Observations and models of inertial waves in the deep ocean

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February, 1980The 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 O(200 m) just below the main thermocline. 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-wavenumber spectrum is given by the model of Garrett and Munk (1972 a, 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 wavenumber 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 the 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 modelled 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.This work was supported by the National Science Foundation through grant OCE 76-80210 and its continuation OEE 78-19833

Basinwide Integrated Volume Transports in an Eddy-Filled Ocean

The temporal evolution of the strength of the Atlantic Meridional Overturning Circulation (AMOC) in the subtropical North Atlantic is affected by both remotely forced, basin-scale meridionally coherent, climate-relevant transport anomalies, such as changes in high-latitude deep water formation rates, and locally forced transport anomalies, such as eddies or Rossby waves, possibly associated with small meridional coherence scales, which can be considered as noise. The focus of this paper is on the extent to which local eddies and Rossby waves when impinging on the western boundary of the Atlantic affect the temporal variability of the AMOC at 26.5°N. Continuous estimates of the AMOC at this latitude have been made since April 2004 by combining the Florida Current, Ekman, and midocean transports with the latter obtained from continuous density measurements between the coasts of the Bahamas and Morocco, representing, respectively, the western and eastern boundaries of the Atlantic at this latitude.Within 100 km of the western boundary there is a threefold decrease in sea surface height variability toward the boundary, observed in both dynamic heights from in situ density measurements and altimetric heights. As a consequence, the basinwide zonally integrated upper midocean transport shallower than 1000 m—as observed continuously between April 2004 and October 2006—varies by only 3.0 Sv (1 Sv 106 m3 s?1) RMS. Instead, upper midocean transports integrated from western boundary stations 16, 40, and 500 km offshore to the eastern boundary vary by 3.6, 6.0, and 10.7 Sv RMS, respectively.The reduction in eddy energy toward the western boundary is reproduced in a nonlinear reduced-gravity model suggesting that boundary-trapped waves may account for the observed decline in variability in the coastal zone because they provide a mechanism for the fast equatorward export of transport anomalies associated with eddies impinging on the western boundary. An analytical model of linear Rossby waves suggests a simple scaling for the reduction in thermocline thickness variability toward the boundary. Physically, the reduction in amplitude is understood as along-boundary pressure gradients accelerating the fluid and rapidly propagating pressure anomalies along the boundary. The results suggest that the local eddy field does not dominate upper midocean transport or AMOC variability at 26.5°N on interannual to decadal time scales.<br/