A parametric numerical model for lake hydrodynamics

In stratified lakes, internal waves generated by various sources play an important role in mixing and may transport momentum and energy between basin-scale and turbulent-scale motions. Internal waves are generated at the base of the surface mixing layer (SML) by pressure perturbations being moved over the interface by surface current. The generated internal waves may propagate downward carrying their energy along rays at the group velocity. It is important to estimate the flow of momentum and energy associated with these propagating internal waves to predict the mixing efficiency in lakes. s model, internal waves generated at the base of the SML are parameterised in terms of angular frequency ω = cω(Ush), the amplitude a = ca(2πUsNh), and the horizontal wave numbers k = ck(2πh) and l = cl(2πh), where cω, ca, ck, cl are the coefficients for the angular frequency, the amplitude and the horizontal wavenumbers, respectively, h is the thickness of the SML, Nh is the buoyancy frequency beneath the SML and Us is the velocity jump evaluated at the base of the SML. A numerical model was constructed which is capable of tracing the internal wave energy along rays in three dimensions. The model includes the effects of bottom geometry, velocity shear and interaction between rays. This model is being coupled to a basin-scale model and a turbulent flux model to provide a full account of all scales of motion.