ANALYTICAL-NUMERICAL SOLUTIONS FOR THE ONE DIMENSIONAL PBL TURBULENCE MODEL

摘要: Analytical and propagator numerical methods are elaborated for solution of Weng-Taylor turbulence model ([1)], that was originally outlined by J. Smagorinsky (see [2-4]). In the Weng-Taylor model the eddy viscosity coefficient nonlinearly depend on velocities and is defined from additional phenomenological consideration, which constitutes a turbulence closure. In such type models sharp vertical boundary layers causes difficulties for traditional numerical methods. In this work a new numerical method is proposed, which is based on analytical representation of Weng-Taylor model solutions. It is shown that these analytical solutions of constituted initial boundary value problem can be resolved by additional solutions of system of ordinary differential equations. This system of equations is solved analytically, by using polynomial type substitutions for generalized Lagrangian variables. The obtained numerical solution, precision and effectiveness are compared to solution by using numerical propagator method ([5]).