Shallow water wave turbulence

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Augier, PierreLEGI, Université Grenoble Alpes (författare)

Shallow water wave turbulence

Artikel/kapitelEngelska2019

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2019-07-15
Cambridge University Press,2019
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LIBRIS-ID:oai:DiVA.org:kth-255057
https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-255057URI
https://doi.org/10.1017/jfm.2019.375DOI

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Språk:engelska
Sammanfattning på:engelska

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QC 20190719
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 d∼Ff1/2/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.

Ämnesord och genrebeteckningar

TEKNIK OCH TEKNOLOGIER Maskinteknik Strömningsmekanik och akustik hsv//swe
ENGINEERING AND TECHNOLOGY Mechanical Engineering Fluid Mechanics and Acoustics hsv//eng
Fysik
Physics
Engineering Mechanics
Teknisk mekanik

Biuppslag (personer, institutioner, konferenser, titlar ...)

Mohanan, Ashwin Vishnu,1989-KTH,Linné Flow Center, FLOW,Mekanik,Erik Lindborg(Swepub:kth)u1l8bzs6 (författare)
Lindborg, ErikKTH,Linné Flow Center, FLOW,Mekanik(Swepub:kth)u1cfhn1t (författare)
LEGI, Université Grenoble AlpesLinné Flow Center, FLOW (creator_code:org_t)

Sammanhörande titlar

Ingår i:Journal of Fluid Mechanics: Cambridge University Press874, s. 1169-11960022-11201469-7645

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Av författaren/redakt...: Augier, Pierre; Mohanan, Ashwin ...; Lindborg, Erik

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TEKNIK OCH TEKNOLOGIER: TEKNIK OCH TEKNO ...; och Maskinteknik; och Strömningsmekani ...

Artiklar i publikationen: Journal of Fluid ...

Av lärosätet: Kungliga Tekniska Högskolan

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