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The Lecture Notes in Physics Part 5

Thực tế có một ngành nghiên cứu thuộc lĩnh vực trung gian giữa toán học và vật lý, đó là Vật lý toán - ngành học phát triển các cấu trúc toán học để phục vụ cho các lý thuyết vật lý. | 74 X. Carton can be represented as a stack of homogeneous layers and that vortices are confined in one layer or in a few of these layers. A central property of these models is conservation of potential vorticity in unforced non-dissipative flows. Indeed potential vorticity conjugates many vortex properties internal vorticity relation with planetary vorticity and the vertical stretching of water columns in a single variable. 3.2.1 Primitive-Equation Model The primitive equations are the Navier-Stokes equations on a rotating planet for an incompressible fluid with Boussinesq and hydrostatic approximations. These dynamical equations are complemented with an equation of state for the fluid and with advection-diffusion equations for temperature and salinity in the ocean . They are usually written as -r f v dxp Fx Dx Dt Po Dv 1 fu dyp Fy Dy Dt Po for the two horizontal momentum equations p0 being an average density dzP Pg for the hydrostatic balance P P T S p for the equation of state dxu dy V dz w 0 for the incompressibility equation and DT KT V2 T Ft Dt T T DS KS V2 Dt S S Fs for the temperature and salinity equations T is temperature and S is salinity . The Lagrangian advection is three-dimensional D Dt dt udx vdy wdz. The 3 Oceanic Vortices 75 Coriolis parameter is f 2Q sin 0 where is the rotation rate of the Earth and 0 is latitude g is gravity. Fx Fy and Dx Dy are the forcing and dissipative terms in the horizontal momentum equations and Ft FS are the source terms in the thermodynamics tracer equations. The thermal and salt diffusivities are KT and KS respectively. This system is associated with a set of boundary conditions mechanical thermal and haline forcing at the sea surface interaction with bottom topography and possible lateral forcing via exchanges between ocean basins. Primitive equations conserve potential vorticity in adiabatic inviscid evolutions this potential vorticity has the form n w f k p with w dzv dzu dxv dyU . The primitive equations can be .