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A numerical study of the unstratified and stratified Ekman layer
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Centre for Mathematical Sciences, Cambridge, England.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-9819-2906
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-9627-5903
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
2014 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 755, 672-704 p.Article in journal (Refereed) Published
Abstract [en]

We study the turbulent Ekman layer at moderately high Reynolds number, 1600 < Re = delta(E)G/v < 3000, using direct numerical simulations (DNS). Here, delta(E) = root 2v/f is the laminar Ekman layer thickness, G the geostrophic wind, v 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 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+ = Lu-tau/v.

Place, publisher, year, edition, pages
2014. Vol. 755, 672-704 p.
Keyword [en]
atmospheric flows, turbulent boundary layers, turbulent flows
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-136943DOI: 10.1017/jfm.2014.318ISI: 000341128600035Scopus ID: 2-s2.0-84930503927OAI: oai:DiVA.org:kth-136943DiVA: diva2:677546
Funder
Knut and Alice Wallenberg Foundation
Note

QC 20140930

Available from: 2013-12-10 Created: 2013-12-10 Last updated: 2017-12-06Bibliographically approved
In thesis
1. Numerical studies in rotating and stratified turbulence
Open this publication in new window or tab >>Numerical studies in rotating and stratified turbulence
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Although turbulence has been studied for more than five hundred years, a thorough understanding of turbulent flows is still missing. Nowadays computing power can offer an alternative tool, besides measurements and experiments, to give some insights into turbulent dynamics. In this thesis, numerical simulations are employed to study homogeneous and wall-bounded turbulence in rotating and stably stratified conditions, as encountered in geophysical flows where the rotation of the Earth as well as the vertical density variation influence the dynamics.

In the context of homogeneous turbulence, we investigate how the transfer of energy among scales is affected by the presence of strong but finite rotation and stratification. Unlike geostrophic turbulence, we show that there is a forward energy cascade towards small scales which is initiated at the forcing scales. The contribution of this process to the general dynamic is secondary at large scales but becomes dominant at smaller scales where it leads to a shallowing of the energy spectrum, from k-3 to k-5/3. Two-point statistics show a good agreement with measurements in the atmosphere, suggesting that this process is an important mechanism for energy transfer in the atmosphere.

Boundary layers subjected to system rotation around the wall-normal axis are usually referred to as Ekman layers and they can be seen as a model of the atmospheric and oceanic boundary layers developing at mid and high latitudes. We study the turbulent dynamics in Ekman layers by means of numerical simulations, focusing on the turbulent structures developing at moderately high Reynolds numbers. For neutrally stratified conditions, we show that there exists a turbulent helicity cascade in the logarithmic region. We focus on the effect of a stable stratification produced by a vertical positive temperature gradient. For moderate stratification, continuously turbulent regimes are produced which are in fair agreement with existing theories and models used in the context of atmospheric boundary layer dynamics. For larger degree of stratification, we show that laminar and turbulent motions coexist and displace along inclined patterns similar to what has been recently observed in other transitional flows.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. xi, 54 p.
Series
Trita-MEK, ISSN 0348-467X ; 2013:21
National Category
Fluid Mechanics and Acoustics Meteorology and Atmospheric Sciences
Identifiers
urn:nbn:se:kth:diva-136947 (URN)978-91-7501-961-1 (ISBN)
Public defence
2014-01-17, Kollegiesalen, Brinellvägen 8, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20131210

Available from: 2013-12-10 Created: 2013-12-10 Last updated: 2013-12-10Bibliographically approved

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Brethouwer, GeertSchlatter, Philipp

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