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A new method for isolating turbulent states in transitional stratified plane Couette flow

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Taylor, JR 
Deusebio, E 
Caulfield, CP 
Kerswell, RR 

Abstract

jats:pWe present a new adaptive control strategy to isolate and stabilize turbulent states in transitional, stably stratified plane Couette flow in which the gravitational acceleration (non-dimensionalized as the bulk Richardson numberjats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112016006273_inline1" />jats:tex-mathRi</jats:tex-math></jats:alternatives></jats:inline-formula>) is adjusted in time to maintain the turbulent kinetic energy (TKE) of the flow. We demonstrate that applying this method at various stages of decaying stratified turbulence halts the decay process and allows a succession of intermediate turbulent states of decreasing energy to be isolated and stabilized. Once the energy of the initial flow becomes small enough, we identify a single minimal turbulent spot, and lower-energy states decay to laminar flow. Interestingly, the turbulent states which emerge from this process have very similar time-averagedjats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112016006273_inline2" />jats:tex-mathRi</jats:tex-math></jats:alternatives></jats:inline-formula>, but TKE levels different by an order of magnitude. The more energetic states consist of several turbulent spots, each qualitatively similar to the minimal turbulent spot. This suggests that the minimal turbulent spot may well be the lowest-energy turbulent state which forms a basic building block of stratified plane Couette flow. The fact that a minimal spot of turbulence can be stabilized, so that it neither decays nor grows, opens up exciting opportunities for further study of spatiotemporally intermittent stratified turbulence.</jats:p>

Description

Keywords

stratified flows, stratified turbulence, transition to turbulence

Journal Title

Journal of Fluid Mechanics

Conference Name

Journal ISSN

0022-1120
1469-7645

Volume Title

808

Publisher

Cambridge University Press (CUP)
Sponsorship
Engineering and Physical Sciences Research Council (EP/K034529/1)
The EPSRC grant EP/K034529/1 entitled ‘Mathematical Underpinnings of Stratified Turbulence’ is gratefully acknowledged for supporting the research presented here.
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