Wave–Vortex Decomposition of One-Dimensional Ship Track Data

Abstract:

Oceanic motions are dominated by geostrophic flows at the mesoscale (order 100 km) and by internal waves at small scales (order 100 m and smaller). It is anticipated that at some intermediate scale, there is a transition from geostrophically dominated flow to wave-dominated flow. Observing the flow at such intermediate scales, the submesoscales, is currently restricted to ship-based measurements. Information is often obtained in one spatial dimension only, with no temporal information available to distinguish between geostrophic flow and internal waves.

We present a simple two-step method by which one-dimensional energy spectra can be decomposed into an internal-wave component and a geostrophic component if measurements of velocity along and across the ship track and buoyancy are available. In the first step a 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 internal 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 geostrophic energy spectrum. We illustrate the method on two data sets from the eastern North Pacific and the Gulf Stream region. The method is also applicable to atmospheric data obtained by commercial aircraft.