Spectra in the Unstable Surface Layer

L. J. Peltier Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

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J. C. Wyngaard Departments of Meteorology and Mechanical Engineering, The Pennsylvania State University, University Park, Pennsylvania

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S. Khanna Department of Mechanical Engineering, The Pennsylvania State University, University Park, Pennsylvania

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J. O. Brasseur Department of Mechanical Engineering, The Pennsylvania State University, University Park, Pennsylvania

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Abstract

A simple approach to modeling spectra in unstable atmospheric surface layers is presented. The authors use a single form for the two-dimensional spectrum of horizontal velocity, vertical velocity, and a scalar in the horizontal plane; it has two free constants, a length scale, and an intensity scale. Continuity is used to relate the vertical and horizontal velocity spectra. The two free constants are determined by matching the variance and the inertial-subrange spectral level with observations. 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 spectra by combining these two limiting forms. The one-dimensional spectra, obtained by integration over one wavenumber component, and their variances agree well with observations. Near the surface the vertical velocity variance follows Monin-Obukhov (M–O) similarity and shows a realistic local free-convection asymptote; at greater heights it shows departures from M–O similarity that also agree well with observations. Finally, the two-dimensional spectra are used to calculate the valances of the resolvable and subgrid-scale components of large eddy simulations and their dependence on grid mesh size, distance from the surface, boundary layer depth, and stability.

Abstract

A simple approach to modeling spectra in unstable atmospheric surface layers is presented. The authors use a single form for the two-dimensional spectrum of horizontal velocity, vertical velocity, and a scalar in the horizontal plane; it has two free constants, a length scale, and an intensity scale. Continuity is used to relate the vertical and horizontal velocity spectra. The two free constants are determined by matching the variance and the inertial-subrange spectral level with observations. 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 spectra by combining these two limiting forms. The one-dimensional spectra, obtained by integration over one wavenumber component, and their variances agree well with observations. Near the surface the vertical velocity variance follows Monin-Obukhov (M–O) similarity and shows a realistic local free-convection asymptote; at greater heights it shows departures from M–O similarity that also agree well with observations. Finally, the two-dimensional spectra are used to calculate the valances of the resolvable and subgrid-scale components of large eddy simulations and their dependence on grid mesh size, distance from the surface, boundary layer depth, and stability.

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