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An Eulerian Model of Dispersion in the Convective Boundary Layer Using Explicit Periodic Advections

John J. CarrollDepartment of Land, Air, and Water Resources, University of California at Davis, Davis, California

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Ming LiuDepartment of Land, Air, and Water Resources, University of California at Davis, Davis, California

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Abstract

The authors have developed a relatively simple, first-order closure, Eulerian diffusion model, in which turbulent coherent structures of the convective boundary layer are explicitly included as periodic velocities imposed on a stationary and horizontally homogeneous wind field. The dimensions of the convective updrafts and downdrafts are assumed to be inversely proportional to the ratio of their respective vertical speeds and are constant with height, and the updraft and downdraft areas are constant in the horizontal. Sinusoidal vertical velocity variations are specified with amplitudes proportional to the mean vertical velocity profiles for skewed distributions described by Weil. The horizontal velocity components of the coherent structures are calculated using the continuity equation. Model simulations for conditions on the afternoon of Wangara day 33 reproduce the major features of the complicated plume dispersion behavior observed in the water tank experiments and the CONDORS experiments. The model produces results comparable to those obtained by complex large-eddy simulation models and random walk Lagrangian models, but is computationally much less demanding. Sensitivity tests are presented that show that the model is insensitive to physically realistic ranges of the modeling parameters.

Abstract

The authors have developed a relatively simple, first-order closure, Eulerian diffusion model, in which turbulent coherent structures of the convective boundary layer are explicitly included as periodic velocities imposed on a stationary and horizontally homogeneous wind field. The dimensions of the convective updrafts and downdrafts are assumed to be inversely proportional to the ratio of their respective vertical speeds and are constant with height, and the updraft and downdraft areas are constant in the horizontal. Sinusoidal vertical velocity variations are specified with amplitudes proportional to the mean vertical velocity profiles for skewed distributions described by Weil. The horizontal velocity components of the coherent structures are calculated using the continuity equation. Model simulations for conditions on the afternoon of Wangara day 33 reproduce the major features of the complicated plume dispersion behavior observed in the water tank experiments and the CONDORS experiments. The model produces results comparable to those obtained by complex large-eddy simulation models and random walk Lagrangian models, but is computationally much less demanding. Sensitivity tests are presented that show that the model is insensitive to physically realistic ranges of the modeling parameters.

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