Frozen waves in turbulent mixing layers

Benoît-Joseph Gréa and Antoine Briard
Phys. Rev. Fluids 4, 064608 – Published 13 June 2019
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Abstract

Strong time-periodic accelerations applied tangentially to an infinite horizontal plane layer between two miscible fluids trigger a parametric instability leading to remarkable sawtooth patterns known as frozen waves. The resulting turbulent mixing zones grow in time and then saturate when the resonance conditions of internal gravity waves are no longer fulfilled. The Floquet analysis of a model equation and direct numerical simulations reveal that the final mixing zone sizes evolve as the square of the forcing amplitude while, by contrast, the horizontal wavelengths grow nearly linearly. This explains why frozen waves sharpen with increasingly intense horizontal oscillations. It also suggests that a horizontal forcing mixes more efficiently fluids than a vertical one at large forcing accelerations.

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  • Received 11 February 2019

DOI:https://doi.org/10.1103/PhysRevFluids.4.064608

©2019 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Benoît-Joseph Gréa

  • CEA, DAM, DIF, F-91297 Arpajon, France

Antoine Briard

  • Centre de Mathématiques et de Leurs Applications, CNRS, ENS Paris-Saclay, Université Paris-Saclay, 94235, Cachan Cedex, France

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Issue

Vol. 4, Iss. 6 — June 2019

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