The degeneration of internal waves in lakes with sloping topography
Limnol. Oceanogr., 50(5), 2005, 1620-1637 | DOI: 10.4319/lo.2005.50.5.1620
ABSTRACT: In a laboratory study, we quantiï¬ed the temporal energy ï¬ux associated with the degeneration of basin-scale internal waves in closed basins. The system is two-layer stratiï¬ed 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 efï¬ciency, and the breaker type were modeled using appropriate forms of an internal Iribarren number, deï¬ned as the ratio of the boundary slope to the wave slope (amplitude/wavelength). This parameter allows generalization to the oceanographic context. Analysis of ï¬eld 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 proï¬le with frequencies near 1024 Hz) and strongly nonlinear waves (hyperbolic-secant-squared proï¬le with frequencies near 1023 Hz). The results suggest that a periodically forced system may sustain a quasi-steady ï¬ux of 20% of the potential energy introduced by the surface wind stress to the benthic boundary layer at the depth of the pycnocline.