Department of Marine Science | Academics | Courses | MAR 663

OCEAN DYNAMICS (MAR 663)
3 credits
Instructor: Vladimir M. Kamenkovich
Office hours are by appointment

COURSE DESCRIPTION

The course is intended to develop the first level understanding of the basic physical mechanisms controlling the ocean circulation. It is directed to graduate students in physical oceanography, and also to those students in math, physics, and computer science, who are interested in the application of their skill in geophysics. First, we will discuss such important concepts of the ocean circulation theory as geostrophy, Ekman boundary layers, Sverdrup relation, and the beta-spiral. Second, we will show how to match these separate elements into one consistent pattern, using for simplicity's sake the Ekman model of the ocean circulation. Third, the detailed analysis of the western boundary currents in the homogeneous ocean will be presented. Fourth, Stommel-Arons ideas about the abyssal circulation will be outlined.

COURSE OBJECTIVES

1. To provide the basic concepts of the modern ocean dynamics required to understand the main physical mechanisms responsible for shaping the horizontal structure of the ocean circulation.
2. To teach skills in applying the general principles of ocean dynamics to the analysis of particular problems.
3. To explain relations between widely used simplified models of the ocean circulation and the first principles of fluid dynamics.

TEXTS

Class notes with home assignments will be provided for each lecture.
The following books are recommended for supplemental reading:
1. Cushman-Roisin, B. Introduction to geophysical fluid dynamics: 1994, Prentice Hall, Inc., 320pp.
2. Kamenkovich, V. M. Fundamentals of ocean dynamics: 1977, Elsevier Sci. Publ. Co., 249pp. (Translation from Russian).
3. Mellor, G. L. Introduction to physical oceanography: 1996, American Institute of Physics, 260pp.
4. Pedlosky, J. Geophysical fluid dynamics: 1987, Springer Verlag, 710pp.
5. Wunsch, C. The ocean circulation inverse problem: 1996, Cambridge University Press, 442pp

GRADING

1. Class participation: 15%.
2. Home assignments: 55%.
3. Final exam: 30%
Final exam consists mainly of a term project. The term project is submitted in written form and is defensed orally. It has to have a
research component.

PREREQUISITES

Basic courses on physics (PHY 351) and calculus (MAT 385) or permission of the instructor.

DETAILED COURSE OUTLINE

Introduction
Meso- and large-scale motions in the ocean. Factors generating such motions. Wind-driven and thermohaline circulation.

Chapter I. Fundamentals of fluid dynamics (11 Lectures)

We will start with the discussion of the concept of vorticity. Then the basic principles of fluid dynamics will be stated both in the integral and differential forms: mass conservation equation, momentum equations, energy equation, and entropy equation . The vorticity equation will be thoroughly analyzed. The Boussinesq approximations will be discussed in detail. Finally we will investigate the boundary conditions, especially conditions at the interface between the atmosphere and ocean.

1.1. Deformation and rotation of a fluid particle. The rate-of-strain tensor. The rate of change of the volume of a fluid particle. Definition of the vorticity vector. The vorticity vector as twice the angular velocity of the rigid-body rotation of a fluid particle. The Stokes theorem.
1.2. Equation of mass conservation. Integral and differential formulations. Material time derivative.
1.3. The flux-form equation. The flux vector (or flux tensor). Density of internal sources.
1.4. Inertial and noninertial frames of reference. The Coriolis acceleration. Formulation of the Newton law of motion in a noninertial frame of reference. Apparent forces.
1.5. Newton’s law of motion. Integral formulation. Volume and surface forces acting on a fluid. The
stress tensor. Differential formulation of Newton’s law of motion.
1.6. Angular momentum equation. The symmetry of stress tensor.
1.7. Thermodynamics of the two-parameter system. Formulation of the First and Second Laws. Entropy. Thermodynamical relations. Thermodynamical parameters in the nonequilibrium state.
1.8. Equation of energy conservation. Integral and differential formulations.
1.9. Energy transformations. Equation for the mechanical energy. Equation for the internal energy. Integral and differential formulations.
I.10. Entropy equation. Entropy inequality Formulation of the Second Law of thermodynamics for the moving fluid. Heat equation.
1.11. Vorticity equation. Generation of the vorticity due to the deformation of vortexlines., baroclinic and frictional effects.
1.12. Boundary conditions at the moving interface. Boundary conditions at the sea surface. Local Cartesian coordinates.
The beta-plane approximation.
1.13. Boussinesq approximations. Heat conduction equation. The vorticity equation in the Boussinesq approximation.

Chapter II. Basic concepts of ocean dynamics (9 Lectures)

First we will very shortly discuss the general approach to handling turbulent flows and formulate some relations for ocean turbulent currents. Then we will analyze such important dynamical concepts as geostrophy, Ekman boundary layers, Sverdrup relation, JEBAR, and beta-spiral. Special attention will be given to the relation of these concepts to the general principles and to the comparison with observations.

II.1. Turbulence. The nature of turbulence. Reynolds decomposition. Averaging of the basic equations. Estimates of turbulent fluxes. The parameterization of turbulent fluxes.
II.2. Geostrophic relations.
II.3. The quasistatic approximation. Thermal wind relations.
II.4. Diagnostic calculations.
II.5. Geostrophic adjustment. The Rossby radius of deformation.
II.6.. Ekman boundary layers. Thickness of the layer. Ekman number. Ekman pumping.
II.7. Sverdrup relation. Depth-averaging of the momentum and continuity equations. The transport velocities and streamfunction. The analysis of validity of the Sverdrup relation.
II.8. Advanced diagnostic calculations. The generalized Sverdrup relation.
The concept of JEBAR. The beta-spiral method.

Chapter III. Ekman model of the wind-driven currents (6 Lectures)

In Chapters III and IV we will assume that the density of sea water is constant. This assumption will result in a substantial simplification: the model horizontal velocity and horizontal pressure gradient will be independent of depth. The ensuing models play an important role in ocean dynamics. They lend themselves to study by means of analytical methods thus providing the simplest opportunity to show how to match the separate elements of the circulation, discussed in Chapter II, into one consistent pattern.

III.1. Basic equations. Ekman scale.
III.2. Asymptotic expressins for large and small Ekman numbers.
III.3. Effect of spatial variation of the wind stress. The mid-section method for the shallow sea.
III.4. Analysis of the vertical structure for the deep sea.
III.5. Boundary-layer analysis of the vertical structure.
III.6. Western intensification of the horizontal circulation. The Stommel model. Stommel's scale.
III.7. The vorticity balance within the boundary layer.
III.8. Alternative analysis of the circulation in a closed basin.
III.9. Dynamical regime with closed geostrophic contours. The Antarctic Circumpolar Current.
III.10. The Island Rule.

Chapter IV. The wind-driven circulation in the homogeneous ocean (3 Lectures)

The detailed theory of the circulation in the homogeneous ocean of constant depth is presented. The formation of different boundary layers is the characteristic feature of the circulation.

IV.1. The Munk model. Munk's scale. Analysis of the vorticity balance. Basic gyres. Equatorial countercurrents.
IV.2. The general model of the wind-driven currents in the homogeneous ocean. Analysis of the vorticity balance. Charney's scale.
IV.3. Rossby waves equation.
IV.4. Some properties of Rossby waves. Physical mechanism supporting Rossby-wave propagation. Group
velocity. Energy propagation in the open ocean and in the coastal region.
IV.5. Rossby-wave mechanism of boundary layer formation.

Chapter V. The Stommel-Arons theory of the abyssal circulation (2 Lectures)

The classical theory that laid the foundation of our understanding of the abyssal circulation in the ocean.

V.1. Observational evidence. Formulation of the model. The total transport of the deep western boundary layer.
V.2. Analysis of different patterns.
V.3. Dynamics of the deep western boundary currents.

ADA COMPLIANCE

If a student has a disability that qualifies under the Americans with Disabilities Act (ADA) and requires accommodations, he/she should contact the Office for Disability Accommodations (ODA) for information on appropriate policies and procedures. Disabilities covered by ADA may include learning, psychiatric, physical disabilities, or chronic health disorders. Students can contact ODA if they are not certain whether a medical condition/disability qualifies.

Address: The University of Southern Mississippi Office for Disability Accommodations
118 College Drive # 8586 Hattiesburg, MS 39406-0001
Voice Telephone: (601) 266-5024 or (228) 214-3232 Fax: (601) 266-6035
Individuals with hearing impairments can contact ODA using the Mississippi Relay Service at 1-800-582-2233 (TTY) or email Suzy Hebert at Suzanne.Hebert@usm.edu <mailto:Suzanne.Hebert@usm.edu> .

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