Directional surface wave spectra from acoustic Doppler current profiler data in sheared and stratified flows

Methods for estimating directional energy spectra of surface water waves from acoustic Doppler current profiler (ADCP) data are presented in cases of (1) waves on arbitrary, horizontal mean flows and (2) waves on a two-layer, density stratified fluid with finite water depth. An existing perturbation expansion method is employed up to second order to compensate for the effect of arbitrary mean velocity profiles. Equations describing characteristics of random waves on a two-layer fluid are utilized to allow determination of directional surface and interfacial wave spectra. Wave-induced velocities based on model wave spectra were synthesized for simulating ADCP measurement schemes to verify the new method, and to investigate misestimation when the two-layer condition was neglected. Errors are typically smaller than other measurement uncertainties but depend greatly on the relationship among wave characteristics, interface depth, relative densities, and measurement locations.