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Spectral analysis of the transition to turbulence from a dipole in stratified fluid
LadHyX, CNRS, Ecole Polytechnique, France.
2012 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 713, 86-108 p.Article in journal (Refereed) Published
Abstract [en]

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).

Place, publisher, year, edition, pages
2012. Vol. 713, 86-108 p.
Keyword [en]
instability, stratified flows, transition to turbulence
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-109604DOI: 10.1017/jfm.2012.437ISI: 000311889500005Scopus ID: 2-s2.0-84870779460OAI: oai:DiVA.org:kth-109604DiVA: diva2:583775
Note

QC 20130108

Available from: 2013-01-08 Created: 2013-01-08 Last updated: 2017-12-06Bibliographically approved

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