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Title: The degeneration of internal waves in lakes with sloping topography Authored by: Boegman, L., Ivey, G.N. and Imberger, J. Abstract:
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 1024 Hz) and strongly nonlinear waves (hyperbolicâ€"secant-squared profile with frequencies
near 1023 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.
Reference: Boegman, L., Ivey, G.N. and Imberger, J., 2005, The degeneration of internal waves in lakes with sloping topography, Limnology and Oceanography, , 50(5):1620-1637 |
