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Transient Growth in Rayleigh-Bénard-Poiseuille/Couette flows

Abstract : OPTIMAL GROWTH MECHANISMS IN WALL-BOUNDED SHEAR FLOWS, IN PARTICULAR, PLANE COUETTE AND PLANE POISEUILLE FLOW, WITH AND WITHOUT A DESTABILIZING WALL-NORMAL TEMPERATURE GRADIENT ARE STUDIED EXTENSIVELY. IN THE CASE WITH A CROSS-STREAM TEMPERATURE GRADIENT IN A BOUSSINESQ FLUID, A COMPREHENSIVE NON-MODAL STABILITY ANALYSIS IS PERFORMED OVER VARIOUS REYNOLDS, RAYLEIGH AND PRANDTL NUMBERS. THE SCALING LAWS PERTAINING TO TRANSIENT GROWTH IN PURE SHEAR FLOWS ARE SHOWN TO HOLD EVEN IN THE PRESENCE OF A DESTABILIZING TEMPERATURE GRADIENT. THE LIFT-UP EFFECT REMAINS THE PREDOMINANT TRANSIENT GROWTH MECHANISM. THE CLASSICAL INVISCID LIFT-UP MECHANISM CHARACTERIZES THE SHORT-TIME BEHAVIOR WHEREAS THE RAYLEIGH-BÉNARD EIGENMODE WITHOUT ITS STREAMWISE VELOCITY COMPONENT CHARACTERIZES THE LONG-TIME BEHAVIOR. THE SQUIRE TRANSFORMATION IS EXTENDED TO PROVIDE NEW INSIGHTS ON THE OPTIMAL GROWTH OF ARBITRARY 3D DISTURBANCES IN PARALLEL SHEAR FLOWS BOUNDED IN THE CROSS-STREAM DIRECTION. IT ALSO PERMITS TO DEMONSTRATE THAT THE LONG-TIME OPTIMAL GROWTH FOR PERTURBATIONS OF ARBITRARY WAVENUMBERS MAY BE DECOMPOSED AS A PRODUCT OF THE RESPECTIVE GAINS ARISING FROM THE 2D ORR-MECHANISM AND THE LIFT-UP MECHANISM. THIS ASYMPTOTIC SOLUTION IS SHOWN TO DESCRIBE THE LONG-TIME AND EVEN THE INTERMEDIATE-TIME DYNAMICS OF THE OPTIMAL DISTURBANCES AND PROVIDES A GOOD ESTIMATE OF THE MAXIMUM OPTIMAL GAIN AT ALL TIME.
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https://pastel.archives-ouvertes.fr/pastel-00680236
Contributor : John Soundar Jerome J. <>
Submitted on : Thursday, March 29, 2012 - 3:51:36 PM
Last modification on : Wednesday, March 27, 2019 - 4:39:25 PM
Long-term archiving on: : Saturday, June 30, 2012 - 2:20:48 AM

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  • HAL Id : pastel-00680236, version 1

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J. John Soundar Jerome. Transient Growth in Rayleigh-Bénard-Poiseuille/Couette flows. Fluids mechanics [physics.class-ph]. Ecole Polytechnique X, 2011. English. ⟨pastel-00680236⟩

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