite direction (out-going surge) is responsible for the second deepening of the thermocline.

ISWs usually pass the measuring station shortly before or together with a surge, i.e. an abrupt deepening of thermocline depth (Fig. 5.2A, ISWs and Fig. 5.2B, ISW2, ISW3), but were once also observed without a close connection to a surge, then passing as ‘pioneer’-ISWs several hours before the surge (Fig. 5.2B, ISW1). These different types of ISW propagation, e.g. with and without a surge, suggest that there are different generation mechanisms of ISWs in Lake Constance. However, since ‘pioneer’-ISWs seem to be an exception, we concentrate on ISWs propagating shortly before or together with an internal surge. Because of the characteristic shape and the large amplitudes of the ISWs we could in all cases clearly identify the leading ISW of the ISW trains.

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Figure 5.3: Evolution of an ISW train along its path from the main basin of Lake Constance to the end of Lake ¨Uberlingen. In the different panels the 11^◦C (blue), 15^◦C (black) and 17^◦C (red) isotherms measured at stations B, C, D, F, G, and H, respectively, and the north component of the current velocity measured at station A and E are shown at different times during the day. The 3.5 h time sections were selected to display the leading solitary waves. The locations of the stations are shown in Fig. 5.1A.

The number of ISWs in the wave package ISW2, which is connected to an internal surge (compare Fig. 5.2B and Fig. 5.3, the drop of isotherms after the passage of the ISWs), increased along the path of the propagating internal surge from station A to station H (Fig. 5.3), indicating that in this case the surge indeed is the location of generation of ISWs. ISWs apparently occur already in the central basin (Fig. 5.3, stations B, C, D) indicating that the generation of the ISWs is not restricted to the Sill of Mainau. This early occurrence of ISWs suggests that the nonlinear steepening of the surge is the source of ISW generation. Topographical effects however probably enhance the degeneration

process of the basin scale wave, in particular the nonlinear steepening of the surge, which may support the generation of ISWs. Such an effect of topography is suggested by the larger number of ISWs at station G in the center of Lake ¨Uberlingen after the surge has passed the Sill of Mainau compared to the number of ISWs in the main basin of Lake Constance (Fig. 5.3).

Figure 5.4: A) Lake depth at the thalweg. Dotted lines indicate the lake depths at the study sites.

Distances refer to a projection of the study sites on a straight line passing through the thalweg (cf.

Fig. 5.1a). (B) Propagation path and phase velocities of propagating ISWs and a thermal front during 31.07. and 01.08.2009. Times refer to the time lag of the first occurrence of the respective ISW at the various study sites relative to 04:00, 31.07.2009. The filled dot marks the time, when the waves should have reached the western end of Lake Constance, the black square the time, when the front should have been reflected. The dotted line corresponds to a hypothetical path of reflected ISW2 assuming the phase velocity is maintained after reflection.

Using a projection of the study sites on the thalweg (Fig. 5.1A, grey line) the distance traveled by the leading ISW can be correlated with the timing of the leading ISW at a particular station. This allows estimating the phase-velocity of the leading ISW. Phase velocities of the ISWs and of an internal front passing after ISW2 (Fig. 5.2B) are shown in Fig. 5.4. The times of the passage of the internal front at the various study sites were derived by evaluating the corresponding times of the lowpass-filtered (butterworth, cut-off frequency 30 min) maximal thermocline depth occurring between ISW2 and ISW3.

According to Fig. 5.4, the phase velocity of the ISWs appears to be independent of the varying water depth even when the waves travel from the main basin of Lake Constance to

Lake ¨Uberlingen at the Mainau Sill (Fig. 5.4A and 5.4B, ISW2, note the positive slope of the path-time function). The reflection or shoaling of the ISWs and the steep-fronted surge takes place at the location where the thermocline intersects with the sloping boundary of the western end of Lake ¨Uberlingen and is thus somewhat before the western boundary is reached (Fig. 5.4B, filled square and circle). The phase velocities of ISW2 and ISW3 determined from the linear regression of the path-time function are c = 0.36 ms⁻¹ and c = 0.42 ms⁻¹ respectively. The phase velocities of these ISWs calculated from the DJL equation using the amplitude of the leading ISWs observed at the long-term measuring station G, are c= 0.36 ms⁻¹ and c= 0.42 ms⁻¹, respectively, in excellent agreement with the values obtained from the path-time analysis. The phase velocity of the ISW1, however, was strongly overestimated by the DJL (c = 0.35 ms⁻¹) compared to the c = 0.26 ms⁻¹ estimated from the observed propagation of these waves, suggesting that the character of the ISW1 propagating far ahead of the surge differs from the character of the waves ISW2 and ISW3 that are closely associated with the internal surge.