General Circulation of the Ocean

The Observational Basis for Large Scale Circulation.- 1. Introduction.- 2. Surface Circulation.- 3. The Subtropical Gyres and Western Boundary Currents.- 4. Deep Circulation.- Thermocline Theories.- 1. Introduction.- 2. Formulation.- 2.1 The Equations of Motion.- 3. Conservation Principles.- 4. Scaling and the Governing Partial Differential Equation.- 5. The Search for Similarity Solutions.- 6. Ideal Fluid Solutions of Welander.- 7. Layered Models.- Inverse Methods for Ocean Circulation.- 1. Introduction.- 2. The Physical Problem.- 3. Treatment of the Data.- 3.1 Interpolation.- 3.2 Data Noise.- 3.3 Choice of Layers.- 3.4 Extrapolation.- 4. An Empirical Search.- 5. The Inverse Problem.- 5.1 Noise-Free Data; the SVD Solution.- 5.2 Representation and Resolution.- 5.3 Weighting.- 5.4 A Special Inverse for Noisy Data.- 5.5 Two Types of Correction.- 6. Results of Inverse Calculations.- 6.1 A Step Beyond the Inverse Calculation.- 7. Concluding Remarks.- Baroclinic Theories of the Wind Driven Circulation.- Abstract.- 1. Scale Analysis of the Equations of Motion.- 1.1 The Rossby Number.- 1.2 The Size of Vertical Velocities.- 1.3 The Consequences of Small Vertical Velocities.- 1.4 The Taylor-Proudman Theorem.- 2. The Two Layer Model.- 2.1 The Equations of Motion.- 2.1.1 The vertical momentum balance.- 2.1.2 The horizontal momentum balance.- 2.1.3 Mass conservation.- 2.2 Conservation of Potential Vorticity.- 2.2.1 Derivation of potential vorticity conservation.- 2.2.2 The relationship between potential vorticity and angular momentum.- 2.3 Quasigeostrophic Potential Vorticity Conservation.- 2.3.1 The approximations leading to quasigeostrophy.- 2.3.2 Derivation of the quasigeostrophic equations.- 2.3.3 Linear Rossby waves.- 2.4 Planetary Geostrophic Potential Vorticity Conservations.- 2.4.1 Simplification of the dynamics on large length scales.- 2.4.2 Nonlinear steepening of the baroclinic Rossby wave.- 2.4.3 Filtering of the barotropic Rossby wave.- 3. The Geometry of Geostrophic Contours.- 3.1 The Concept of a Geostrophic Contour.- 3.1.1 Definition of a geostrophic contour.- 3.2 A Topographic Problem.- 3.2.1 Potential vorticity conservation for a single layer.- 3.2.2 Introduction of a transport streamfunction.- 3.2.3 Determination of G from boundary conditions.- 3.2.4 Selection of a unique solution by weak dissipation and forcing.- 3.2.5 Forced flow across blocked geostrophic contours.- 3.2.6 Conclusion 156.- 3.3 Closed Geostrophic Contours in a Two Layer Circulation Model.- 3.3.1 The Quasigeostrophic equations in the limit ?L2/U > 1.- 3.3.2 The barotropic mode.- 3.3.3 The lower layer geostrophic contours.- 3.3.4 Numerical estimates of F*.- 3.3.5 Closed vs. blocked geostrophic contours.- 3.3.6 Justification of the preceding approximations.- 3.4 Conclusion.- 4. The Eddy Flux of Passive Scalar and Potential Vorticity.- 4.1 Introduction.- 4.1.1 The mesoscale eddy field.- 4.1.2 Eddy fluxes in a numerical model.- 4.2 Taylor's Diffusivity.- 4.2.1 Taylor's assumptions.- 4.2.2 The Lagrangian solution of (4.4).- 4.2.3 The mean field equation: statistical scrambling.- 4.3 A Model with Explicit Diffusivity.- 4.4 A Linear Relation Between Inline$$/overline {u'q'} $$ and Inline $$/nabla /overline q $$.- 4.5 The Mean Field Approximation.- 4.5.1 Scale analysis of the fluctuation equation.- 4.5.2 Solution of the simplified equation for q'.- 4.6 Turbulent Diffusion at High Peclet Number.- 4.6.1 Enhanced dissipation due to the smallest eddies.- 4.6.2 Averaging over successively larger eddies.- 4.7 More Complicated Explicit Dissipation.- 4.7.1 A simple model.- 4.7.2 A general model of dissipation.- 4.7.3 Enhanced dissipation due to high wavenumber eddies.- 4.7.4 Renormalization.- 4.7.5 Conclusion.- 5. Homogenization of Tracer Inside Closed Streamlines.- 5.1 Introduction.- 5.2 Potential Vorticity Homogenization.- 5.3 The Time Dependent Problem.- 5.4 A Simple Example: Departures from Homogenization.- 5.4.1 Formulation of the problem.- 5.4.2 Simplification of the steady state problem.- 5.4.3 The diffusive limit.- 5.4.4 The weakly diffusive limit.- 5.4.5 Introduction of a boundary layer variable.- 5.5 General Circulation Theory Revisited.- 5.5.1 Determination of G in (3.32).- 5.5.2 What is the value of q2?.- 5.5.3 How deep is the wind gyre?.- 5.6 Observational Confirmation of Potential Vorticity Homogenization.- 5.6.1 Numerical models.- 5.6.2 North Atlantic Ocean.- 5.7 Conclusion.- 5.7.1 Summary.- 5.7.2 A three-fold division of the wind gyre.- Single Layer Models of the General Circulation.- 1.1 Introduction.- 1.2 From the Sphere to the Beta Plane.- 1.3 Linear Models.- 1.4 Quasigeostrophy.- 1.5 Ekman Layers.- 1.6 The Quasigeostrophic Potential Vorticity Equation.- 1.7 Layered Models.- 2.1 The Sverdrup Balance.- 2.2 The Stommel Problem.- 2.3 The Munk Problem.- 2.4 Comparison with Observations.- 2.5 Nonlinear Perturbation of the Linear Problem.- 2.6 Free Nonlinear Solutions and Inertial Boundary Layers.- 2.7 The Nonlinear Stommel Problem.- 2.8 The Nonlinear Munk Problem.- 2.9 Abyssal Circulation.- 2.10 Effects of Relief.- 3.1 Impulsively Started Midlatitude Flow.- 3.2 Rossby Waves in a Rectangular Midlatitude Basin.- 3.3 The Midlatitude Initial Value Problem.- 3.4 The Relationship Between Transient and Steady Midlatitude Flows.- 3.5 Free Waves in the Tropics.- 3.6 The Tropical Initial Value Problem.- 3.7 The Relationship Between Transient and Steady Tropical Flows.