Spectral analysis of the transition to turbulence from a dipole in stratified fluid

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Augier, PierreLadHyX, CNRS, Ecole Polytechnique, France (författare)

Spectral analysis of the transition to turbulence from a dipole in stratified fluid

Artikel/kapitelEngelska2012

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2012-10-11
Cambridge University Press (CUP),2012
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LIBRIS-ID:oai:DiVA.org:kth-109604
https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-109604URI
https://doi.org/10.1017/jfm.2012.437DOI

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Språk:engelska
Sammanfattning på:engelska

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QC 20130108
We investigate the spectral properties of the turbulence generated during the nonlinear evolution of a Lamb-Chaplygin dipole in a stratified fluid for a high Reynolds number Re = 28 000 and a wide range of horizontal Froude number F-h epsilon [0.0225 0.135] and buoyancy Reynolds number R = ReFh2 epsilon [14 510]. The numerical simulations use a weak hyperviscosity and are therefore almost direct numerical simulations (DNS). After the nonlinear development of the zigzag instability, both shear and gravitational instabilities develop and lead to a transition to small scales. A spectral analysis shows that this transition is dominated by two kinds of transfer: first, the shear instability induces a direct non-local transfer toward horizontal wavelengths of the order of the buoyancy scale L-b = U/N, where U is the characteristic horizontal velocity of the dipole and N the Brunt-Vaisala frequency; second, the destabilization of the Kelvin-Helmholtz billows and the gravitational instability lead to small-scale weakly stratified turbulence. The horizontal spectrum of kinetic energy exhibits epsilon(2/3)(K)k(h)(-5/3) power law (where k(h) is the horizontal wavenumber and epsilon(K) is the dissipation rate of kinetic energy) from k(b) = 2 pi/L-b to the dissipative scales, with an energy deficit between the integral scale and k(b) and an excess around k(b). The vertical spectrum of kinetic energy can be expressed as E(k(z)) = C(N)N(2)k(z)(-3) + C epsilon(2/3)(K)k(z)(-5/3) where C-N and C are two constants of order unity and k(z) is the vertical wavenumber. It is therefore very steep near the buoyancy scale with an N(2)k(z)(-3) shape and approaches the epsilon(2/3)(K)k(z)(-5/3) spectrum for k(z) > k(o), k(o) being the Ozmidov wavenumber, which is the cross-over between the two scaling laws. A decomposition of the vertical spectra depending on the horizontal wavenumber value shows that the N(2)k(z)(-3) spectrum is associated with large horizontal scales vertical bar k(h)vertical bar < k(b) and the epsilon(2/3)(K)k(z)(-5/3) spectrum with the scales vertical bar k(h)vertical bar > k(b).

Ämnesord och genrebeteckningar

instability
stratified flows
transition to turbulence

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

Chomaz, Jean-MarcLadHyX, CNRS, Ecole Polytechnique, 91128 Palaiseau CEDEX, France (författare)
Billant, PaulLadHyX, CNRS, Ecole Polytechnique, 91128 Palaiseau CEDEX, France (författare)
LadHyX, CNRS, Ecole Polytechnique, FranceLadHyX, CNRS, Ecole Polytechnique, 91128 Palaiseau CEDEX, France (creator_code:org_t)

Sammanhörande titlar

Ingår i:Journal of Fluid Mechanics: Cambridge University Press (CUP)713, s. 86-1080022-11201469-7645

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Av författaren/redakt...: Augier, Pierre; Chomaz, Jean-Mar ...; Billant, Paul

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Av lärosätet: Kungliga Tekniska Högskolan

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