Abstract
Abstract. For many lakes the nonlinear transfer of energy from basin-scale internal waves to short-period motions, such as solitary internal waves (SIW) and wave trains, their successive interaction with lake boundaries, as well as over-turning and breaking are important mechanisms for an enhanced mixing of the turbulent benthic boundary layer. In the present paper, the evolution of plane SIWs in a variable depth channel, typical of a lake of variable depth, is considered, with the basis being the Reynolds equations. The vertical fluid stratification, wave amplitudes and bottom parameters are taken close to those observed in Lake Constance, a typical mountain lake. The problem is solved numerically. Three different scenarios of a wave evolution over variable bottom topography are examined. It is found that the basic parameter controlling the mechanism of wave evolution is the ratio of the wave amplitude to the distance from the metalimnion to the bottom d. At sites with a gentle sloping bottom, where d is small, propagating (weak or strong) internal waves adjust to the local ambient conditions and preserve their form. No secondary waves or wave trains arise during wave propagation from the deep part to the shallow water. If the amplitude of the propagating waves is comparable with the distance between the metalimnion and the top of the underwater obstacle ( d ~ 1), nonlinear dispersion plays a key role. A wave approaching the bottom feature splits into a sequence of secondary waves (solitary internal waves and an attached oscillating wave tail). The energy of the SIWs above the underwater obstacle is transmitted in parts from the first baroclinic mode, to the higher modes. Most crucially, when the internal wave propagates from the deep part of a basin to the shallow boundary, a breaking event can arise. The cumulative effects of the nonlinearity lead to a steepening and overturning of the rear wave face over the inclined bottom and to the formation of a turbulent jet propagating upslope. Some time later, after the breaking event, a new stable stratification is formed at the site of wave destruction. The breaking criterion of ISWs is discussed.Key words. Oceanography: general (limnology; numerical modeling) – Oceanography: physical (internal and inertial waves)
Highlights
Internal waves play an important role in water dynamics of stratified lakes
Taking into account that for the summer and for the autumn stratifications the maximum of the solitary internal waves (SIW) amplitude lies very far from the bottom, internal waves under conditions of a weakly variable bottom are not destroyed and do not transform into a secondary wave packet during their evolution
No secondary SIWs or wave trains arise during wave propagation from the deep to the shallower part of the water
Summary
Internal waves play an important role in water dynamics of stratified lakes. They intensify the momentum and energy transport, enhance the turbulence and water mixing through the water column, and in turn, facilitate the ventilation of a thermocline, as well as energize the vertical diffusion of oxygen, nitrate, hydrogen sulfide and other chemical elements between near-surface and near-bottom waters (Eckert et al, 2000). We apply the mathematical numerical model developed on the basis of the Reynolds equations in the Boussinesq approximation, to examine the influence of the bottom topography and nonlinearity of the wave processes on the mechanism of the energy transfer from the large- to the small-scale motions and even farther – to turbulence and mixing, as extreme situations. Once inserted in the numerical scheme the strong, nonlinear wave will evolve in the basin of constant depth During this evolutional process the initial large amplitude K-dV soliton will be modified, and a new stationary solitary wave will be formed at the frontal side of the wave field. Is the description of the three different scenarios of a wave evolution in the considered area, which are found for different bottom profiles
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
