Transformation and disintegration of strongly nonlinear internal waves by topography in stratified lakes

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)