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Helicity in the Ekman boundary 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.
2014 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 755, 654-671 p.Article in journal (Refereed) Published
Abstract [en]

Helicity, which is defined as the scalar product of velocity and vorticity, H = u . omega, is an inviscidly conserved quantity in a barotropic fluid. Mean helicity is zero in flows that are parity invariant. System rotation breaks parity invariance and has therefore the potential of giving rise to non-zero mean helicity. In this paper we study the helicity dynamics in the incompressible Ekman boundary layer. Evolution equations for the mean field helicity and the mean turbulent helicity are derived and it is shown that pressure flux injects helicity at a rate 2 Omega G(2) over the total depth of the Ekman layer, where G is the geostrophic wind far from the wall and Omega = Omega e(y) is the rotation vector and e(y) is the wall-normal unit vector. Thus right-handed/left-handed helicity will be injected if Omega is positive/negative. We also show that in the uppermost part of the boundary layer there is a net helicity injection with opposite sign as compared with the totally integrated injection. Isotropic relations for the helicity dissipation and the helicity spectrum are derived and it is shown that it is sufficient to measure two transverse velocity components and use Taylor's hypothesis in the mean flow direction in order to measure the isotropic helicity spectrum. We compare the theoretical predictions with a direct numerical simulation of an Ekman boundary layer and confirm that there is a preference for right-handed helicity in the lower part of the Ekman layer and left-handed helicity in the uppermost part when Omega > 0. In the logarithmic range, the helicity dissipation conforms to isotropic relations. On the other hand, spectra show significant departures from isotropic conditions, suggesting that the Reynolds number considered in the study is not sufficiently large for isotropy to be valid in a wide range of scales. Our analytical and numerical results strongly suggest that there is a turbulent helicity cascade of right-handed helicity in the logarithmic range of the atmospheric boundary layer when Omega > 0, consistent with recent measurements by Koprov, Koprov, Ponomarev & Chkhetiani (Dokl. Phys., vol. 50, 2005, pp. 419-422). The isotropic relations which are derived may facilitate future measurements of the helicity spectrum in the atmospheric boundary layer as well as in controlled wind tunnel experiments.

Place, publisher, year, edition, pages
2014. Vol. 755, 654-671 p.
Keyword [en]
atmospheric flows, rotating turbulence, turbulence theory
National Category
Meteorology and Atmospheric Sciences
URN: urn:nbn:se:kth:diva-136944DOI: 10.1017/jfm.2014.307ISI: 000341128600034ScopusID: 2-s2.0-84930507567OAI: diva2:677547
Knut and Alice Wallenberg Foundation

QC 20140930

Available from: 2013-12-10 Created: 2013-12-10 Last updated: 2015-06-29Bibliographically 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.
Trita-MEK, ISSN 0348-467X ; 2013:21
National Category
Fluid Mechanics and Acoustics Meteorology and Atmospheric Sciences
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)

QC 20131210

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

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