Spin-up and spin-down in linearly stratified fluid over flat bottom

Abstract : We present an experimental investigation of spin-up and spin-down for a linearly stratified fluid over bottom. This study has revealed two very different behaviors depending on the value of the Burger number, a measure of the relative importance of stratification and Coriolis effects. For Burger number > 1, the flow remains remarkably axisymmetric in the bulk of the fluid in spite of the large Reynolds number, and noinstability is observed. The confinement of the secondary circulation due to the stratification is well described by the theory of Walin (1969). Thetheory was scaled using the homogeneous spin-up time scale and thus viscous-diffusion effects were omitted. However, the non-uniform spin-up of the interior gives rise to vertical flow gradients which introduce viscous-diffusion sooner than anticipated by the theory. Consequently, the comparison with the theory shows a faster rate of decay of the azimuthal flow even over the shorter spin-up time scale. An attempt to provide an easy procedure to include vertical diffusion of momentum in the Walin's analytical solution is proposed. The early stage of the flow is correctly described by the addition of viscous-diffusion effects, but the faster decay rate ofthe measurements persists over intermediate times.For Burger numbers < 1, the flow behavior is substantially different. The deeper penetration of the secondary circulation notably reduces the vertical flow gradients. The decay of the azimuthal velocity is almost vertically uniform and the development of non-axisymmetric disturbances is observed. The flow decay is well described in the early stage by the Walin's theory, but after the initial agreement the experimental results decay slower than the theoretical predictions. The discrepancies correspond to the onset of the instability, at variance with Smirnov et al. (2005) claiming that the formation of large-scale eddies provides an additional mechanism for the transport of momentum from the solid boundaries. Nevertheless, the radial transport of momentum from the sidewall boundary layer may account for the stronger decay observed over long times. The classical Eady's model is shown to be consistent with the structure of the observed waves in our experimental investigation. Its derivation by Smirnov et al. (2005) in cylindrical geometry assuming reliable initial conditions allows a reasonable estimation of the growth rate, which was untenable in the classical theory. Indeed, the mechanism of baroclinic instability becomes the most plausible explanation forthe existence of the long-wave instability in spin-up or spin-down process.
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https://tel.archives-ouvertes.fr/tel-00271943
Contributor : Mattia Romani <>
Submitted on : Thursday, April 10, 2008 - 3:58:19 PM
Last modification on : Thursday, January 3, 2019 - 4:30:08 PM
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Mattia Romani. Spin-up and spin-down in linearly stratified fluid over flat bottom. Ocean, Atmosphere. Université Joseph-Fourier - Grenoble I, 2008. English. ⟨tel-00271943⟩

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