Transient growth in Rayleigh-B\'enard-Poiseuille/Couette convection
| Autor: | Jerome, J. John Soundar, Chomaz, Jean-Marc, Huerre, Patrick |
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| Rok vydání: | 2016 |
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| Zdroj: | Physics of Fluids 24, 044103 (2012) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/1.4704642 |
| Popis: | An investigation of the effect of a destabilizing cross-stream temperature gradient on the transient growth phenomenon of plane Poiseuille flow and plane Couette flow is presented. Only the streamwise-uniform and nearly streamwise-uniform disturbances are highly influenced by the Rayleigh number Ra and Prandtl number Pr. The maximum optimal transient growth G max of streamwise-uniform disturbances increases slowly with increasing Ra and decreasing Pr. For all Ra and Pr, at moderately large Reynolds numbersRe, the supremum of G max is always attained for streamwise-uniform perturbations (or nearly streamwise-uniform perturbations, in the case of plane Couette flow) which produce large streamwise streaks and Rayleigh-B\'enard convection rolls (RB). The optimal growth curves retain the same large-Reynolds-number scaling as in pure shear flow. A 3D vector model of the governing equations demonstrates that the short-time behavior is governed by the classical lift-up mechanism and that the influence of Ra on this mechanism is secondary and negligible. The optimal input for the largest long-time response is given by the adjoint of the dominant eigenmode with respect to the energy scalar product: the RBeigenmode without its streamwise velocity component. These short-time and long-time responses depict, to leading order, the optimal transient growth G(t). At moderately large Ra (or small Pr at a fixed Ra), the dominant adjoint mode is a good approximation to the optimal initial condition for all time. Over a general class of norms that can be considered as growth functions, the results remain qualitatively similar, for example, the dominant adjoint eigenmode still approximates the maximum optimal response. Comment: accepted for publication (Mar. 2012) |
| Databáze: | arXiv |
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