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Rectified Flow over an Elongated Topographic Feature along a Vertical Wall

Jacques VerronLaboratoire des Ecoulements Géophysiques et Industriels, Institut de Mécanique de Grenoble, Grenoble, France

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Dominique RenouardLaboratoire des Ecoulements Géophysiques et Industriels, Institut de Mécanique de Grenoble, Grenoble, France

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Gabriel Chabert D'HieresLaboratoire des Ecoulements Géophysiques et Industriels, Institut de Mécanique de Grenoble, Grenoble, France

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Thong NguyenLaboratoire des Ecoulements Géophysiques et Industriels, Institut de Mécanique de Grenoble, Grenoble, France

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Henri DidelleLaboratoire des Ecoulements Géophysiques et Industriels, Institut de Mécanique de Grenoble, Grenoble, France

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Don L. BoyerCollege of Engineering and Applied Sciences, Environmental Fluid Dynamics Program and Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, Arizona

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Abstract

Alongshore oscillatory flows over an elongated topographic feature next to a vertical wall for a homogeneous, rotating fluid were investigated by means of numerical and laboratory experiments. The physical experiments were conducted in the Grenoble 13-m diameter rotating tank, in which an elongated obstacle of limited longitudinal extent was placed along the vertical sidewall. The background oscillating motion was obtained by periodically varying the platform angular velocity. Fluid motions were visualized and quantified by direct velocity measurements and particle tracking. The numerical model employed was a tridimensional model developed by Haidvogel et al. It consists of the traditional primitive equations, that is, the Navier-Stokes equations for a rotating fluid with the addition of the hydrostatic, Boussinesq, and incompressibility approximations. (The experiments described here employ the homogeneous version.) The numerical formulation uses finite differences in the horizontal and spectral representation in the vertical dimensions.

Both the laboratory and numerical experiments show that in the range of dimensionless parameters considered, two distinct flow regimes, based on general properties of the rectified flow patterns observed, can be defined. It is further shown that the flow regime designation depends principally on the magnitude of the temporal Rossby number, Rot, defined as the ratio of the flow oscillation to the background rotation frequency. Good qualitative and quantitative agreement is found between the laboratory experiments and the numerical model for such observables as the spatial distribution of rectified flow patterns. Several other flow observables are defined and their relation with the system parameters delineated.

Abstract

Alongshore oscillatory flows over an elongated topographic feature next to a vertical wall for a homogeneous, rotating fluid were investigated by means of numerical and laboratory experiments. The physical experiments were conducted in the Grenoble 13-m diameter rotating tank, in which an elongated obstacle of limited longitudinal extent was placed along the vertical sidewall. The background oscillating motion was obtained by periodically varying the platform angular velocity. Fluid motions were visualized and quantified by direct velocity measurements and particle tracking. The numerical model employed was a tridimensional model developed by Haidvogel et al. It consists of the traditional primitive equations, that is, the Navier-Stokes equations for a rotating fluid with the addition of the hydrostatic, Boussinesq, and incompressibility approximations. (The experiments described here employ the homogeneous version.) The numerical formulation uses finite differences in the horizontal and spectral representation in the vertical dimensions.

Both the laboratory and numerical experiments show that in the range of dimensionless parameters considered, two distinct flow regimes, based on general properties of the rectified flow patterns observed, can be defined. It is further shown that the flow regime designation depends principally on the magnitude of the temporal Rossby number, Rot, defined as the ratio of the flow oscillation to the background rotation frequency. Good qualitative and quantitative agreement is found between the laboratory experiments and the numerical model for such observables as the spatial distribution of rectified flow patterns. Several other flow observables are defined and their relation with the system parameters delineated.

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