A Preliminary Numerical Study of Atmospheric Turbulent Flows in the Idealized Planetary Boundary Layer

Abstract

A turbulent transport model is developed to study atmospheric turbulence in the planetary boundary layer. A total of nine equations governing the mean motion, mean turbulent stresses, and turbulence length scale are integrated numerically. In this preliminary study, only the ideal case of neutral lapse rate, barotropic, statistically stationary, and horizontally homogeneous conditions is treated. The height of the boundary layer is investigated and found to be about 0.5 u*/f, where u* and f are the friction velocity and Coriolis force parameter, respectively. The computed friction coefficient, the crossisobaric angle, the vertical profiles of mean wind, mean turbulent stresses, the turbulent length scale, and eddy coefficients agree well with observations and with Deardorff's results. Various terms in the turbulent stress equations, which are difficult to measure, are discussed. The direction of the stresses seems to align with the direction of the wind shear. The profiles of the turbulent diffusivity (a ratio of the turbulent to turbulent quantities) are similar to those of the eddy coefficient (a ratio of the turbulent to mean quantities). The profiles of the nondimensional eddy coefficient can he described by the simple form as KN=kze?4z. The profiles of the turbulent energy and the magnitude of the horizontal shear stresses can be approximately described by (1?z)α. The Coriolis force is found not to affect the turbulence significantly.