SPECTRA IN THE UNSTABLE SURFACE-LAYER

A simple approach to modeling spectra in unstable atmospheric surface layers is presented. The authors use a single form for the two-dimensi onal spectrum of horizontal velocity, vertical velocity, and a scalar in the horizontal plane; it has two free constants, a length scale, an d an intensity scale. Continuity is used to relate the vertical and ho rizontal velocity spectra. The two free constants are determined by ma tching the variance and the inertial-subrange spectral level with obse rvations. The scales are chosen so that the spectra follow law of the wall and mixed-layer scaling in the neutral and free-convection limits , respectively. The authors model the stability dependence of the spec tra by combining these two limiting forms. The one-dimensional spectra , obtained by integration over one wavenumber component, and their var iances agree well with observations. Near the surface the vertical vel ocity variance follows Monin-Obukhov (M-O) similarity and shows a real istic local free-convection asymptote; at greater heights it shows dep artures from M-O similarity that also agree well with observations. Fi nally, the two-dimensional spectra are used to calculate the variances of the resolvable and subgrid-scale components of large eddy simulati ons and their dependence on grid mesh size, distance from the surface, boundary layer depth, and stability.