Abstract
Based on simulations with the Dubreil-Jacotin-Long (DJL) equation, the limiting amplitude and the breaking mechanisms of internal solitary waves of depression (ISWs) are predicted for different background stratifications. These theoretical predictions are compared to the amplitude and the stability of the leading internal solitary waves of more than 200 trains of ISWs observed in the centre of a sub-basin of Lake Constance. The comparison of the model results with the field observations indicates that the simulated limiting amplitude of the ISWs provides an excellent prediction of the critical wave height above which ISWs break in the field. Shear instabilities and convective instabilities are each responsible for about half of the predicted wave breaking events. The data suggest the presence of core-like structures within the convectively unstable waves, but fully developed and stable cores were not observed. The lack of stable trapped cores in the field can be explained by the results from dynamic simulations of ISWs with trapped cores which demonstrate that even slight disturbances of the background stratification cause trapped cores to become unstable.
Highlights
The degeneration of basin-scale waves to internal solitary waves of depression (ISWs) and of the ISWs to turbulence by wave breaking is one of the main processes of energy transfer from large to small scales in the thermocline and deeper water regions of lakes [1,2]
It is known that the stability of ISWs in undisturbed water is determined by the ISW amplitude [9,10,11,12]
Assuming that the leading ISW is generated at or before the Sill of Mainau [20] or at the western end of Lake Uberlingen after the reflection of the steepened front of the basin-scale seiche [18], the wave evolution distance from the location of generation to the longterm measuring station B in the center of Lake Uberlingen is at least 5 km (Fig. 1A)
Summary
The degeneration of basin-scale waves to ISWs and of the ISWs to turbulence by wave breaking is one of the main processes of energy transfer from large to small scales in the thermocline and deeper water regions of lakes [1,2]. Two qualitatively different mechanisms are responsible for ISW breaking in deep water, breaking due to shear instabilities or breaking due to convective instabilities, which results in the formation of a trapped, or recirculating, core [11]. These breaking mechanisms have different ecological consequences, in lakes as well as in the ocean. It is important to classify the breaking mechanism of breaking waves in the field
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