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Published October 10, 2014 | public
Journal Article

Wave–vortex decomposition of one-dimensional ship-track data


We present a simple two-step method by which one-dimensional spectra of horizontal velocity and buoyancy measured along a ship track can be decomposed into a wave component consisting of inertia–gravity waves and a vortex component consisting of a horizontal flow in geostrophic balance. The method requires certain assumptions for the data regarding stationarity, homogeneity, and horizontal isotropy. In the first step an exact Helmholtz decomposition of the horizontal velocity spectra into rotational and divergent components is performed and in the second step an energy equipartition property of hydrostatic inertia–gravity waves is exploited that allows a diagnosis of the wave energy spectrum solely from the observed horizontal velocities. The observed buoyancy spectrum can then be used to compute the residual vortex energy spectrum. Further wave–vortex decompositions of the observed fields are possible if additional information about the frequency content of the waves is available. We illustrate the method on two recent oceanic data sets from the North Pacific and the Gulf Stream. Notably, both steps in our new method might be of broader use in the theoretical and observational study of atmosphere and ocean fluid dynamics.

Additional Information

© 2014 Cambridge University Press. (Received 22 May 2014; revised 29 July 2014; accepted 19 August 2014; first published online 9 September 2014) O.B. thanks M. Holmes-Cerfon for interesting discussions and gratefully acknowledges financial support under grants CMG-1024180, DMS-1312159, and DMS-1009213 of the United States National Science Foundation. J.C. and R.F. thank G. Flierl for offering useful feedback during the preparation of the manuscript and acknowledge financial support under grants N-00014-09-1-0458 and GMG-1024198. We also thank three anonymous referees for their very helpful comments.

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