The westward intensification of wind‐driven ocean currents
01 Apr 1948-Eos, Transactions American Geophysical Union (John Wiley & Sons, Ltd)-Vol. 29, Iss: 2, pp 202-206
TL;DR: In this article, the authors made a study of the wind-driven circulation in a homogeneous rectangular ocean under the influence of surface wind stress, linearised bottom friction, horizontal pressure gradients caused by a variable surface height, and Corlolie force.
Abstract: A study is made of the wind-driven circulation in a homogeneous rectangular ocean under the influence of surface wind stress, linearised bottom friction, horizontal pressure gradients caused by a variable surface height, and Corlolie force.
An intense crowding of streamlines toward the western border of the ocean is discovered to be caused by variation of the Cortolis parameter with latitude. It is suggested that this process is the main reason for the formation of the intense currents (Gulf stream and others) observed in the actual oceans.
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TL;DR: A preconditioner is used which, in the hydrostatic limit, is an exact integral of the Poisson operator and so leads to a single algorithm that seamlessly moves from nonhydrostatic to hydrostatic limits, competitive with the fastest ocean climate models in use today.
Abstract: The numerical implementation of an ocean model based on the incompressible Navier Stokes equations which is designed for studies of the ocean circulation on horizontal scales less than the depth of the ocean right up to global scale is described. A "pressure correction" method is used which is solved as a Poisson equation for the pressure field with Neumann boundary conditions in a geometry as complicated as that of the ocean basins. A major objective of the study is to make this inversion, and hence nonhydrostatic ocean modeling, efficient on parallel computers. The pressure field is separated into surface, hydrostatic, and nonhydrostatic components. First, as in hydrostatic models, a two-dimensional problem is inverted for the surface pressure which is then made use of in the three-dimensional inversion for the nonhydrostatic pressure. Preconditioned conjugate-gradient iteration is used to invert symmetric elliptic operators in both two and three dimensions. Physically motivated preconditioners are designed which are efficient at reducing computation and minimizing communication between processors. Our method exploits the fact that as the horizontal scale of the motion becomes very much larger than the vertical scale, the motion becomes more and more hydrostatic and the three- dimensional Poisson operator becomes increasingly anisotropic and dominated by the vertical axis. Accordingly, a preconditioner is used which, in the hydrostatic limit, is an exact integral of the Poisson operator and so leads to a single algorithm that seamlessly moves from nonhydrostatic to hydrostatic limits. Thus in the hydrostatic limit the model is "fast," competitive with the fastest ocean climate models in use today based on the hydrostatic primitive equations. But as the resolution is increased, the model dynamics asymptote smoothly to the Navier Stokes equations and so can be used to address small- scale processes. A "finite-volume" approach is employed to discretize the model in space in which property fluxes are defined normal to faces that delineate the volumes. The method makes possible a novel treatment of the boundary in which cells abutting the bottom or coast may take on irregular shapes and be "shaved" to fit the boundary. The algorithm can conveniently exploit massively parallel computers and suggests a domain decomposition which allocates vertical columns of ocean to each processing unit. The resulting model, which can handle arbitrarily complex geometry, is efficient and scalable and has been mapped on to massively parallel multiprocessors such as the Connection Machine (CM5) using data-parallel FORTRAN and the Massachusetts Institute of Technology data-flow machine MONSOON using the implicitly parallel language Id. Details of the numerical implementation of a model which has been designed for the study of dynamical processes in the ocean from the convective, through the geostrophic eddy, up to global scale are set out. The "kernel" algorithm solves the incompressible Navier Stokes equations on the sphere, in a geometry as complicated as that of the ocean basins with ir- regular coastlines and islands. (Here we use the term "Navier Stokes" to signify that the full nonhydrostatic equations are being employed; it does not imply a particular constitutive relation. The relevant equations for modeling the full complex- ity of the ocean include, as here, active tracers such as tem- perature and salt.) It builds on ideas developed in the compu- tational fluid community. The numerical challenge is to ensure that the evolving velocity field remains nondivergent. Most
2,315 citations
TL;DR: In this paper, the authors provide an introduction to lattice gas cellular automata (LGCA) and lattice Boltzmann models (LBM) for numerical solution of nonlinear partial differential equations.
Abstract: Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new andpromising methods for the numerical solution of nonlinear partial differential equations. The bookprovides an introduction for graduate students and researchers. Working knowledge of calculus isrequired and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellularautomata are outlined in Chapter 2. The properties of various LGCA and special coding techniquesare discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessarytheoretical background for LGCA and LBM. The properties of lattice Boltzmann models and amethod for their construction are presented in Chapter 5.
1,543 citations
Book•
18 Feb 2000
TL;DR: This book provides an introduction for graduate students and researchers of lattice-gas cellular automata and lattice Boltzmann models for the numerical solution of nonlinear partial differential equations.
Abstract: Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new andpromising methods for the numerical solution of nonlinear partial differential equations. The bookprovides an introduction for graduate students and researchers. Working knowledge of calculus isrequired and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellularautomata are outlined in Chapter 2. The properties of various LGCA and special coding techniquesare discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessarytheoretical background for LGCA and LBM. The properties of lattice Boltzmann models and amethod for their construction are presented in Chapter 5.
731 citations
01 Jan 2008
TL;DR: In this paper, the authors present an overview of what is known about the ocean, including the equations of motion, the influence of earth's rotation, and viscosity of the ocean.
Abstract: This book is written for college juniors and seniors and new graduate students in meteorology, ocean engineering, and oceanography. It begins with a brief overview of what is known about the ocean. This is followed by a description of the ocean basins, for the shape of the seas influences the physical processes in the water. Next, students will study the external forces, wind and heat, acting on the ocean, and the ocean's response. It also includes the equations describing dynamic response of the ocean. For example, the equations of motion, the influence of earth's rotation, and viscosity. Finally, students consider some particular examples: the deep circulation, the equatorial ocean and El NiEœno, and the circulation of particular areas of the ocean. Contents: 1) A Voyage of Discovery. 2) The Historical Setting. 3) The Physical Setting. 4) Atmospheric Influences. 5) The Oceanic Heat Budget. 6) Temperature, Salinity and Density. 7) The Equations of Motion. 8) Equations of Motion with Viscosity. 9) Response of the Upper Ocean to Winds. 10) Geostrophic Currents. 11) Wind Driven Ocean Circulation. 12) Vorticity in the Ocean. 13) Deep Circulation in the Ocean. 14) Equatorial Processes. 15) Numerical Models. 16) Ocean Waves. 17) Coastal Processes and Tides.
596 citations
TL;DR: In this paper, the authors used a Sverdrup model with Hellerman and Rosenstein's (1983) annual mean wifids to calculate the annual mean depth-integrated steric height P and stream function ψ of the world ocean.
Abstract: The annual mean depth-integrated steric height P and stream function ψ of the world ocean are calculated from a Sverdrup model with Hellerman and Rosenstein's (1983) annual mean wifids The parameterization of friction is unspecified, but friction is assumed to be important only along western boundaries A simple rule, based on Sverdrup interior flow and geostrophy of longshore flow along western boundary currents, is used to calculate P at the inshore edge of the western boundary current The substantial predicted longshore gradients of P drive the model western boundary currents against friction, independent of frictional parameterization One corollary is an “Island Rule”–an explicit expression for circulation around an island, in terms of wind stress, again independent of frictional parameterization The circulations around Australasia, New Zealand and Malagasy are calculated as 16±4 Sv, 29±v, and 4±3 Sverdrups respectively Inclusion of island effects result in more accurate flow estimates i
452 citations