Energetics and damping of basin-scale internal waves in a strongly stratified lake

Energetics and damping of basin-scale internal waves and subsequent near-bottom transport processes in Lake Kinneret were investigated using the modal analysis in a layer-stratified irregular basin. The theory was extended to include small linear damping, and energy budgets and damping rates of five dominant internal waves were extracted by fitting numerically calculated internal waves to isotherm displacements measured by six thermistor chains distributed throughout the lake. Energy contained in the dominant internal waves (,3 GJ) resulted from a balance between energy input from diurnal winds and dissipation within a day, both of which were estimated to be 3,4 GJ d21. Damping was caused primarily by bottom friction, and the damping rates (e-folding time) varied from 1 to 3 d, depending on the velocity structure. Currents induced by the internal waves caused considerable spatial variability of the bottom shear stress and near-bottom transport processes, such as entrainment rate at the top of the benthic boundary layer and mass transfer at the sediment–water interface. The primary sources of energy in a lake are the solar radiation and the rate of wind working on the surface. Solar radiation sets up the stratification due to surface heating; it may also create weak currents through differential cooling and heating (Monismith et al. 1990; Okely and Imberger 2007). On the other hand, winds excite a variety of motions ranging from energetic basin-scale internal waves to small-scale turbulent motions (Imberger 1998), all of which support transport of materials. In the water column, part of the turbulent kinetic energy (TKE) is converted to potential energy through diapycnal mixing, whereas energy dissipation near the bottom causes resuspension of particulate materials (Gloor et al. 1994), entrainment at the top of the benthic boundary layer (BBL) (Gloor et al. 2000; Lemckert et al. 2004), and enhancement of mass transfer at the sediment–water interface (Lorke et al. 2003). These links make energetics of internal waves relevant not only for physical processes but also for chemical and biological processes. The energy flux path in lakes has been studied by both ‘‘bottom-up’’ and ‘‘top-down’’ approaches. The bottom-up approach employs microstructure measurements, where turbulent fluctuations of temperature (Osborn and Cox 1972; Dillon and Caldwell 1980) and velocity (EtemadShahidi and Imberger 2001; Saggio and Imberger 2001) are measured in a water column and converted into turbulent properties, such as the dissipation rate of TKE and turbulent diffusion coefficient. This method yields direct estimation of energy dissipation and mixing, but it is difficult to measure the spatiotemporal variability due to the intermittent nature of the turbulence (Baker and Gibson 1987). As a result, TKE budget is usually calculated in a basin-averaged sense (e.g., Gloor et al. 2000; Ravens et al. 2000; Wüest et al. 2000). The top-down approach is to estimate the energy budget in basin-scale internal waves (Gloor et al. 2000; Antenucci and Imberger 2001). In a strongly stratified lake, basin-scale internal waves receive a large part of the energy input from the wind (Shimizu et al. 2007), and then they cascade this energy, as they dissipate, down to smaller scales over the damping period (Imberger 1998). Although this approach may provide this information only in the metalimnion and hypolimnion of the lake away from the direct wind stirring, it has the advantage that it allows estimation of the net energy cascade, overcoming the spatiotemporal uncertainty inherent in the bottom-up approach. Theoretically, these two approaches could be combined to obtain an estimate of the spatiotemporal variability of the turbulent field, but this does not seem to have been attempted. The spatial structure of internal waves may conveniently be visualized through their vertical and horizontal structure in flat-bottomed elliptical basins (Antenucci and Imberger 2001). The vertical mode 1 (V1) internal waves induce coherent vertical oscillation in the water column and antisymmetric currents in the epilimnion and hypolimnion, while the vertical mode 2 (V2) internal waves cause periodic change of the metalimnion thickness accompanied by strong horizontal jet-like currents within the layer (Lighthill 1969; Csanady 1982; Monismith 1985). The horizontal structure of internal waves in a rotating basin is typified by Kelvin and Poincaré waves. A Kelvin wave is a cyclonically rotating wave (counterclockwise in the Northern Hemisphere and the opposite in the Southern Hemisphere) with the interface displacement (and velocity) concentrated near the coast (Antenucci and Imberger 2001). On the other hand, a Poincaré wave rotates anticyclonically (clockwise in Northern Hemisphere) and has a significant interface displacement over the lake and small velocity near the coast. In real lakes, these simplified pictures are modified by the irregular bathymetry, and the spatial structure needs to be computed using a modal analysis (e.g., Platzman 1 Corresponding author ([email protected]). Acknowledgments We thank Jason Antenucci and two anonymous reviewers for constructive discussions and comments on earlier versions of the manuscript. We are grateful for the close collaboration of the Kinneret Limnological Laboratory. The first author acknowledges the financial support of Tokyo Tech Long-Term Overseas Study Support Program. This article represents Centre for Water Research reference ED 2146-KS. Limnol. Oceanogr., 53(4), 2008, 1574–1588 E 2008, by the American Society of Limnology and Oceanography, Inc.