# Propagation of Ocean Swell across the Pacific

F. E. Snodgrass, G. W. Groves, K. F. Hasselmann, G. R. Miller, W. H. Munk, W. H. Powers

## Abstract

Six wave stations were occupied for 2$\frac{1}{2}$ months along a great circle between New Zealand and Alaska. Twice-daily wave records were analysed to yield energy spectra E$_{i}$(f, t) for station i as functions of frequency and time. Events from major storms appear as slanting ridges in the E$_{i}$(f, t) field; the ridge lines f$_{i}$ = (g/4$\pi$) (t - t$_{0}$)/$\Delta _{i}$ determine source time, t$_{0}$, and source distance, $\Delta _{i}$; rough estimates of direction $\theta _{i}$(f) were made at two stations. Twelve major events, including several from antipodal storms ($\Delta \approx$ 180 degrees) in the Indian Ocean, could be clearly tracked from station to station. Source parameters are found to be mutually consistent, and usually in accord with weather information. Cuts in E$_{i}$(f, t) along the ridges give spectra from which the effect of dispersion is removed. These were corrected for geometric spreading and island shadowing. Comparison of the corrected ridge spectra between stations indicate negligible attenuation for frequencies below 70 mc/s (less than 0$\cdot$02 dB/deg between New Zealand and Alaska), and 0$\cdot$15 dB/deg at 80 mc/s, with a considerable scatter from event to event. At higher frequencies the events disappear into a background spectrum which is remarkably uniform over the Pacific, and presumably the result of global high winds along the entire storm belt of the South Pacific. The attenuation in the near zone of the storm (within a distance comparable to the storm diameter) is estimated at 0$\cdot$2 dB/deg at 70 mc/s and 0$\cdot$4 dB/deg at 80 mc/s. Wave-wave interactions have been derived from a perturbation expansion of the Navier-Stokes equations. The computed attenuation due to interaction between wave groups from a storm is not inconsistent with observations in both the near and far zones. The observed super-exponential decay is attributed to the decrease in interaction efficiency with diminishing wave energy along the path and dispersive narrowing of the spectral peak. Interaction with background (such as the trade wind sea) is unimportant. The conclusion is that the observed propagation could be accounted for by the effects of Stokes interaction (section b, c, figure 38) between wave groups from a single storm.