Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
The route to dissipation in strongly stratified and rotating flows
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
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.

Place, publisher, year, edition, pages
2013. Vol. 720, 66-103 p.
Keyword [en]
geostrophic turbulence, rotating turbulence, stratified turbulence
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-98801DOI: 10.1017/jfm.2012.611ISI: 000315456800004Scopus ID: 2-s2.0-84875023330OAI: oai:DiVA.org:kth-98801DiVA: diva2:539108
Note

QC 20130403. Updated from submitted to published.

Available from: 2012-07-03 Created: 2012-07-03 Last updated: 2017-12-07Bibliographically approved
In thesis
1. Numerical Investigation of Rotating and Stratified Turbulence
Open this publication in new window or tab >>Numerical Investigation of Rotating and Stratified Turbulence
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
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:nbn:se:kth:diva-98683 (URN)978-91-7501-415-9 (ISBN)
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
2. 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

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Deusebio, EnricoVallgren, AndreasLindborg, Erik
By organisation
MechanicsLinné Flow Center, FLOW
In the same journal
Journal of Fluid Mechanics
Mechanical Engineering

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 95 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf