The degeneration of internal waves in lakes with sloping topography

In a laboratory study, we quantified the temporal energy flux associated with the degeneration of basin-scale internal waves in closed basins. The system is two-layer stratified and subjected to a single forcing event creating available potential energy at time zero. A downscale energy transfer was observed from the wind-forced basin-scale motions to the turbulent motions, where energy was lost due to high-frequency internal wave breaking along sloping topography. Under moderate forcing conditions, steepening of nonlinear basin-scale wave components was found to produce a high-frequency solitary wave packet that contained as much as 20% of the available potential energy introduced by the initial condition. The characteristic lengthscale of a particular solitary wave was less than the characteristic slope length, leading to wave breaking along the sloping boundary. The ratio of the steepening timescale required for the evolution of the solitary waves to the travel time until the waves shoaled controlled their development and degeneration within the domain. The energy loss along the slope, the mixing efficiency, and the breaker type were modeled using appropriate forms of an internal Iribarren number, defined as the ratio of the boundary slope to the wave slope (amplitude/wavelength). This parameter allows generalization to the oceanographic context. Analysis of field data shows the portion of the internal wave spectrum for lakes, between motions at the basin and buoyancy scales, to be composed of progressive waves: both weakly nonlinear waves (sinusoidal profile with frequencies near 10(-4) Hz) and strongly nonlinear waves (hyperbolic-secant-squared profile with frequencies near 10(-3) Hz). The results suggest that a periodically forced system may sustain a quasi-steady flux of 20% of the potential energy introduced by the surface wind stress to the benthic boundary layer at the depth of the pycnocline.