k–epsilon Turbulence Modeling of Density Currents Developing Two Dimensionally on a Slope

Dense underflows developing two dimensionally on a slope are simulated numerically. The k–epsilon model is used for the turbulence closure. The boundary-layer approximation renders the governing equations in the form of parabolic partial differential equations, which are easier to solve numerically than elliptic equations. Evolution of vertical structures of dense underflows is computed along the streamwise direction. Excellent similarity collapses of the computed vertical structures are obtained. The computed profiles of velocity and concentration are compared with measured data, resulting in good agreement. The impact of a parameter representing the stratification level in the k–epsilon model is investigated. Appropriate values of this parameter, yielding results that are nearly identical to the integral model, are proposed. Water entrainment coefficients are estimated from computed solutions, and are observed to fall within the range of previous measurements. Finally, by using the collapsed vertical structures, profile constants defined in the integral model are calculated, which assures that the top-hat assumption necessary for deriving the integral model is valid.