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Vertical Velocity Generated Over Non-Homogeneous Rough Terrain, Theory and Subgrid-Scale Parameterization

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A systematic evaluation of vertical velocities associated with stratified atmospheric flows over non-homogeneous terrains apparently has not been reported in the literature. This study approaches the problem numerically and analytically. A non-linear model evaluates the range of the parameters for validity of the linear theory. Simple analytical theory estimates the role played by the relevant parameters. Results indicate that, when the transition in surface roughness is gradual between a smooth and a rough surface, the perturbation of the vertical velocity has the same horizontal scale as the perturbing source. The nature of the perturbation depends on the product between the horizontal scale of the rough patch and the Scorer parameter of the ambient atmosphere i.e. very small values of this product weakly stratified atmosphere gives a wave trapped around the top of the stress layer, while values of the order of unity give a non-hydrostatic gravity wave which propagates away from the top of the stress layer. Values larger than unity yield a propagating hydrostatic wave. When the transition in surface roughness is abrupt, the wave is nonhydrostatic with a horizontal and vertical wave number equal to the ambient Scorer parameter. When the product between the horizontal width of the rough patch and the Scorer parameter is large, there is no significant interference between the wave upstream and the wave downstream of the rough patch the two waves are of the same nature and amplitude, but opposite sign. When this product is small, however, the wave upstream interferes destructively with the wave downstream, i.e., the amplitude of the resulting wave is accordingly reduced.

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  • Meteorology

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