Seasonal variation of solitary wave properties in Lake Constance

Abstract

The properties of internal solitary waves (ISWs) depend on the stratification of the water body. In most climatic regions the stratification in lakes and oceans varies during the year, and hence the properties of the ISWs can also be expected to change over the seasons. On the basis of a long-term temperature time series recorded over 6 years, this paper investigates seasonal changes in the characteristic properties of ISWs in Lake Überlingen, a subbasin of Lake Constance. A large number of ISWs with amplitudes ranging from 3 m to 30 m were identified. More than 15% of the leading ISWs of a wave train were associated with density inversions, often indicating shear instabilities or trapped cores. For all waves the propagation depth and the value of a nonlinearity index nlp providing the degree of nonlinearity were determined, propagation depth being the rest height of the isotherm undergoing maximum displacement and nlp the ratio between wave amplitude and propagation depth. The index nlp was found to be a good parameter for predicting the occurrence of inversions. The statistical analysis of the wave properties derived from the observations revealed that the degree of nonlinearity of the ISWs changes with season. Complementary to the statistical analysis, the seasonally averaged ISW properties were compared with wave prototypes obtained numerically from the Dubreil-Jacotin-Long (DJL) and the stratified Korteweg-deVries (KdV) models. The simulations indicate that the typical stratification and its seasonal variation are responsible for the degree and the seasonality of nonlinearity of the ISWs.