Oliver Bühler New York University Courant Institute of Mathematical Science A simple two-step method is presented 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. 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. Examples based on two recent oceanic data sets from the North Pacific and the Gulf Stream are given, and some on-going work on the atmospheric spectrum is reported.