Effect of wave directional spread on the radiation stress: comparing theory and observations

Abstract

Nearshore circulation and shoreline setup are forced through the wave radiation stress, which is a function of the frequency-directional wave spectrum. The radiation stress components often are approximated by assuming a spectrum that is narrow-band in frequency and direction. These narrow-band approximations overestimate the true radiation stress components in 8-m water depth on the Outer Banks, NC where locally generated (broad in frequency and direction) sea conditions are prevalent. Using the empirical Pierson-Moskowitz spectrum, frequency-spread is shown not to be the cause of this overestimation. Analytic expressions derived by Battjes [J. Mar. Res. 30 (1972) 56], for the ratio of true to narrow-band approximated radiation stress, which depend only on the directional spread, are compared to field data. The observed ratio of true to narrow-band approximated radiation stress is a strong function of the observed bulk (energy-weighted) directional spread, and closely follows the analytic expressions. Thus the narrow-band radiation stresses approximation can be augmented with a directional-spread dependence. These results are expected to apply to other geographic areas where waves are often locally generated.