The stability of stratified spatially periodic shear flows at low Péclet number
- Department of Applied Mathematics and Statistics, Baskin School of Engineering, University of California at Santa Cruz, 1156 High Street, Santa Cruz, California 95064 (United States)
- Service de Physique de l’Etat Condensé, DSM/IRAMIS, CNRS UMR 3680, CEA Saclay, 91191 Gif-sur-Yvette cedex (France)
- Division of Geological and Planetary Sciences, California Institute of Technology, Mail Code 170-25, 1200 E. California Blvd., Pasadena, California 91125 (United States)
This work addresses the question of the stability of stratified, spatially periodic shear flows at low Péclet number but high Reynolds number. This little-studied limit is motivated by astrophysical systems, where the Prandtl number is often very small. Furthermore, it can be studied using a reduced set of “low-Péclet-number equations” proposed by Lignières [“The small-Péclet-number approximation in stellar radiative zones,” Astron. Astrophys. 348, 933–939 (1999)]. Through a linear stability analysis, we first determine the conditions for instability to infinitesimal perturbations. We formally extend Squire’s theorem to the low-Péclet-number equations, which shows that the first unstable mode is always two-dimensional. We then perform an energy stability analysis of the low-Péclet-number equations and prove that for a given value of the Reynolds number, above a critical strength of the stratification, any smooth periodic shear flow is stable to perturbations of arbitrary amplitude. In that parameter regime, the flow can only be laminar and turbulent mixing does not take place. Finding that the conditions for linear and energy stability are different, we thus identify a region in parameter space where finite-amplitude instabilities could exist. Using direct numerical simulations, we indeed find that the system is subject to such finite-amplitude instabilities. We determine numerically how far into the linearly stable region of parameter space turbulence can be sustained.
- OSTI ID:
- 22482473
- Journal Information:
- Physics of Fluids (1994), Vol. 27, Issue 8; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-6631
- Country of Publication:
- United States
- Language:
- English
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