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Numerical Investigation of Rotating and Stratified Turbulence
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
2012 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Atmospheric and oceanic flows are strongly affected by rotation and stratification. Rotation is exerted through Coriolis forces which mainly act in horizontal planes whereas stratification largely affects the motion along the vertical direction through buoyancy forces, the latters related to the vertical variation of the fluid density. Aiming at a better understanding of atmospheric and oceanic processes, in this thesis the properties of turbulence in rotating and stably stratified flows are studied by means of numerical simulations, with and without the presence of solid walls.                                                                                                                                                                                           A new code is developed in order to carry out high-resolution numerical simulations of geostrophic turbulence forced at large scales. The code was heavily parallelized with MPI (Message Passing Interface) in order to be run on massively parallel computers. The main problem which has been investigated is how the turbulent cascade is affected by the presence of strong but finite rotation and stratification. As opposed to the early theories in the field of geostrophic turbulence, we show that there is a forward energy cascade which is initiated at large scales. The contribution of this process to the general dynamic is secondary at large scales but becomes dominant at smaller scales where leads to a shallowing of the energy spectrum. Despite the idealized set-up of the simulations, two-point statistics show remarkable agreement with measurements in the atmosphere, suggesting that this process may be an important mechanism for energy transfer in the atmosphere.                                                                                                                                                                                                                                                                               The effect of stratification in wall-bounded turbulence is investigated by means of direct numerical simulations of open-channel flows. An existing full-channel code was modified in order to optimize the grid in the vertical direction and avoid the clustering of grid points at the upper boundary, where the solid wall is replaced by a free-shear condition. The stable stratification which results from a cooling applied at the solid wall largely affects the outer structures of the boundary layer, whereas the near-wall structures appear to be mostly unchanged. The effect of gravity waves is also studied, and a new decomposition is introduced in order to separate the gravity wave field from the turbulent field.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. , v, 34 p.
Series
TRITA-MEK, ISSN 0348-467X ; 12/14
Keyword [en]
Geostrophic turbulence, stable stratification, rotation, wall-bounded turbulence, gravity waves, atmospherical dynamics, direct numertical simulations
National Category
Mechanical Engineering
Research subject
SRA - E-Science (SeRC)
Identifiers
URN: urn:nbn:se:kth:diva-98683ISBN: 978-91-7501-415-9 (print)OAI: oai:DiVA.org:kth-98683DiVA: diva2:538489
Presentation
2012-06-15, Seminarierrummet, KTH, Brinellvägen 32, Stockholm, 10:00
Opponent
Supervisors
Funder
Swedish Research CouncilSwedish e‐Science Research Center
Note

QC 20120703

Available from: 2012-07-03 Created: 2012-06-29 Last updated: 2015-03-04Bibliographically 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. Direct numerical simulations of stratified open channel flows
Open this publication in new window or tab >>Direct numerical simulations of stratified open channel flows
2011 (English)In: 13th European Turbulence Conference (ETC13): Wall-Bounded Flows And Control Of Turbulence, 2011, 022009- p.Conference paper, Published paper (Refereed)
Abstract [en]

We carry out numerical simulations of wall-bounded stably stratified flows. We mainly focus on how stratification affects the near-wall turbulence at moderate Reynolds numbers, i.e. Re-tau = 360. A set of fully-resolved open channel flow simulations is performed, where a stable stratification has been introduced through a negative heat flux at the lower wall. In agreement with previous studies, it is found that turbulence cannot be sustained for h/L values higher than 1.2, where L is the so-called Monin-Obukhov length and h is the height of the open channel. For smaller values, buoyancy does not re-laminarize the flow, but nevertheless affects the wall turbulence. Near-wall streaks are weakly affected by stratification, whereas the outer modes are increasingly damped as we move away from the wall. A decomposition of the wall-normal velocity is proposed in order to separate the gravity wave and turbulent flow fields. This method has been tested both for open channel and full channel flows. Gravity waves are likely to develop and to dominate close to the upper boundary (centerline for full channel). However, their intensity is weaker in the open channel, possibly due to the upper boundary condition. Moreover, the presence of internal gravity waves can also be deduced from a correlation analysis, which reveals (together with spanwise spectra) a narrowing of the outer structures as the stratification is increased.

Series
Journal of Physics Conference Series, ISSN 1742-6588 ; 318
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-93030 (URN)10.1088/1742-6596/318/2/022009 (DOI)000301292300009 ()2-s2.0-84856351989 (Scopus ID)
Conference
13th European Turbulence Conference (ETC) SEP 12-15, 2011 Warsaw, Poland
Note
QC 20120410Available from: 2012-04-10 Created: 2012-04-10 Last updated: 2012-07-03Bibliographically approved
4. 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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