Observations and models of inertial waves in the deep ocean
Authors: Fu Lee‐Lueng 
Published: February 2008

The structure of the inertial peak in deep ocean kinetic energy spectra is studied here. Records were obtained from Polymode arrays deployed in the Western North Atlantic Ocean (40°W to 70°W, 15°N to 42°N). The results are interpreted both in terms of local sources and of turning point effects on internal waves generated at lower latitudes. In most of the data, there is a prominent inertial peak slightly above f; however, the peak height above the background continuum varies with depth and geographical environment. Three classes of environment and their corresponding spectra emerge from peak height variations: class 1 is the 1500‐m level near the Mid‐Atlantic Ridge, with the greatest peak height of 18 dB; class 2 includes (a) the upper ocean (depth less than 2000 m), (b) the deep ocean (depth greater than 2000 m) over rough topography, and (c) the deep ocean underneath the Gulf Stream, with intermediate peak height of 11.5 dB; class 3 is the deep ocean over smooth topography, with the lowest peak height of 7.5 dB. Near f, the horizontal coherence scale is 0 (60 km) at depths from 200 m to 600 m, and the vertical coherence scale is 0 (200 m) in the lower part of the main thermocline and 0 (1000 m) in the deep water; the phase difference suggests a downward energy propagation in the lower thermocline and standing waves in the deep water. A one‐turning‐point model is developed to describe inertial waves at mid‐latitudes, based on the assumption that inertial waves are randomly generated at lower latitudes (global generation) where their frequency‐wave number spectrum is given by the model of Garrett and Munk (1972, 1975). Using the globally valid wave functions obtained by Munk and Phillips (1968), various frequency spectra near f are calculated numerically. The model yields a prominent inertial peak of 7 dB in the horizontal velocity spectrum but no peaks in the temperature spectrum. The model is latitudinally dependent: the frequency shift and bandwidth of the inertial peak decrease with latitude; energy level near f is minimum at about 30° and higher at low and high latitudes. The observations of class 3 can be well described by the model; a low zonal wave number cutoff is required to produce the observed frequency shift of the inertial peak. The differences between the global generation model and the observations of class 1 and class 2 are interpreted as the effects of local sources. A locally forced model is developed based on the latitudinal modal decomposition of a localized source function. Asymptotic eigensolutions of Laplace’s tidal equation are therefore derived and used as a set of expansion functions. The forcing is through a vertical velocity field specified at the top or bottom boundaries of the ocean. For white noise forcing, the horizontal velocity spectrum of the response has an inertial peak which diminishes in the far field. With the forcing located at either the surface or the bottom, several properties of the class 2 observations can be described qualitatively by a combination of the global and local models. The reflection of inertial waves from a turbulent benthic boundary layer is studied by a slab model of given depth. Frictional effects are confined to the boundary layer and modeled by a quadratic drag law. For given incident waves, reflection coefficients are found to be greater than 0.9 for the long waves which contain most of the energy. This result suggests that energy‐containing inertial waves can propagate over great distance as is required by the validity of the model of global generation.