An Estimate of Tidal Energy Lost to Turbulence at the Hawaiian Ridge

Abstract

An integrated analysis of turbulence observations from four unique instrument platforms obtained over the Hawaiian Ridge leads to an assessment of the vertical, cross-ridge, and along-ridge structure of turbulence dissipation rate and diffusivity. The diffusivity near the seafloor was, on average, 15 times that in the midwater column. At 1000-m depth, the diffusivity atop the ridge was 30 times that 10 km off the ridge, decreasing to background oceanic values by 60 km. A weak (factor of 2) spring–neap variation in dissipation was observed. The observations also suggest a kinematic relationship between the energy in the semidiurnal internal tide (E) and the depth-integrated dissipation (D), such that D ∼ E1±0.5 at sites along the ridge. This kinematic relationship is supported by combining a simple knife-edge model to estimate internal tide generation, with wave–wave interaction time scales to estimate dissipation. The along-ridge kinematic relationship and the observed vertical and cross-ridge structures are used to extrapolate the relatively sparse observations along the length of the ridge, giving an estimate of 3 ± 1.5 GW of tidal energy lost to turbulence dissipation within 60 km of the ridge. This is roughly 15% of the energy estimated to be lost from the barotropic tide.

Preliminary simulations of internal waves and mixing generated by finite amplitude tidal flow over isolated topography

“…high R L ) in the simulations is the appearance of higher harmonic frequencies, as predicted by Bell (1975), but not yet resolved in the observational record. The "tall wide" topography shows a response dominated by the gravest vertical mode and the forcing frequency: similar behavior is seen observations from the Hawaiian Ridge (Klymak et al, 2005), which has a similar topographic structure. At the Hawaiian Ridge about 10% of the energy converted from the barotropic tide is found to be dissipated locally -this again agrees with our simulations for the "tall wide" topography.…”

“…For example, the large-scale structure of the Mid-Atlantic ridge has a subcritical slope, like our "low, wide" topography, while the smaller features found on this slope may be narrow and have supercritical slope like our "low, narrow" topography (St Laurent and Nash, 2004). The Hawaiian ridge is similar in character to our "tall, wide" topography, which has a supercritical slope but relatively large horizontal scale (St Laurent and Nash, 2004;Klymak et al, 2005), while the Knight inlet sill is similar to our "tall, thin" topography, with large amplitude changes in topography in a very short distance (Klymak and Gregg, 2004). Of course a significant difference between our simulations and real ocean locations is the constant stratification and absence of pycnocline in the simulations.…”

Internal tides and energy fluxes over Great Meteor Seamount

“…Still, to get an idea of the order of magnitude, we extrapolate the value found here to the entire seamount, multiplying 2.3 kW m −1 by the circumference of a circle, the radius of which is (roughly) estimated to be 20 km. This gives a total conversion of 0.3 GW, which is about sixty times less than at the Hawaiian Ridge (Klymak et al, 2006).…”

“…Observations at the Hawaiian Ridge support this idea; internal-tide energy fluxes of the order of 10 kW m −1 were found at various locations (Rainville and Pinkel, 2006;Nash et al, 2006), and the total loss of barotropic tidal energy, for all the tidal constituents together, in the near-Hawaiian area is estimated at nearly 25 GW (Zaron and Egbert, 2006). Of this amount, an estimated 15% is lost to turbulence in the vicinity of the ridge, Correspondence to: T. Gerkema (gerk@nioz.nl) presumably by cascading of internal-tide energy to smaller scales (Klymak et al, 2006).…”

Spatial distribution of turbulent mixing in the upper ocean of the South China Sea

“…Therefore, it has been argued that elevated turbulent mixing concentrated over rough topography (Ledwell et al, 2000;Wu et al, 2011) would aid in explaining this discrepancy. In the past decade, elevated diapycnal diffusivities, i.e., O (10 −4 m 2 s −1 ) or higher, have been found in mixing hotspots such as seamounts (Carter et al, 2006;Lueck and Mudge, 1997), ridges (Klymak et al, 2006a;Lee et al, 2006), and canyons (Carter and Gregg, 2002). However, these elevated mixing events are highly localized.…”