Internal tide generation by abyssal hills using analytical theory

Abstract

[1] Internal tide driven mixing plays a key role in sustaining the deep ocean stratification and meridional overturning circulation. Internal tides can be generated by topographic horizontal scales ranging from hundreds of meters to tens of kilometers. State of the art topographic products barely resolve scales smaller than 10 km in the deep ocean. On these scales abyssal hills dominate ocean floor roughness. The impact of abyssal hill roughness on internal-tide generation is evaluated in this study. The conversion of M 2 barotropic to baroclinic tidal energy is calculated based on linear wave theory both in real and spectral space using the Shuttle Radar Topography Mission SRTM30_PLUS bathymetric product at 1/120 resolution with and without the addition of synthetic abyssal hill roughness. Internal tide generation by abyssal hills integrates to 0.1 TW globally or 0.03 TW when the energy flux is empirically corrected for supercritical slope (i.e., 10% of the energy flux due to larger topographic scales resolved in standard products in both cases). The abyssal hill driven energy conversion is dominated by mid-ocean ridges, where abyssal hill roughness is large. Focusing on two regions located over the Mid-Atlantic Ridge and the East Pacific Rise, it is shown that regionally linear theory predicts an increase of the energy flux due to abyssal hills of up to 100% or 60% when an empirical correction for supercritical slopes is attempted. Therefore, abyssal hills, unresolved in state of the art topographic products, can have a strong impact on internal tide generation, especially over mid-ocean ridges.

Comparison of calculated energy flux of internal tides with microstructure measurements

“…There are several limitations to the computation by Nycander (2005): (1) it is not valid when the slope is supercritical, although a correction for supercritical slopes has recently been proposed by Melet et al (2013), (2) it uses the WKB approximation, which simplifies the treatment of non-uniform stratification, and (3) small-scale topographic features are generally not well resolved in currently available topographic datasets. In spite of these limitations, some support for the validity of Nycander's approach (2005) is given by the results of Green and Nycander (2013), who used this scheme to parameterise the wave drag in a prognostic tidal model.…”

“…They found that the parameterisation substantially improved the performance of the tidal model compared to two other parameterisations based on simple scaling arguments. Melet et al (2013) have used Nycander's method to assess the effect of small-scale abyssal hills on estimates of the energy flux of the M 2 internal tide. These small-scale features are not resolved in the global bathymetry dataset, and were therefore synthetically generated and added to the dataset.…”

“…Using an empirical correction for supercritical slopes, they also tried to quantify the overestimate of the energy flux of the M 2 internal tide predicted by linear wave theory for supercritical slopes. Taking into account the abyssal hills, Melet et al (2013) found a 10% increase in the global energy conversion rate, and up to 89% in a region in the Brazil Basin. Melet et al (2013) did not compare their results to measurement.…”

“…Taking into account the abyssal hills, Melet et al (2013) found a 10% increase in the global energy conversion rate, and up to 89% in a region in the Brazil Basin. Melet et al (2013) did not compare their results to measurement.…”

“…We also examine the sensitivity of the calculated energy flux to spatial and temporal smoothing, as well as to the bathymetry resolution. To assess the contribution of the supercritical slopes to the energy flux, we extend the empirical correction for supercritical slopes proposed by Melet et al (2013) for the M 2 internal tide, so that it applies to the eight major tidal constituents.…”