Horizontal Dispersion in Gyres-Internal Wave Flow Field in a Rotating Circular Lake

Abstract

A combined stream function is derived for investigating horizontal dispersion of pollutants in a moderate-sized circular rotating basin when internal wave and gyre flow field coexist in the upper mixing layer. The combined flow field is analogous to wave-current flow in which the steady part is the depthwise velocity profile of circumferential gyre that is simulated using a depthwise cosine function. The periodic components of the Kelvin-type internal wave (assuming a small Burger number) are derived up to the second order in which the variation in the wave amplitude in the radial direction is governed by the modified Bessel function of the first kind. The combined vertical diffusivity is estimated by adding its wave-induced and current-induced components. The resultant closed-form solution of the wave-current longitudinal dispersion coefficient (WCLDC) shows additional wave-induced dispersion over the dispersion due to codirectional gyres. The celerity for the combined flow shows a consistently higher magnitude than does the wave-only celerity. As the lack of data on combined gyre-internal wave flow did permit validation of the model, the analysis was applied to a few lakes using the data available for Kelvin waves superimposed on hypothetical gyre flow. For higher wave amplitudes, the combined flow structure shows enhanced wave influence over flow depth that result in higher WCLDC.