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Response of a stratified boundary layer on a tilted wall to surface undulations

  • Pierre-Yves Passaggia (a1) (a2), Patrice Meunier (a1) and Stéphane Le Dizès (a1)

Abstract

The structure of a stratified boundary layer over a tilted bottom with a small streamwise undulation is studied theoretically and numerically. We show that the tilt of the boundary can induce strong density variations and wall-transverse velocities in the critical layer when the frequency of the forcing by the topography $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}kU(z_c)$ is equal to the transverse Brunt–Väisälä frequency $N \sin \alpha $ ( $N$ being the vertical Brunt–Väisälä frequency). The viscous solution in the critical layer, obtained and compared with direct numerical simulation results, is in good agreement for both the scaling and the spatial structure. The amplitude of the transverse velocity response is also shown to exhibit quasi-resonance peaks when the stratification strength is varied.

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Corresponding author

Email address for correspondence: meunier@irphe.univ-mrs.fr

References

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Response of a stratified boundary layer on a tilted wall to surface undulations

  • Pierre-Yves Passaggia (a1) (a2), Patrice Meunier (a1) and Stéphane Le Dizès (a1)

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