The Numerical Solution of the Mellor-Yamada Level 2.5 Turbulent Kinetic Energy Equation in the Eta Model

Abstract

Abstract A new method is presented for obtaining the numerical solution of the production-dissipation component of the turbulent kinetic energy equation that arises in the Mellor-Yamada level 2.5 turbulent closure model. The development of this new method was motivated by the occasional appearance of large temporal oscillations in the solution provided by a previously used method. Analysis of the equation revealed that the solution should tend toward a stationary asymptotic value, which is the equilibrium value of turbulent kinetic energy for the level 2, Mellor-Yamada model. Failure to identify the correct asymptotic value in the formalism underlying the numerical solution of the equation allows the solution to overshoot the equilibrium. Repeated overshooting gives rise to an oscillation in the solution from one time step to the next. The new method prevents this from happening. Idealized cases are used to demonstrate the performance of the new method. It has been incorporated into the eta coordinate, nu...