Propagation of Low-Mode Internal Waves through the Ocean

Abstract

The baroclinic tides play a significant role in the energy budget of the abyssal ocean. Although the basic principles of generation and propagation are known, a clear understanding of these phenomena in the complex ocean environment is only now emerging. To advance this effort, a ray model is developed that quantifies the effects of spatially variable topography, stratification, and planetary vorticity on the horizontal propagation of internal gravity modes. The objective is to identify “baroclinic shoals” where wave energy is spatially concentrated and enhanced dissipation might be expected. The model is then extended to investigate the propagation of internal waves through a barotropic mesoscale current field. The refraction of tidally generated internal waves at the Hawaiian Ridge is examined using an ensemble of mesoscale background realizations derived from weekly Ocean Topography Experiment (TOPEX)/Poseidon altimetric measurements. The path of mode 1 is only slightly affected by typical currents, although its phase becomes increasingly random as the propagation distance from the source increases. The effect of the currents becomes more dramatic as mode number increases. For modes 3 and higher, wave phase can vary between realizations by ±π only a few wavelengths from the source. This phase variability reduces the magnitude of the baroclinic signal seen in altimetric data, creating a fictitious energy loss along the propagation path. In the TOPEX/Poseidon observations, the mode-1 M2 internal tide does appear to lose significant energy as it propagates southwestward from the Hawaiian Ridge. The simulations suggest that phase modulation by mesoscale flows could be responsible for a large fraction of this apparent loss. In contrast, northeast-propagating internal tides encounter a less energetic mesoscale and should experience limited refraction. The apparent energy loss seen in the altimetric data on the north side of the ridge might indeed be real.

The Cascade of Tidal Energy from Low to High Modes on a Continental Slope

“…For a mode-1 tide propagating from Hawaii, Rainville and Pinkel estimated that a 41-h travel time may vary by 1.7%. Using this standard deviation, Martini et al's (2011) estimate of the mode-1 travel time between the Mendocino Escarpment and our study site is 55 6 1 h. However, mesoscale currents along the Oregon coast produce jets, fronts, and instabilities (Koch et al 2010) that are more than twice as variable as mesoscale currents southwest of Hawaii (Rainville and Pinkel 2006). We therefore hypothesize that arrival times may vary by as much 63 h.…”

“…Previous studies have examined the time variability of internal-tide generation (Kelly and Nash 2010;Zilberman et al 2011), propagation (Rainville and Pinkel 2006) and incidence on continental slopes (Martini et al 2011), but little is understood about the time variability of tidally driven TKE dissipation. Here, terms are derived that represent modal-energy conversion (section 2a) and the energy conversion to high modes is characterized in terms of internal-tide intermittency (section 3c).…”

“…The resulting internal tide has 1500 W m 21 of energy flux. In the real ocean the amplitude and phase of the internal tide are determined by forcing at Mendocino Escarpment (Althaus et al 2003), mesoscale stratification and currents during propagation (Rainville and Pinkel 2006), and surface/ internal-tide feedbacks (Kelly and Nash 2010). In section 3c, time variability in these processes is modeled by altering the phase of the incident internal tide.…”

“…The Rainville and Pinkel (2006) analysis of internaltide propagation through mesoscale variability suggests realistic variability in arrival time. For a mode-1 tide propagating from Hawaii, Rainville and Pinkel estimated that a 41-h travel time may vary by 1.7%.…”

Are Any Coastal Internal Tides Predictable?

“…and mesoscale eddies. As a result, variation at the mesoscale and submesoscale (i.e., eddies and other ocean variability that produce slowly varying fluctuations in velocity and density over 10−500 km scales) alters an internal tide's propagation speed, causing internal tides to horizontally refract as they radiate from their generation sites (Rainville and Pinkel, 2006). Temporal variation of this background structure also results in Doppler shifting, which alters the arrival times of the internal ebb and flow.…”