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A numerical study of the unstratified and stratified Ekman layer

Published online by Cambridge University Press:  26 August 2014

Enrico Deusebio ,
G. Brethouwer ,
P. Schlatter  and
E. Lindborg
Enrico Deusebio*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Cambridge CB3 0WA, UK Linné Flow Centre, Department of Mechanics, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
G. Brethouwer
Affiliation:
Linné Flow Centre, Department of Mechanics, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
P. Schlatter
Affiliation:
Linné Flow Centre, Department of Mechanics, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
E. Lindborg
Affiliation:
Linné Flow Centre, Department of Mechanics, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

We study the turbulent Ekman layer at moderately high Reynolds number, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}1600 < \mathit{Re} = \delta _{E}G/\nu < 3000$, using direct numerical simulations (DNS). Here, $\delta _{E} = \sqrt{2\nu /f}$ is the laminar Ekman layer thickness, $G$ the geostrophic wind, $\nu $ the kinematic viscosity and $f$ is the Coriolis parameter. We present results for both neutrally, moderately and strongly stably stratified conditions. For unstratified cases, large-scale roll-like structures extending from the outer region down to the wall are observed. These structures have a clear dominant frequency and could be related to periodic oscillations or instabilities developing near the low-level jet. We discuss the effect of stratification and $\mathit{Re}$ on one-point and two-point statistics. In the strongly stratified Ekman layer we observe stable co-existing large-scale laminar and turbulent patches appearing in the form of inclined bands, similar to other wall-bounded flows. For weaker stratification, continuously sustained turbulence strongly affected by buoyancy is produced. We discuss the scaling of turbulent length scales, height of the Ekman layer, friction velocity, veering angle at the wall and heat flux. The boundary-layer thickness, the friction velocity and the veering angle depend on $Lf/u_\tau $, where $u_\tau $ is the friction velocity and $L$ the Obukhov length scale, whereas the heat fluxes appear to scale with $L^+=L u_\tau /\nu $.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 755 , 25 September 2014 , pp. 672 - 704
Copyright
© 2014 Cambridge University Press 

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