Buhler
Oliver
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Wave–vortex decomposition of one-dimensional ship track data
Buhler
Oliver
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Preprint
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 diagnosing 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.