Short wind waves on the ocean: Long-wave and wind-speed dependences

This second paper of our set on short wind waves on the ocean utilizes the wavenumber-frequency spectrum of short wave heights, F(k,f), derived in our previous paper to investigate kinematic effects on the dependence of the frequency spectrum, F(f), and the wavenumber spectrum, F(k), on long-wave height. We show that the model predicts that neither F(f) nor F(k) are exactly power law functions of their independent variables and that F(f) varies with significant wave height much more than F(k) does. After calibrating the model against wave gauges, we also investigate the dependence of mean-square-slopes (mss), mean-square heights (msh) and root-mean-square orbital velocities (rmsv) of short ocean waves on wind speed and maximum frequency or wavenumber. We use data from the wire wave gauges on University of Miami's Air-Sea Interaction Spar (ASIS) buoy for calibration purposes. Frequency spectra from the wave gauges begin to be affected by noise at about 2.5 Hz. Therefore, above 1 Hz, we utilize F(f) from the modeled F(k,f) to extend the frequency dependence up to 180 Hz. We set modeled spectral densities by matching measured spectra at 1 Hz. Using the calibrated F(f,k), we are able to estimate the average value of the total mss, for long and short waves, and its upwind and crosswind components up to 180 Hz for a variety of wind speeds. The average mss values are in good agreement with the measurements of Cox and Munk [1954], although the upwind and crosswind components agree less well.