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[BEST SELLING] Physical Oceanography: A Mathematical Introduction wi…
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Email Required, but never shown. The Overflow for October 4, Featured on Meta. Unicorn Meta Zoo 9: How do we handle problem users? An apology to our community, and next steps. Related 8. Hot Network Questions. Question feed. Potential vorticity conservation and homogenization. Reference text: Samelson, R. Prereq: OC and Fundamental mass, force and energy balances of the ocean: geostrophy; planetary boundary layers; wind-driven and thermohaline circulation; vorticity; air-sea fluxes of heat, salt, moisture and momentum.
Application of these balances through descriptive examination of the ocean: global heat budget; surface current systems; abyssal circulation. Study of variability on a variety of time and space scales. Instrumentation and platforms used for observing the ocean. Governing equations, turbulent kinetic energy, vorticity dynamics; turbulent transports of mass and momentum; statistical description of turbulent flows, spectral dynamics; turbulent boundary layers, planetary boundary layers in the atmosphere and ocean, convective mixed layers, stable boundary layers; deep ocean turbulence.
Review of theoretical models of ocean circulation, including shallow water, barotropic, quasigeostrophic, and primitive equation models; adjustment times, internal length and time scales; the role of advection, bathymetry and coastlines; global models, basin models, regional models and models of jets, eddies and boundary currents. Review of numerical techniques and problems specific to ocean modeling. Local facilities are used to develop models on remote supercomputers.
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Survey of methods for combining oceanographic observations and observing systems with numerical models of ocean circulation. Topics include: finite-dimensional least squares theory with inequality constraints, optimal interpolation, the representation theory of smoothing; the Kalman smoother and filter; gradient descent methods for minimization; spatial and temporal regularity of filters and smoothers; linear theory of array design; nonlinear optimization, practical assimilation methods.
Physical Oceanography: A Mathematical Introduction with MATLAB
Prereq: Strong background in linear algebra and advanced calculus, geophysical fluid dynamics, numerical modeling of ocean circulation. Theory and applications of satellite remote sensing observations of the ocean with emphasis on strengths and limitations in the measurements. Topics include review of electricity and magnetism, absorption and scattering in the atmosphere radiative transfer , satellite orbital mechanics, measurements of ocean color, infrared remote sensing, microwave radiometry, scatterometry, and satellite altimetry. Subjects of current interest in Physical Oceanography, not covered in depth in other courses.
May be repeated on different topics for credit. Baroclinic instability: linear and nonlinear stability problems; models of Eady and Charney.
Instability of parallel shear flow: linear inviscid theory; Rayleigh's theorem; nonlinear contour dynamics; effects of stratification; Taylor-Rayleigh-Bernard problem; nonlinear models; the Lorenz equations, chaos and strange attractors. Geostrophic turbulence: resonant Rossby wave interactions; energy and enstrophy. Instability of nonparallel flow: Arnold's criteria.
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Fundamentals of wave dynamics applied to geophysical fluids. Hyperbolic waves: linear and nonlinear; characteristics; shock waves. Dispersive waves: linear waves, dispersion relations, group velocity; isotropic and anisotropic dispersion; nonlinear solitary waves. Application to geophysical waves: surface gravity, capillary, internal gravity, Kelvin, planetary, coastal.