Investigation of the Regime Diagram of Hydrostatic Flow over a Mountain with a Primitive Equation Model. Part I: Two-Dimensional Flows

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  • 1 Météo-France, Centre National de Recherches Météorologiques, Toulouse, France
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Abstract

The different airflow regimes for prototype orographic problems are controlled by a reduced set of nondimensional numbers. A regime diagram is deduced for the Long problem from a set of numerical simulations made with a primitive equation hydrostatic model. Two transitions separating the quasi-linear regime, the high-drag state and the blocked state, are recovered. The first critical inverse Froude number F = Nh/U (corresponding to the onset of wave breaking) depends smoothly on S = NU/g, which quantifies the wave amplification, in contrast with the second critical inverse Froude number (corresponding to the onset of blocking), which is quasi-independent of S. The dimensional drag in function of F is found in F2 for the quasi-linear regime, in F≥2 for the high-drag regime, and in F1.3 for the blocked regime. The study of the blocked configuration shows that the depth of the blocked region and the top of the turbulent region increase linearly with F.

The regime diagram for the case where a critical layer (U = 0) is inserted in the basic flow is also established. Our study reproduces the main conclusion of the hydraulic theory: a discrete spectrum with a period equal to the vertical wavelength for the critical-level heights leads to a high-drag configuration, and the values of this spectrum are dependent on the mountain height. A global conclusion of this study is that the hydrostatic model has the capacity to reproduce all of the transitions due to the effects of the nonlinearities, provided that the mountain half-width is large enough.

Abstract

The different airflow regimes for prototype orographic problems are controlled by a reduced set of nondimensional numbers. A regime diagram is deduced for the Long problem from a set of numerical simulations made with a primitive equation hydrostatic model. Two transitions separating the quasi-linear regime, the high-drag state and the blocked state, are recovered. The first critical inverse Froude number F = Nh/U (corresponding to the onset of wave breaking) depends smoothly on S = NU/g, which quantifies the wave amplification, in contrast with the second critical inverse Froude number (corresponding to the onset of blocking), which is quasi-independent of S. The dimensional drag in function of F is found in F2 for the quasi-linear regime, in F≥2 for the high-drag regime, and in F1.3 for the blocked regime. The study of the blocked configuration shows that the depth of the blocked region and the top of the turbulent region increase linearly with F.

The regime diagram for the case where a critical layer (U = 0) is inserted in the basic flow is also established. Our study reproduces the main conclusion of the hydraulic theory: a discrete spectrum with a period equal to the vertical wavelength for the critical-level heights leads to a high-drag configuration, and the values of this spectrum are dependent on the mountain height. A global conclusion of this study is that the hydrostatic model has the capacity to reproduce all of the transitions due to the effects of the nonlinearities, provided that the mountain half-width is large enough.

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