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A two-dimensional toy model for geophysical turbulence
KTH, Skolan för teknikvetenskap (SCI), Mekanik. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.ORCID-id: 0000-0002-1560-7855
KTH, Skolan för teknikvetenskap (SCI), Mekanik. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW. (Erik Lindborg)ORCID-id: 0000-0002-2979-6327
2017 (engelsk)Inngår i: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 29, nr 11, artikkel-id 111114Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

A toy model for large scale geophysical turbulence is constructed by making two modifications of the shallow water model. Unlike the shallow water model, the toy model has a quadratic expression for total energy, which is the sum of Available Potential Energy (APE) and Kinetic Energy (KE). More importantly, in contrast to the shallow water model, the toy model does not produce any shocks. Three numerical simulations with different forcing are presented and compared with the simulation of a full General Circulation Model (GCM). The energy which is injected cascades in a similar way as in the GCM. First, some of the energy is converted from APE to KE at large scales. The wave field then undergoes a forward energy cascade displaying shallow spectra, close to k−5/3, for both APE and KE, while the vortical field either displays a k−3-spectrum or a more shallow spectrum, close to k−5/3, depending on the forcing. In a simulation with medium forcing wave number, some of the energy which is converted from APE to KE undergoes an inverse energy cascade which is produced by nonlinear interactions only involving the rotational component of the velocity field. The inverse energy cascade builds up a vortical field at larger scales than the forcing scale. At these scales, coherent vortices emerge with a strong dominance of anticyclonic vortices. The relevance of the simulation results to the dynamics of the atmosphere is discussed as in possible continuations of the investigation.

sted, utgiver, år, opplag, sider
American Institute of Physics (AIP), 2017. Vol. 29, nr 11, artikkel-id 111114
Emneord [en]
shallow water equation, 2D turbulence, geophysical flows
HSV kategori
Forskningsprogram
Teknisk mekanik; Fysik
Identifikatorer
URN: urn:nbn:se:kth:diva-218094DOI: 10.1063/1.4985990ISI: 000416067400014Scopus ID: 2-s2.0-85035141675OAI: oai:DiVA.org:kth-218094DiVA, id: diva2:1159542
Forskningsfinansiär
Swedish Research Council, D0519101
Merknad

QC 20171211

Tilgjengelig fra: 2017-11-22 Laget: 2017-11-22 Sist oppdatert: 2024-03-18bibliografisk kontrollert
Inngår i avhandling
1. Advancements in stratified flows through simulation, experiment and open research software development
Åpne denne publikasjonen i ny fane eller vindu >>Advancements in stratified flows through simulation, experiment and open research software development
2019 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Alternativ tittel[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.

sted, utgiver, år, opplag, sider
Stockholm, Sweden: KTH Royal Institute of Technology, 2019. s. 65
Serie
TRITA-SCI-FOU ; 2019:37
Emneord
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
HSV kategori
Forskningsprogram
Teknisk mekanik
Identifikatorer
urn:nbn:se:kth:diva-256564 (URN)978-91-7873-270-8 (ISBN)
Disputas
2019-09-27, F3, Lindstedtsvägen 26, Stockholm, 10:00 (engelsk)
Opponent
Veileder
Forskningsfinansiär
Swedish Research Council, 2013-5191
Merknad

QC20190902

QC 20200113

Tilgjengelig fra: 2019-09-02 Laget: 2019-08-28 Sist oppdatert: 2022-06-26bibliografisk kontrollert

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