Fundamentals Of Geophysical Fluid Dynamics Part 5 docx

... interfaces is w n+ .5 = Dη n+ .5 Dt , n = 1, . . . , N − 1 . (5. 22) And the buoyancy field is b n+ .5 = − 2g  n+ .5 H n + H n+1 η n+ .5 , n = 1, . . . , N − 1 . (5. 23) Because of the evident similarity ... geopotential function is g  n+ .5 η n+ .5 = φ n+1 − φ n , n = 1, . . . , N − 1 , (5. 20) and g  n+ .5 = g ρ n+1 − ρ n ρ 0 (5. 21) is the reduced gravity for the interface n +...

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... thin, insofar as their L is larger than the depth of the ocean (≈ 5 km) or height of the troposphere (≈ 10 km). This is demonstrated with a scale analysis of the vertical component of the momentum ... L, is sufficiently small, 2.1 Fluid Dynamics 29 2.1.4 Energy Conservation The principle of energy conservation is a basic law of physics, but in the context of fluid dynamics...

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... Vortex Dynamics The primed summation again excludes all terms with α = β. As is often true in Hamiltonian mechanics, H is interpreted as the energy of the system. In 2D dynamics the only type of ... the equations of motion. These quantities are point-vortex counterparts of the vorticity centroid,  xζ dx, and angular momentum,  r 2 ζ dx, in- tegral invariants of conservative...

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... mode odd mode 0 1.0 2.0 0 1.0 2.0 1.0 0 .5 0. 15 0.10 0. 05 c r kL 0 Fig. 3.12. Eigenvalues for the barotropic instability of the Bickley Jet: (a) the real part of the zonal phase speed, c r , and (b) ... forcing of the flow. The common means of representing the scale distribution of a field is through its Fourier transform and spectrum. For example, the Fourier 3.6 Emergence...

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... speed. Thus, the dynamics of a Kelvin wave is a hybrid combination of the influences of rotation and stratification. The ocean is full of Kelvin waves near the coasts, generated as part of the response ... ∂ x v H 0 + η , (4 .56 ) from (4.24). The other parcel invariants that are functionally related to these pri- mary ones (e.g., Q n for any n from (4. 25) ) are redundant with (4...

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... the other dependent variables, because the linear partial differential equations in (5. 55) have constant coeffi- cients. Inserting (5. 56) into (5. 55) and factoring out the exponential function gives (C ... across the layer interfaces. This process is represented by D n+ .5 , defined by D n+ .5 = φ n+ .5 ∂η n+ .5 ∂x = −f 0 v g,n+ .5 η n+ .5 . (5. 87) There is an obvious isomorphism with D...

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... without loss of generality, been presumed to 6.1 Planetary Boundary Layer 2 15 5 10 15 20 0 1 2 3 0900 1030 1200 1330 Virtual potential temperature, C Height AGL, km 0 5 10 15 20 25 0 1 2 3 Water ... yields v a, 1 = − D 1 .5 f 0 H 1 v a, n = D n− .5 − D n+ .5 f 0 H n , 2 ≤ n ≤ N −1 v a, N = D N− .5 − D bot f 0 H N . (5. 94) From the structure of the D n+ .5 (y) in Fig. 5. 17,...

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... in three different layers with mean depths of 150 , 850 , and 1 750 m (in rows) from an 8-layer model of a double wind-gyre at two different times 60 days apart (in columns). Note the meandering separated ... the x, z integrals of v) of the boundary-layer and Sverdrup circulations are in balance at every latitude. 252 Boundary-Layer and Wind-Gyre Dynamics Grouping the terms in powers...

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... 258 General Circulation Model, 54 , 1 05, 209, 216, 2 25, 2 35 geophysical fluid dynamics (GFD), 15, 24, 27, 28, 32, 66, 1 05, 117, 157 , 256 , 262, 263 geopotential function, 37, 53 , 59 , 60, 100, 167, 171 geopotential ... gyre, 262, 2 75 rectification, 209, 273 reduced gravity, 120, 167, 171 regime diagram, 183 resting state, 32, 45, 1 25, 1 45, 168, 258 , 2 65, 266 Reynolds num...

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