The degeneration of large-scale interfacial gravity waves in lakes

Abstract

Mechanisms for the degeneration of large-scale interfacial gravity waves are identified for lakes in which the effects of the Earth's rotation can be neglected. By assuming a simple two-layer model and comparing the timescales over which each of these degeneration mechanisms act, regimes are defined in which particular processes are expected to dominate. The boundaries of these regimes are expressed in terms of two lengthscale ratios: the ratio of the amplitude of the initial wave to the depth of the thermocline, and the ratio of the depth of the thermocline to the overall depth of the lake. Comparison of the predictions of this timescale analysis with the results from both laboratory experiments and field observations confirms its applicability. The results suggest that, for small to medium sized lakes subject to a relatively uniform windstress, an important mechanism for the degeneration of large-scale internal waves is the generation of solitons by nonlinear steepening. Since solitons are likely to break at the sloping boundaries, leading to localized turbulent mixing and enhanced dissipation, the transfer of energy from an initial basin-scale seiche to shorter solitons has important implications for the lake ecology.

Impact of internal waves on the spatial distribution of Planktothrix rubescens (cyanobacteria) in an alpine lake

“…The abrupt wave front is associated with a marked depletion of biomass and shows the strong impact of nonlinear effect on the biomass distribution by strong mixing (Macintyre et al, 2009). As shown by Horn et al (2001), the conditions required to generate nonlinear fronts may frequently occur in lakes as soon as the seiche amplitude becomes comparable to the epilimnion width. This was the case in the Lac du Bourget in August 2003.…”

A weakly nonlinear model for multi-modal evolution of wind-generated long internal waves in a closed basin

“…This suggests that the wind stress penetration depth may depend on the strength of the wind stress (Wedderburn number), and such vertical penetration of the wind stress in conjunction with the vertical stratification profile determines the initial energy input to each vertical mode. Recently, Stashchuk et al (2005) conducted numerical experiments to simulate the fully-nonlinear, baroclinic response of a near two-layer fluid in a rectangular, long, narrow tank, an experimental configuration similar to that employed by Horn et al (2001). Stashchuk et al (2005) discovered that the metalimnion (interfacial) layer thickens behind the nonlinear wave front (see Figs.…”

“…(30) is the Wedderburn number W . This parameter is inversely proportional to the magnitude of the wind stress (cf., Patterson, 1990 andHorn et al, 2001), is defined by the relation…”

“…Using measured values of the drag coefficient induced by wind blowing over a wavy free surface, as summarized by Phillips (1966), typical values of the Wedderburn number can be roughly estimated by the relation W ≈10 5 SU −2 10 , where U 10 is the wind speed in ms −1 measured at an elevation of 10 m above the mean water surface. Data from both laboratory experiments and field measurements reveal that significant internal wave dynamics are observed when the Wedderburn number lies in the range 1<W <5 (cf., Horn et al, 2001). The quantityk sn in Eq.…”

“…Based on the data presented by Horn et al (2001), showing that the regime of active, wind-driven, V1 nonlinear internal wave motion occurs when 0.2<W −1 <1, and the representation of the Wedderburn number in terms of the shallow water parameter S and the 10 m wind speed U 10 given in the discussion following Eq. (32), it is clear that the present model is capable of simulating stable, two-mode internal wave dynamics provided the metalimnion is not too thin (i.e., h 2 ≥0.8, say).…”