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The energy cascade in a strongly stratified fluid
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence.
2006 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 550, 207-242 p.Article in journal (Refereed) Published
Abstract [en]

A cascade hypothesis for a strongly stratified fluid is developed on the basis of the Boussinesq equations. According to this hypothesis, kinetic and potential energy are transferred from large to small scales in a highly anisotropic turbulent cascade. A relation for the ratio, l(v)/l(h), between the vertical and horizontal length scale is derived, showing how this ratio decreases with increased stratification. Similarity expressions are formulated for the horizontal and vertical spectra of kinetic and potential energy. A series of box simulations of the Boussinesq equations are carried out and a good agreement between the proposed hypothesis and the simulations is seen. The simulations with strongest stratification give horizontal kinetic and potential energy spectra of the form EKh = C1 is an element of E-K(2/3) k(h)(-5/3) and E-Ph = C-2 is an element of(P)k(h)(-5/3)/is an element of(1/3)(k), where k(h) is the horizontal wavenumber, EK and ep are the dissipation of kinetic and potential energy, respectively, and C-1 and C-2 are two constants. Within the given numerical accuracy, it is found that these two constants have the same value: C-1 approximate to C-2 = 0.51 +/- 0.02.

Place, publisher, year, edition, pages
2006. Vol. 550, 207-242 p.
Keyword [en]
direct numerical simulations, velocity structure functions, 2-level model simulation, columnar vortex pair, lower stratosphere, inertial-range, atmospheric-turbulence, upper troposphere, wave spectra, fluctuations
URN: urn:nbn:se:kth:diva-15538DOI: 10.1017/s0022112005008128ISI: 000236195700013ScopusID: 2-s2.0-33645671722OAI: diva2:333579
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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Lindborg, Erik
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