Internal‐tide energy over topography

The method used to separate surface and internal tides ultimately defines properties such as internal‐tide generation and the depth structure of internal‐tide energy flux. Here, we provide a detailed analysis of several surface‐/internal‐tide decompositions over arbitrary topography. In all decompositions, surface‐tide velocity is expressed as the depth average of total velocity. Analysis indicates that surface‐tide pressure is best expressed as the depth average of total pressure plus a new depth‐dependent profile of pressure, which is due to isopycnal heaving by movement of the free surface. Internal‐tide velocity and pressure are defined as total variables minus the surface‐tide components. Corresponding surface‐ and internal‐tide energy equations are derived that contain energy conversion solely through topographic internal‐tide generation. The depth structure of internal‐tide energy flux produced by the new decomposition is unambiguous and differs from that of past decompositions. Numerical simulations over steep topography reveal that the decomposition is self‐consistent and physically relevant. Analysis of observations over Kaena Ridge, Hawaii; and the Oregon continental slope indicate O (50 W m −1 ) error in depth‐integrated energy fluxes when internal‐tide pressure is computed as the residual of pressure from its depth average. While these errors are small at major internal‐tide generation sites, they may be significant where surface tides are larger and depth‐integrated fluxes are weaker (e.g., over continental shelves).