Effects of Small-scale Bathymetric Roughness on the Global Internal Wave Field

The small-scale roughness properties of the seafloor are increasingly being recognized as critical parameters in determining important processes in physical oceanography. For instance, in situ observations (e.g., Polzin et al., 1997) find that mixing levels are greatly elevated in regions of rough topography. Gille et al. (2000) demonstrate that mesoscale eddy energy tends to be lower in areas where the bottom is rough (suggesting the possibility that dissipation of eddy energy takes place in such areas), and Egbert and Ray (2003) show that substantial tidal dissipation occurs in such areas. The dissipation is generally thought to arise from the breaking of internal waves generated by flows over the rough seafloor. On the time scales of internal waves, mesoscale eddies and the general circulation can be regarded as steady, while tides are oscillatory. The physics of linear internal wave generation is different for these two classes of motions (e.g., Bell 1975), but for both types of flows the wave generation is strongly dependent on the horizontal and vertical scales inherent in the bottom topography. Using the classical formulation for lee waves (e.g., Cushman-Roisin, 1994, St. Laurent, 1999), one can argue that horizontal wavelengths ranging from ~60 m to 6 km generate internal waves when forced by steady flows. Features typical of abyssal hill morphology (e.g., 50 m height over 1 km horizontal scale) will generate a significant vertical internal wave energy flux. High-resolution regional models (e.g., Zilberman and Merrifield, 2006) demonstrate that topographic information on scales of order 3 km are also important for internal tides. Non-linear effects may be important as well, as some oceanographers (e.g., Thurnherr and Richards, 2001; Thurnherr et al., 2002; Thurnherr and Speer, 2003; St. Laurent and Thurherr, 2007) have argued from observational data that turbulence associated with hydraulic jumps occurs in area of rough topography when the Froude number exceeds an order one threshold. This occurs when topography over scales of 1 km exceeds 20 m in height, which is typically the case for abyssal hill morphology.