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Anisotropic Helmholtz and wave–vortex decomposition of one-dimensional spectra

Published online by Cambridge University Press:  21 February 2017

Oliver Bühler Open the ORCID record for Oliver Bühler [Opens in a new window] ,
Max Kuang  and
Esteban G. Tabak
Oliver Bühler*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Max Kuang
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Esteban G. Tabak
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
*
†Email address for correspondence: [email protected]
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Abstract

We present an extension to anisotropic flows of the recently developed Helmholtz and wave–vortex decomposition method for one-dimensional spectra measured along ship or aircraft tracks in Bühler et al. (J. Fluid Mech., vol. 756, 2014, pp. 1007–1026). Here, anisotropy refers to the statistical properties of the underlying flow field, which in the original method was assumed to be homogeneous and isotropic in the horizontal plane. Now, the flow is allowed to have a simple kind of horizontal anisotropy that is chosen in a self-consistent manner and can be deduced from the one-dimensional power spectra of the horizontal velocity fields and their cross-correlation. The key result is that an exact and robust Helmholtz decomposition of the horizontal kinetic energy spectrum can be achieved in this anisotropic flow setting, which then also allows the subsequent wave–vortex decomposition step. The anisotropic method is as easy to use as its isotropic counterpart and it robustly converges back to it if the observed anisotropy tends to zero. As a by-product of our analysis we also found a simple test for statistical correlation between rotational and divergent flow components. The new method is developed theoretically and tested with encouraging results on challenging synthetic data as well as on ocean data from the Gulf Stream.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Quasi-geostrophic flows Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 815 , 25 March 2017 , pp. 361 - 387
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Copyright
© 2017 Cambridge University Press 

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