Abstract
The existence of exact coherent structures in stably stratified plane Couette flow (gravity perpendicular to the plates) is investigated over Reynolds-Richardson number (Re-Rib) space for a fluid of unit Prandtl number .Pr D 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 (J. Fluid Mech., vol. 745, 2014, pp. 25-61)-and found to connect with two-dimensional convective roll solutions when tracked to negative Rib (the Rayleigh-Bénard problem with shear). Both these states and Nagata's (J. Fluid Mech., vol. 217, 1990, pp. 519-527) original exact solution feel the presence of stable stratification when Rib DO.Re..2/or equivalently when the Rayleigh number Ra VD ..RibRe2Pr D O.1/. This is confirmed via a stratified extension of the vortex wave interaction theory of Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178-205). If the stratification is increased further, EQ7 is found to progressively spanwise and cross-stream localise until a second regime is entered at Rib D O.Re..2=3/. This corresponds to a stratified version of the boundary region equations regime of Deguchi, Hall & Walton (J. Fluid Mech., vol. 721, 2013, pp. 58-85). Increasing the stratification further appears to lead to a third, ultimate regime where Rib D 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 language | English |
|---|---|
| Pages (from-to) | 583-614 |
| Number of pages | 32 |
| Journal | Journal of Fluid Mechanics |
| Volume | 826 |
| Early online date | 8 Aug 2017 |
| DOIs | |
| Publication status | Published - 10 Sep 2017 |
Fingerprint
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
Cite this
Exact coherent structures in stably stratified plane Couette flow. / Olvera, D.; Kerswell, R. R.
In: Journal of Fluid Mechanics, Vol. 826, 10.09.2017, p. 583-614.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Exact coherent structures in stably stratified plane Couette flow
AU - Olvera, D.
AU - Kerswell, R. R.
PY - 2017/9/10
Y1 - 2017/9/10
N2 - The existence of exact coherent structures in stably stratified plane Couette flow (gravity perpendicular to the plates) is investigated over Reynolds-Richardson number (Re-Rib) space for a fluid of unit Prandtl number .Pr D 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 (J. Fluid Mech., vol. 745, 2014, pp. 25-61)-and found to connect with two-dimensional convective roll solutions when tracked to negative Rib (the Rayleigh-Bénard problem with shear). Both these states and Nagata's (J. Fluid Mech., vol. 217, 1990, pp. 519-527) original exact solution feel the presence of stable stratification when Rib DO.Re..2/or equivalently when the Rayleigh number Ra VD ..RibRe2Pr D O.1/. This is confirmed via a stratified extension of the vortex wave interaction theory of Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178-205). If the stratification is increased further, EQ7 is found to progressively spanwise and cross-stream localise until a second regime is entered at Rib D O.Re..2=3/. This corresponds to a stratified version of the boundary region equations regime of Deguchi, Hall & Walton (J. Fluid Mech., vol. 721, 2013, pp. 58-85). Increasing the stratification further appears to lead to a third, ultimate regime where Rib D 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.
AB - The existence of exact coherent structures in stably stratified plane Couette flow (gravity perpendicular to the plates) is investigated over Reynolds-Richardson number (Re-Rib) space for a fluid of unit Prandtl number .Pr D 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 (J. Fluid Mech., vol. 745, 2014, pp. 25-61)-and found to connect with two-dimensional convective roll solutions when tracked to negative Rib (the Rayleigh-Bénard problem with shear). Both these states and Nagata's (J. Fluid Mech., vol. 217, 1990, pp. 519-527) original exact solution feel the presence of stable stratification when Rib DO.Re..2/or equivalently when the Rayleigh number Ra VD ..RibRe2Pr D O.1/. This is confirmed via a stratified extension of the vortex wave interaction theory of Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178-205). If the stratification is increased further, EQ7 is found to progressively spanwise and cross-stream localise until a second regime is entered at Rib D O.Re..2=3/. This corresponds to a stratified version of the boundary region equations regime of Deguchi, Hall & Walton (J. Fluid Mech., vol. 721, 2013, pp. 58-85). Increasing the stratification further appears to lead to a third, ultimate regime where Rib D 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.
UR - http://www.scopus.com/inward/record.url?scp=85020017776&partnerID=8YFLogxK
U2 - 10.1017/jfm.2017.447
DO - 10.1017/jfm.2017.447
M3 - Article
VL - 826
SP - 583
EP - 614
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
ER -