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Numerical studies in rotating and stratified turbulence
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
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: urn:nbn:se:kth:diva-136947ISBN: 978-91-7501-961-1 (print)OAI: oai:DiVA.org:kth-136947DiVA: diva2:677554
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
List of papers
1. Possible Explanation of the Atmospheric Kinetic and Potential Energy Spectra
Open this publication in new window or tab >>Possible Explanation of the Atmospheric Kinetic and Potential Energy Spectra
2011 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 107, no 26, 268501- p.Article in journal (Refereed) Published
Abstract [en]

We hypothesize that the observed wave number spectra of kinetic and potential energy in the atmosphere can be explained by assuming that there are two related cascade processes emanating from the same large-scale energy source, a downscale cascade of potential enstrophy, giving rise to the k(-3) spectrum at synoptic scales and a downscale energy cascade giving rise to the k(-5/3) spectrum at mesoscales. The amount of energy which is going into the downscale energy cascade is determined by the rate of system rotation, with negligible energy going downscale in the limit of very fast rotation. We present a set of simulations of a system with strong rotation and stratification, supporting these hypotheses and showing good agreement with observations.

National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-63245 (URN)10.1103/PhysRevLett.107.268501 (DOI)000298607400011 ()2-s2.0-84455205259 (Scopus ID)
Note
QC 20120127Available from: 2012-01-27 Created: 2012-01-23 Last updated: 2017-12-08Bibliographically approved
2. The route to dissipation in strongly stratified and rotating flows
Open this publication in new window or tab >>The route to dissipation in strongly stratified and rotating flows
2013 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 720, 66-103 p.Article in journal (Refereed) Published
Abstract [en]

We investigate the route to dissipation in strongly stratified and rotating systems through high-resolution numerical simulations of the Boussinesq equations (BQs) and the primitive equations (PEs) in a triply periodic domain forced at large scales. By applying geostrophic scaling to the BQs and using the same horizontal length scale in defining the Rossby and the Froude numbers, R0 and Fr, we show that the PEs can be obtained from the BQs by taking the limit Fr-2/R0(2)-> 0. When Fr-2/R0(2) is small the difference between the results from the BQ and the PE simulations is shown to be small. For large rotation rates, quasi-geostrophic dynamics are recovered with a forward enstrophy cascade and an inverse energy cascade. As the rotation rate is reduced, a fraction of the energy starts to cascade towards smaller scales, leading to a shallowing of the horizontal spectra from k(h)(-3) to k(h)(-5/3) h at the small-scale end. The vertical spectra show a similar transition as the horizontal spectra and we find that Charney isotropy is approximately valid also at larger wavenumbers than the transition wavenumber. The high resolutions employed allow us to capture both ranges within the same simulation. At the transition scale, kinetic energy in the rotational and in the horizontally divergent modes attain comparable values. The divergent energy is several orders of magnitude larger than the quasi-geostrophic divergent energy given by the Omega-equation. The amount of energy cascading downscale is mainly controlled by the rotation rate, with a weaker dependence on the stratification. A larger degree of stratification favours a downscale energy cascade. For intermediate degrees of rotation and stratification, a constant energy flux and a constant enstrophy flux coexist within the same range of scales. In this range, the enstrophy flux is a result of triad interactions involving three geostrophic modes, while the energy flux is a result of triad interactions involving at least one ageostrophic mode, with a dominant contribution from interactions involving two ageostrophic and one geostrophic mode. Dividing the ageostrophic motions into two classes depending on the sign of the linear wave frequency, we show that the energy transfer is for the largest part supported by interactions within the same class, ruling out the wave-wave-vortex resonant triad interaction as a mean of the downscale energy transfer. The role of inertia-gravity waves is studied through analyses of time-frequency spectra of single Fourier modes. At large scales, distinct peaks at frequencies predicted for linear waves are observed, whereas at small scales no clear wave activity is observed. Triad interactions show a behaviour which is consistent with turbulent dynamics, with a large exchange of energy in triads with one small and two large comparable wavenumbers. The exchange of energy is mainly between the modes with two comparable wavenumbers.

Keyword
geostrophic turbulence, rotating turbulence, stratified turbulence
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-98801 (URN)10.1017/jfm.2012.611 (DOI)000315456800004 ()2-s2.0-84875023330 (Scopus ID)
Note

QC 20130403. Updated from submitted to published.

Available from: 2012-07-03 Created: 2012-07-03 Last updated: 2017-12-07Bibliographically approved
3. Third order structure function in rotating and stratified turbulence: analytical and numerical results compared with data from the stratosphere
Open this publication in new window or tab >>Third order structure function in rotating and stratified turbulence: analytical and numerical results compared with data from the stratosphere
(English)Manuscript (preprint) (Other academic)
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-136941 (URN)
Note

QS 2013

Available from: 2013-12-10 Created: 2013-12-10 Last updated: 2013-12-10Bibliographically approved
4. Dimensional transition in rotating turbulence
Open this publication in new window or tab >>Dimensional transition in rotating turbulence
2014 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 90, no 2Article in journal (Refereed) Published
Abstract [en]

In this work we investigate, by means of direct numerical hyperviscous simulations, how rotation affects the bidimensionalization of a turbulent flow. We study a thin layer of fluid, forced by a two-dimensional forcing, within the framework of the "split cascade" in which the injected energy flows both to small scales (generating the direct cascade) and to large scale (to form the inverse cascade). It is shown that rotation reinforces the inverse cascade at the expense of the direct one, thus promoting bidimensionalization of the flow. This is achieved by a suppression of the enstrophy production at large scales. Nonetheless, we find that, in the range of rotation rates investigated, increasing the vertical size of the computational domain causes a reduction of the flux of the inverse cascade. Our results suggest that, even in rotating flows, the inverse cascade may eventually disappear when the vertical scale is sufficiently large with respect to the forcing scale. We also study how the split cascade and confinement influence the breaking of symmetry induced by rotation.

Keyword
velocity structure functions, intermediate rossby number, 3-dimensional turbulence, 2-dimensional turbulence, isotropic turbulence, upper troposphere, wave turbulence, energy, transfers, confinement
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-136942 (URN)10.1103/PhysRevE.90.023005 (DOI)000341113400008 ()
Note

QC 20141007. Updated from manuscript to article in journal.

Available from: 2013-12-10 Created: 2013-12-10 Last updated: 2017-12-06Bibliographically approved
5. A numerical study of the unstratified and stratified Ekman layer
Open this publication in new window or tab >>A numerical study of the unstratified and stratified Ekman layer
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.

Keyword
atmospheric flows, turbulent boundary layers, turbulent flows
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-136943 (URN)10.1017/jfm.2014.318 (DOI)000341128600035 ()2-s2.0-84930503927 (Scopus ID)
Funder
Knut and Alice Wallenberg Foundation
Note

QC 20140930

Available from: 2013-12-10 Created: 2013-12-10 Last updated: 2017-12-06Bibliographically approved
6. Helicity in the Ekman boundary layer
Open this publication in new window or tab >>Helicity in the Ekman boundary layer
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.

Keyword
atmospheric flows, rotating turbulence, turbulence theory
National Category
Meteorology and Atmospheric Sciences
Identifiers
urn:nbn:se:kth:diva-136944 (URN)10.1017/jfm.2014.307 (DOI)000341128600034 ()2-s2.0-84930507567 (Scopus ID)
Funder
Knut and Alice Wallenberg Foundation
Note

QC 20140930

Available from: 2013-12-10 Created: 2013-12-10 Last updated: 2017-12-06Bibliographically approved
7. The open-channel version of SIMSON
Open this publication in new window or tab >>The open-channel version of SIMSON
2010 (English)Report (Other academic)
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-98802 (URN)
Note
QC 20120703Available from: 2012-07-03 Created: 2012-07-03 Last updated: 2013-12-10Bibliographically approved

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