Method of directional spectrum estimation accounting for the ambient shearing currents

Realistic currents in seas and oceans are almost always changing in depth thus indicative on the presence of shear in the profile of the mean ambient flow. However, analysis methodologies interpreting directional wave data gathered by in situ measurement instruments such as buoys, pressure gauges, and acoustic Doppler current profilers (ADCPs) utilize potential irrotational flow theory which cannot account for the rotational shearing currents. The effects of shearing currents on the wave direction estimations were studied on numerically simulated ADCP data of waves propagating in a predetermined spread. The numerical data was generated employing the Rayleigh boundary-value problem (BVP) and a selected ambient current profile. The potential data processing led to significant errors in wave directional spread estimation for common shearing currents (up to ≈10∘ in mean wave direction for the presented example). This finding is of great importance because it addresses the influence of an ambient current profile on wave propagation direction. The obtained results suggest that there is an uncertainty with the confidence of any wave directional spread ever presented by in situ wave measurement devices. Here, we developed an approach for estimating directional wave spectra based on rotational flow physics by acquiring terms emanating from wave-shearing current interaction governing equations. This included a derivation of numerical transfer functions for the fluid's physical properties based on the Rayleigh BVP. Then, by applying classical cross- and auto-spectral analysis on time-series data sets, the directional spread function was numerically reconstructed. This derived data processing methodology was applied to the same numerically simulated ADCP data sets. It was found to be capable of reconstructing the spread with great accuracy (0.4∘ in mean wave direction for the presented example). This makes it a prominent methodology for estimating directional wave spectra in realistic oceanic conditions.