The vertical propagation of inertial waves in the ocean

Abstract

A set of vertical profiles of horizontal ocean currents, obtained by electro-magnetic profilers in the Atlantic Ocean southwest of Bermuda in the spring of 1973, has been analyzed in order to study the vertical structure and temporal behavior of internal waves, particularly those with periods near the local inertial period. An important feature of the observed structure is the polarization of horizontal velocity components in the vertical. This polarization, along with temporal changes of the vertical wave structure seen in a time series of profiles made at one location, has been related to the direction of vertical energy flux due to the observed waves. Whereas the observed vertical phase propagation can be affected by horizontal advection of waves past the point of observation, the use of wave polarization to infer the direction of vertical energy propagation has the advantage that it is not influenced by horizontal advection. The result shows that at a location where profiles were obtained over smooth topography, the net energy flux was downward, indicating that the energy sources for these waves were located at or near the sea surface. An estimate of the net, downward energy flux (~ .2 - .3 erg/cm2/sec) has been obtained. Calculations have been made which show that a frictional bottom boundary layer can be an important energy sink for near-inertial waves. A rough estimate suggests that the observed, net, downward energy flux coul d be accounted for by energy losses in this frictional boundary layer. A reflection coefficient for the observed waves as they reflect off the bottom has been estimated. In contrast, some profiles made over a region of rough topography indicate that the rough bottom may also be acting to generate near-inertial waves which propagate energy upward. Ca1culations of vertical flux of horizontal kinetic energy, using an empirical form for the energy spectrum of internal waves, show that this vertical flux reaches a maximum for frequencies 10% - 20% greater than the local inertial frequency. Comparison with profiler velocity data and frequency spectra supports the conclusion that the dominant waves had frequencies 10% - 20% greater than the inertial frequency. The fact that the waves were propagating energy in the vertical is proposed as the reason for the observed frequency shift. Finally, energy spectra in vertical wave number have been calculated from the profiles in order to compare the data with an empirical model of the energy density spectrum for internal waves proposed by C. Garrett and W. Munk (1975). The result shows that although the general shape and magnitude of the observed spectrum compares well with the empirica1 model, the two-sided spectrum is not symmetric in vertical wave number. This asymmetry has been used to infer that more energy was propagating downward than upward. These calculations have also been used to obtain the coherence between profiles made at the same location, but separated in time (the so-called dropped, lagged, rotary coherence). This coherence is compared with the aforementioned empirical model. The coherence results show that the contribution of the semidiurnal tide to the energy of the profiles is restricted to long vertical wave lengths.