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Article Dans Une Revue Journal of Fluid Mechanics Année : 2011

Frontal instabilities and waves in a differentially rotating fluid

Résumé

We present an experimental investigation of the stability of a baroclinic front in a rotating two-layer salt-stratified fluid. A front is generated by the spin-up of a differentially rotating lid at the fluid surface. In the parameter space set by rotational Froude number, F, dissipation number, d (i.e. the ratio between disk rotation time and Ekman spin-down time) and flow Rossby number, a new instability is observed that occurs for Burger numbers larger than the critical Burger number for baroclinic instability. This instability has a much smaller wavelength than the baroclinic instability, and saturates at a relatively small amplitude. The experimental results for the instability regime and the phase speed show overall a reasonable agreement with the numerical results of Gula, Zeitlin & Plougonven (J. Fluid Mech., vol. 638, 2009, pp. 27-47), suggesting that this instability is the Rossby-Kelvin instability that is due to the resonance between Rossby and Kelvin waves. Comparison with the results of Williams, Haines & Read (J. Fluid Mech., vol. 528, 2005, pp. 1-22) and Hart (Geophys. Fluid Dyn., vol. 3, 1972, pp. 181-209) for immiscible fluid layers in a small experimental configuration shows continuity in stability regimes in (F, d) space, but the baroclinic instability occurs at a higher Burger number than predicted according to linear theory. Small-scale perturbations are observed in almost all regimes, either locally or globally. Their non-zero phase speed with respect to the mean flow, cusped-shaped appearance in the density field and the high values of the Richardson number for the observed wavelengths suggest that these perturbations are in many cases due to Hölmböe instability. © 2011 Cambridge University Press.
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Dates et versions

hal-01119144 , version 1 (23-02-2015)

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Jan-Bert Flór, Hélène Scolan, Jonathan Gula. Frontal instabilities and waves in a differentially rotating fluid. Journal of Fluid Mechanics, 2011, 685 (october), pp.532-542. ⟨10.1017/jfm.2011.338⟩. ⟨hal-01119144⟩
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