Field observations of orbital velocities and pressure in weakly nonlinear surface gravity waves

Abstract

Field measurements of wave orbital velocities and pressure, collected in the lower part of the water column in 7 m depth with a three-component acoustic Doppler current meter and a co-located pressure transducer, are compared to the second-order theory for weakly nonlinear surface gravity waves in arbitrary water depth (Hasselmann 1962). Pressure and velocity spectra and cross-spectra are in excellent agreement with (linear) free wave transfer functions, even at (and higher than) twice the spectral peak frequency where nonlinearities (forced secondary waves) are expected to be important. Theoretical predictions show that although secondary waves sometimes contribute a significant fraction of the energy observed at double swell and sea frequencies, their effect on velocity-pressure transfer functions is small. However, forced waves are more apparent in deviations from Gaussian statistics. Good agreement between observed and predicted third-order statistics shows that Hasselmann's weakly nonlinear theory accurately describes the secondary pressure and orbital velocity (both horizontal and vertical components) field at double swell and sea frequencies, even for moderately large (0(0.1–0.2)) values of the nonlinear perturbation parameter. Only with near-breaking swell and relatively strong nonlinearities (perturbation parameter ≈ 0.22), do the observed third-order statistics diverge significantly from Hasselmann's theory.