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Experiments on the structure and dynamics of forced, quasi-two-dimensional turbulence

Published online by Cambridge University Press:  26 April 2006

S. Narimousa ,
T. Maxworthy  and
G. R. Spedding
S. Narimousa
Affiliation:
University of Southern California, Department of Mechanical Engineering, Los Angeles, CA 90089-1453, USA
T. Maxworthy
Affiliation:
University of Southern California, Departments of Aerospace and Mechanical Engineering, Los Angeles, CA 90089-1191, USA
G. R. Spedding
Affiliation:
University of Southern California, Department of Mechanical Engineering, Los Angeles, CA 90089-1453, USA
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Abstract

Simulated upwelling fronts have been generated around the outer edge of a cylindrical tank filled with a two-layer fluid system and driven by a surface stress. Initially, an axisymmetric front was observed which subsequently became unstable to small baroclinic eddies. These eddies continued to grow until they reached an equilibrium size. Under some circumstances, cyclonic eddies pinched-off from the fully developed front and moved away from the mean position of the front into the fluid interior. Streak photographs of the fully developed flow field were digitized to generate a velocity field interpolated on to a regular grid. A direct two-dimensional Fourier transform was performed on the turbulent kinetic energy field deduced from such images and one-dimensional energy E(k) spectra were extracted. Consistent $k^{-\frac{5}{3}}$ energy spectra were found at lower wavenumber, k and approximately k−5.5 spectra at higher k. In any given experiment, the two spectral slopes meet close to a wavenumber kw = 2π/λw (where λw is the mean diameter of a frontal eddy and kw is the associated wavenumber). According to classical theories, kw would be the input wavenumber, and the range of k with a $k^{-\frac{5}{3}}$ spectrum would correspond to an inverse energy cascade range; this yielded a Kolmogorov constant (C) that varied within the limits 2.8 [les ] C [les ] 3.8. The approximately k−5.5 range, which is much steeper than that predicted by the original statistical theories, is nevertheless consistent with those found frequently in numerical experiments.

The spectral slopes inferred from particle dispersion methods and from one-dimensional Fourier transforms of the longitudinal velocity correlations were compared with the results obtained above and in previous laboratory experiments. In general, the global energy spectra are consistent with an interpretation of the fluid dynamics as being that of two-dimensional turbulence. This in turn implies that known properties of such flows may be invoked to explain the appearance of a number of naturally occurring phenomena in coastal upwelling fronts.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 113 - 133
Copyright
© 1991 Cambridge University Press

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