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
Shallow water wave turbulence
LEGI, Université Grenoble Alpes.ORCID iD: 0000-0001-9481-4459
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. (Erik Lindborg)ORCID iD: 0000-0002-2979-6327
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0002-1560-7855
2019 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 874, p. 1169-1196Article in journal (Refereed) Published
Abstract [en]

The dynamics of irrotational shallow water wave turbulence forced in large scales and dissipated at small scales is investigated. First, we derive the shallow water analogue of the `four-fifths law' of Kolmogorov turbulence for a third order structure function involving velocity and displacement increments. Using this relation and assuming that the flow is dominated by shocks we develop a simple model predicting that the shock amplitude scales as (ϵd)1/3, where ϵ is the mean dissipation rate and d the mean distance between the shocks, and that the pth order displacement and velocity structure functions scale as (ϵd)p/3r/d, where r is the separation. Then we carry out a series of forced simulations with resolutions up to 76802, varying the Froude number, Ff=ϵ1/3/ckf1/3, where kf is the forcing wave number and c is the wave speed. In all simulations a stationary state is reached in which there is a constant spectral energy flux and equipartition between kinetic and potential energy in the constant flux range. The third order structure function relation is satisfied with a high degree of accuracy. Mean energy is found to scale as E∼√(ϵc/kf), and is also dependent on resolution, indicating that shallow water wave turbulence does not fit into the paradigm of a Richardson-Kolmogorov cascade. In all simulations shocks develop, displayed as long thin bands of negative divergence in flow visualisations. The mean distance between the shocks is found to scale as dFf1/2/kf. Structure functions of second and higher order are found to scale in good agreement with the model. We conclude that in the weak limit, Ff→0, shocks will become denser and weaker and finally disappear for a finite Reynolds number. On the other hand, for a given Ff, no matter how small, shocks will prevail if the Reynolds number is sufficiently large.

Place, publisher, year, edition, pages
Cambridge University Press, 2019. Vol. 874, p. 1169-1196
National Category
Fluid Mechanics and Acoustics
Research subject
Physics; Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-255057DOI: 10.1017/jfm.2019.375ISI: 000475481700001OAI: oai:DiVA.org:kth-255057DiVA, id: diva2:1337872
Funder
Swedish Research Council, 2013-5191
Note

QC 20190719

Available from: 2019-07-17 Created: 2019-07-17 Last updated: 2019-08-28Bibliographically approved
In thesis
1. Advancements in stratified flows through simulation, experiment and open research software development
Open this publication in new window or tab >>Advancements in stratified flows through simulation, experiment and open research software development
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Framsteg inom stratifierade strömningar genom simulering, experiment och utveckling av öppen mjukvara
Abstract [en]

Two studies of two-dimensional models of flows influenced by stratification and stratification/rotation are carried out in order to investigate whether a two-dimensional model can reproduce a downscale energy cascade with an associated k − 5/3 wavenumber spectrum. Firstly, a series of highly resolved numerical simulations of the classical shallow water model is carried out. A forward energy cascade is observed but the dynamics is dominated by shocks, with an associated k −2-spectrum. A theory for shallow water wave turbulence is formulated and compared to the results from the simulations. Secondly, a series of simulations of a new two-dimensional toy model is carried out, showing that the model is not generating shocks and can reproduce a downscale energy cascade with an associated k − 5/3 spectrum. The energy transfer is studied in detail in Fourier space and is compared with results from a general circulation model. An experimental study of strongly stratified turbulence at the Coriolis platform in Grenoble is carried out, with the aim of testing novel theories of stratified turbulence. Turbulence is generated by traversing an array of cylinders through a tank containing stratified salt water. Velocity is measured by Particle Image Velocimetry (PIV) and density is measured by conductivity probes. In particular, the author has developed the software system analysing the PIV images. Preliminary results from the experiment are presented. To realise the research objectives, a set of open-source software packages are developed in Python, under the umbrella of the FluidDyn project. The packages enable execution of simulations, experiments and processing of data. The codes are well documented, tested and designed to promote development and reuse.

Abstract [sv]

Två studier av tvådimensionella modeller av strömningar influerade av stratifiering respektive stratifiering och rotation genomförs, i syfte att undersöka huruvida en tvådimensionell modell kan reproducera en energikaskad till mindre skalor med ett associerat vågtalsspektrum av formen k−5/3. Först genomförs enserie högupplösta simuleringar av den klassiska modellen för strömningar i grunt vatten (shallow water model). En energikaskad till mindre skalor observeras,men strömningen domineras av stötar med ett associerat k−2-spektrum. Sedan genomförs en serie simuleringar av en ny tvådimensionell leksaksmodell, som visar att modellen kan reproducera en energikaskad till mindre skalor med ett associerat k−5/3-spektrum. Energiöverföringen studeras i detalj i Fourier-rummet och jämförs med resultat från en global cirkulationsmodell. En experimentell studie av starkt stratifierad turbulens genomförs vid Coriolisplattformen i Grenoble, med målet att testa nya teorier för stratifierad turbulens. Turbulensen genereras genom att traversera en rad cylindrar genom en tank innehållande stratifierat saltvatten. Hastighet mäts med Particle ImageVelocimetry (PIV) och densitet mäts med konduktivitetssonder. I synnerhet har författaren utvecklat den programvara som analyserar bilder från PIVmätningarna. Preliminära resultat från experimentet presenteras. För att realisera forskningsmålen utvecklas en mängd mjukvarupaket för öppet bruk i Python, i ett projekt med namnet FluidDyn. Paketen erbjuder möjligheter att utföra simuleringar, experiment och databehandling. Koderna är väl dokumenterade, testade och designade för att underlätta utveckling och återanvändning.

Place, publisher, year, edition, pages
Stockholm, Sweden: KTH Royal Institute of Technology, 2019. p. 65
Series
TRITA-SCI-FOU ; 2019:37
Keywords
geophysical flows, shallow water wave turbulence, energy cascade, stratified turbulence, waves and vortices, open source software, geofysikaliska strömningar, vågturbulens i grunt vatten, energi- kaskad, stratifierad turbulens, vågor och virvlar, öppen mjukvara
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-256564 (URN)978-91-7873-270-8 (ISBN)
Public defence
2019-09-27, F3, Lindstedtsvägen 26, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 2013-5191
Note

Available from: 2019-09-02 Created: 2019-08-28 Last updated: 2019-09-11Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Search in DiVA

By author/editor
Augier, PierreMohanan, Ashwin VishnuLindborg, Erik
By organisation
Linné Flow Center, FLOWMechanics
In the same journal
Journal of Fluid Mechanics
Fluid Mechanics and Acoustics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 61 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