Lectures on Geophysical Fluid Dynamics offers an introduction to several topics in geophysical fluid dynamics, including the theory of large-scale ocean circulation, geostrophic turbulence, and Hamiltonian fluid dynamics. Since each chapter is a self-contained introduction to its particular topic, the book will be useful to students and researchers in diverse scientific fields.

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We have applied the methods of classical statistical mechanics to derive the inviscid equilibrium states for one- and two-layer nonlinear quasi-geostrophic flows, with and without bottom topography and variable rotation rate. In the one-layer case without topography we recover the equilibrium energy spectrum given by Kraichnan (1967). In the two-layer case, we find that the internal radius of deformation constitutes an important dividing scale: at scales of motion larger than the radius of deformation the equilibrium flow is nearly barotropic, while at smaller scales the stream functions in the two layers are statistically uncorrelated. The equilibrium lower-layer flow is positively correlated with bottom topography (anticyclonic flow over seamounts) and the correlation extends to the upper layer at scales larger than the radius of deformation. We suggest that some of the statistical trends observed in non-equilibrium flows may be looked on as manifestations of the tendency for turbulent interactions to maximize the entropy of the system.

In the case of equal layer depths and uniform vertical energy density, the quadratic integral invariants of two-layer rotating flow are close analogs of the corresponding invariants of twndimensional turbulence. A simple theory based on the invariants and on the selection rules governing triad interactions qualitatively explains the major features of forced equilibrium flow. The general physical picture is very similar to that of Rhines (1977). In the geophysically interesting case. net baroclinic energy is produced at low wavenumbers and moves toward hisher wavenumbers in relatively nonlocal triad interactions which are unhampered by the constraint to conserve enstrophy. The energy converts to barotropic mode and moves back toward low wavenumbers in more local interactions which are similar to those in two-dimensional turbulence. Equilibrium wavenumber spectra are obtainable from a simple Markovian turbulence closure model in which the estimate of turbulent scramhling rate includes a contribution from vortex stretching along the axis of rotation. Numerical experiments with the closure model confirm the qualitative predictions and demonstrate the sensitivity ofthe flow at low wavenumbers to changes in the forcing and dissipation.