Exact coherent structures in stably-stratified plane Couette flow

Daniel Olvera Cabrera, Richard Kerswell

Research output: Contribution to journalArticle (Academic Journal)peer-review

6 Citations (Scopus)
199 Downloads (Pure)

Abstract

The existence of exact coherent structures in stably-stratified plane Couette
ow (gravity perpendicular to the plates) is investigated over Reynolds-Richardson number (Re-Rib) space for a fluid of unit Prandtl number (Pr = 1) using a combination of numerical and asymptotic techniques. Two states are repeatedly discovered using edge-tracking - EQ7 and EQ7-1 in the nomenclature of Gibson & Brand (2014) - and found to connect with 2-dimensional convective roll solutions when tracked to negative Rib (the Rayleigh-Benard problem with shear). Both these states and Nagata's (1990) original exact solution feel the presence of stable stratification when Rib = O(Re-2) or equivalently when the Rayleigh number Ra := -RibRe2Pr = O(1). This is confirmed via a stratified extension of the Vortex-Wave-Interaction (VWI) theory of Hall & Sherwin (2010). If the stratification is increased further, EQ7 is found to progressively spanwise and cross-stream localise until a second regime is entered at Rib = O(Re-2/3). This corresponds to a stratified version of the Boundary Reduced Equation (BRE) regime of Deguchi, Hall & Walton (2013). Increasing the stratification further, appears to lead to a third, ultimate regime where Rib = O(1) in which the flow fully localises in all three directions at the minimal Kolmogorov scale which then corresponds to the Osmidov scale. Implications for the laminar-turbulent boundary in the (Re-Rib) plane are briefly discussed.
Original languageEnglish
Pages (from-to)583-614
Number of pages32
JournalJournal of Fluid Mechanics
Volume826
Early online date8 Aug 2017
DOIs
Publication statusPublished - 10 Sep 2017

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