Basin-scale internal waves provide the driving forces for vertical and horizontal fluxes in a stratified lake below the wind-mixed layer. Thus, correct modeling of lake mixing and transport requires accurate modeling of basinscale internal waves: examining this capability with a hydrostatic, z-coordinate three-dimensional (3D) numerical model at coarse grid resolutions is the focus of this paper. It is demonstrated that capturing the correct thermocline forcing with a 3D mixed-layer model for surface dynamics results in a good representation of low-frequency internal wave dynamics. The 3D estuary and lake computer model ELCOM is applied to modeling Lake Kinneret, Israel, and is compared with field data under summer stratification conditions to identify and illustrate the spatial structure of the lowest-mode basin-scale Kelvin and Poincaré waves that provide the largest two peaks in the internal wave energy spectra. The model solves the unsteady Reynolds-averaged Navier-Stokes equations using a semi-implicit method similar to the momentum solution in the TRIM code with the addition of quadratic Euler-Lagrange discretization, scalar (e.g., temperature) transport using a conservative flux-limited approach, and elimination of vertical diffusion terms in the governing equations. A detailed description is provided of turbulence closure for the vertical Reynolds stress terms and vertical turbulent transport using a 3D mixed-layer model parameterized on wind and shear energy fluxes instead of the convential eddy viscosity/diffusivity assumption. This approach gives a good representation of the depth of the mixed-layer at coarse vertical grid resolutions that allows the internal waves to be energized correctly at the basin scale.Wind stresses, surface heating, and density currents form the driving energy fluxes of a stratified lake. The basin-scale energy flux from the wind is of particular interest because of its dominant role in setting the thermocline in motion, which, in the absence of inflows and outflows, is the primary energy store for transport and mixing below the wind-mixed layer. Thus, modeling the basin-scale internal wave behavior is an a priori requirement to modeling and quantifying the flux paths of nutrients in a stratified lake (Imberger 1994). This paper takes a first step in this direction by analyzing our ability to model basin-scale internal waves that are seen in Lake Kinneret, Israel.Energy flux path in a stratified lake-Energy flux through a stratified lake has a fundamental dependence on forced and free baroclinic motions. The wind imparts both momentum and turbulent kinetic energy (TKE) to the water in the surface layer. The TKE distributes momentum vertically in the 1 Corresponding author
The response of the water column to varying conditions of stratification and wind forcing was investigated in Lake Kinneret (Israel) using data collected from thermistor chains and acoustic Doppler current profilers during 1997 and 1998. The strong daily sea breeze was found to generate a vertical mode 1 internal Kelvin wave and basin-scale internal Poincaré waves of vertical modes 1, 2, and 3. The Kelvin wave, the dominant component of the internal wave field, was responsible for alongshore velocities in the nearshore regions. In the upwind nearshore regions, velocities were dominated by the forced response to the wind and were cross-shore in nature. In the lake interior, the Kelvin wave effect on the horizontal velocity field was minor compared to the higher vertical mode Poincaré waves. The Kelvin wave is shown to exist in resonant and nonforced states with the wind, whereas the vertical mode 1 Poincaré wave energy remained relatively constant, despite large variability in the forcing conditions. The energy in the higher mode Poincaré waves varied greatly, both on daily and seasonal timescales. The results demonstrate that the wind energy forces multiple basin-scale internal wave modes and that prior motion in the water column must be considered when determining the subsequent internal wave response in periodically forced systems.
Turbulent mixing within the metalimnion of a stratified lake was investigated using a portable flux profiler (PFP) capable of resolving all three components of the velocities, the conductivity, and the temperature microstructure. Presented is a detailed description of the techniques used in the data processing, particularly in the separation of the turbulence from the internal wave signal. The sampling, carried out in Lake Kinneret (Israel) during the summer for 3 consecutive years, showed that most of the time the vertical flux through the metalimnion was negligible, but, at times, the eddy diffusivity did reach values as high as 10 Ϫ2 m 2 s Ϫ1 . A comparison between direct measurement of the vertical fluxes obtained from the PFP data with that from indirect estimates of the fluxes shows good agreement for the 6 Յ Fr ␥ Ͻ 100 range. Scaling of the turbulence based on Fr ␥ and Ri reveal two classes of turbulent regimes: (1) due to traumata characteristic of internal wave-wave interaction and, another, (2) more energetic and due to shear-driven turbulence. The PFP penetrated the water relatively slowly (0.1 m s Ϫ1) allowing the measurement of temperature fluctuations down to 1 mm and, at the same time, also providing information of the velocity fluctuations. This is different from previous oceanographic measurements, which are always gathered with instrument traversing the water column at velocities closer to 1 m s Ϫ1 , preventing regime (1) from being detected.The vertical exchange between the surface and deep waters in stratified lakes is a central issue in the understanding of the fluxes of particles and nutrients and, consequently, the eutrophication in these water bodies. Imberger (1998) drew a conceptual model of these flux paths in a stratified lake where the wind induces mixing in the surface layer and energizes basin scale internal waves that, in turn, distribute this energy around the lake, leading to mixing mainly near the boundaries (Gloor et al. 1994;Lemckert and Imberger 1998) and reduced fluxes through the metalimnion in the interior of the lake.Even though the vertical fluxes in the metalimnion are small, their quantification is essential for the interpretation of observed biological and chemical parameter variations (Nishri et al. 2000). Naturally, two questions arise as we approach the mixing in the metalimnion: first, what is the magnitude and, second, what are the mechanisms energizing the mixing. Direct measurements of the buoyancy fluxes carried out in the ocean (Moum 1990(Moum , 1996a Yamazaki and Osborn 1993) show the difficulties in making these measurements and provide the first comparison between the direct determination of the fluxes with the more easily ob-1 Corresponding author (saggio@iris.ufscar.br).
Thermistor chain data collected in Lake Biwa (Japan) during a period of strong stratification were used to determine the nature of the water column response to wind forcing. The evolution of the basin-scale waves in the lake were reproduced in three-dimensional numerical simulations and the time variability of the internal wave spectrum is discussed based on spectral analysis of the thermistor chain records. Severe winds associated with the passage of three typhoons during the sampling period excited basin-scale Kelvin and PoincarC waves, which, by interaction with the topography of the lake and non-linear effects, generate trains of high-frequency internal waves. Time-frequency analysis of the temperature signals suggests that the u-* slope of the internal wave spectrum is probably the result of the composition of groups of waves with high intermittence travelling through the wave guide. The observed rapid decay of internal wave energy after severe wind events seemed to be due mostly to high dissipation at the sloping boundaries of the lake.
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