Analytical formulas for estimation of phase-averaged parameters of random waves

New analytical formulas for the estimation of wave radiation stress and wave mass flux are developed in this study based on asymptotic analysis of linear wave theory with the aid of non-directional parameterized wave spectra. Verification against synthetic wave data shows that the new formulas can allow up to 10% more accurate results compared to the use of the traditional representative wave approach. Sensitivity analysis based on reliable wave buoy data reveals that the performance of the new formulas may vary by up to 20% depending on the relative wave height, wave steepness, and spectral width. For a common sea state dominated by wind-induced waves, the formulas are most sensitive to the relative water depth kph and their best applicable range is in upper transitional to deep water conditions (kph≥π/2). The formulas were finally validated against nine independent sets of field wave spectra to reassure their superiority over the representative wave approach. The validation confirms that the new formulas can offer up to 10% and 15% improvements in terms of the estimation accuracy and the estimation precision, respectively.