Fundamentals Of Geophysical Fluid Dynamics Part 3 potx

... un- stable (Sec. 3. 3), indicating that the limit of vanishing separation and width is a delicate one. 3. 2.2 Chaos and Limits of Predictability An important property of chaotic dynamics is the ... . (3. 93) Analogous to Sec. 3. 3.1, a Rayleigh necessary condition for instability of a parallel flow can be derived for normal-mode eigensolutions of the form, ψ = Real  Ψ(y)e ik(x...

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... line of 2.28 are essentially equivalent based on the following scale estimates for characteristic magnitudes of the relevant entities: u ∼ V , 36 Fundamental Dynamics (10 3 kg m 3 , 2 83 K (10 ... 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 it...

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... (3. 35) −∇∇∇φ −→ −∇ 2 φ ; (3. 36) f ˆ z ×u −→ ∂ ∂x (−fv) + ∂ ∂y (fu) = −∇∇∇·(f ∇∇∇ψ) ; (3. 37) and F −→ ∇∇∇· F . (3. 38) The result is ∇ 2 φ = ∇∇∇· (f ∇∇∇ψ) + 2J  ∂ψ ∂x , ∂ψ ∂y  + ∇∇∇· F . (3. 39) This ... part of ψ is physically meaningful) and eigenvalues (eigen- frequencies), ω = − β 0 k k 2 +  2 . (3. 33) This can be verified as a solution by substitution into (3. 31). The type of...

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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 ... on the short- and long-wave limits (4 .38 )-(4 .39 ), the second set of modes (4 .37 ) are called inertia-gravity waves, or, in the terminology of Pedlosky (Sec. 3. 9, 1987...

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... cf., Sec. 3. 4), an idealized problem for the statistical equilibrium of a baro- clinic zonal jet is analyzed at the end of the chapter. Of course, there are many other aspects of baroclinic dynamics ... (5. 23) Because of the evident similarity among the governing equations, this N-layer model is often called the stacked shallow-water model. It rep- resents a particular vertica...

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... though the 202 Baroclinic and Jet Dynamics 3 τ s x = n=1 n =3 stress ] −2 s 2 [10 m − 4 stress ] −2 s 2 [10 m − 4 y [10 ]m 6 y [10 ]m 6 u 3 H 1 ∂ y R 1 ∂ y R 3 3 ε bot −D 1.5 D 2.5 H − − − 0 0 1 1 −1 −1 2 2 −2 −2 Fig. ... of vertical basis functions because it assures that the inverse transformation for (5 .30 ) is well defined as ˜ ψ m = Σ N n=1 H n H ψ n G m (n) (5 .33 ) or ˜ ψ m...

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... without loss of generality, been presumed to 6.1 Planetary Boundary Layer 215 5 10 15 20 0 1 2 3 0900 1 030 1200 133 0 Virtual potential temperature, C Height AGL, km 0 5 10 15 20 25 0 1 2 3 Water vapor ... discussed in Secs. 3. 3 -3. 4. The eddy process here is highly non-local, with the eddy generation site (within the jet) distant from 222 Boundary-Layer and Wind-Gyre Dynamics a...

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... value of ν e = . 03 u 2 ∗ f = 0. 13 u ∗ h ∗ . (6.47) The second relation is consistent with widespread experience that eddy viscosity magnitudes diagnosed from the negative of the ratio of eddy flux ... mechanism is a mixture of barotropic and baroclinic types (Secs 3. 3 and 5.2), a relevant oceanic model must also be fully baroclinic. For all of these reasons, the model of a li...

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... drift, 149, 242, 270, 2 73 Stokes’ integral relation, 32 Stommel, Henry, 2 43 strain rate, 32 , 33 , 78 stratification, 36 , 39 , 45, 49, 62, 71, 115, 116, 119, 128, 129, 131 , 133 , 1 73, 179, 189, 190, 207, ... 55, 59, 2 43 Rossby radius, 129, 138 Rossby wave, 73, 155, 181, 2 03, 209, 256, 262, 271, 2 73 Rossby, Carl, 133 rotating coordinates, 57, 266 rotation, 55, 56, 58, 62, 6...

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