Propagation of the Semidiurnal Internal Tide: Phase Velocity Versus Group Velocity

Abstract

AbstractThe superposition of two waves of slightly different wavelengths has long been used to illustrate the distinction between phase velocity and group velocity. The first‐mode M2 and S2 internal tides exemplify such a two‐wave model in the natural ocean. The M2 and S2 tidal frequencies are 1.932 and 2 cycles per day, respectively, and their superposition forms a spring‐neap cycle in the semidiurnal band. The spring‐neap cycle acts like a wave, with its frequency, wave number, and phase being the differences of the M2 and S2 internal tides. The spring‐neap cycle and energy of the semidiurnal internal tide propagate at the group velocity. Long‐range propagation of M2 and S2 internal tides in the North Pacific is observed by satellite altimetry. Along a 3,400 km beam spanning 24°–54°N, the M2 and S2 travel times are 10.9 and 11.2 days, respectively. For comparison, it takes the spring‐neap cycle 21.1 days to travel over this distance. Spatial maps of the M2 phase velocity, the S2 phase velocity, and the group velocity are determined from phase gradients of the corresponding satellite observed internal tide fields. The observed phase and group velocities agree with theoretical values estimated using the World Ocean Atlas 2013 annual‐mean ocean stratification.