Fundamentals Of Geophysical Fluid Dynamics Part 4 pptx

... f 2 η 0 = gf c 2 η 0 , (4. 44) using the relations following (4. 26), the modal form (4. 29), and the dis- persion relation (4. 37). A linearized approximation of q from (4. 24) is q − f H = f + ζ H ... ∂ 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. 52)- (4....

Ngày tải lên: 09/08/2014, 11:21

... side of (6.58) for the particular choice of the bottom-drag coefficient,  bot = Hf 0  E 2 =  ν e f 0 2 , consistent with (6.33) and (6 .44 ). 6.2 Oceanic Wind Gyre and Western Boundary Layer 247 = ... depth-averaged 256 Boundary-Layer and Wind-Gyre Dynamics f 0 = 10 4 s −1 (at 45 o N) , β = 2 ×10 −11 m −1 s −1 , τ 0 = 0.1 N m −2 = ρ o × 10 4 m 2 s −2 , h ek, top = 100 m , =⇒ v i...

Ngày tải lên: 09/08/2014, 11:21

... 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 is derived from ... Equation of State: The equation of state for seawater, ρ(T, S, p), is known only by empirical evaluation, usually in the form of a polynomial expansion series in powers of the de...

Ngày tải lên: 09/08/2014, 11:21

... is deferred to the topic of quasigeostrophy in Chap. 4. Now make a scaling analysis in which the magnitudes of various fields are estimated in terms of the typical magnitudes of a few primary quan- tities ... diagnos- tic relation like (3 .41 ) or (3 .42 ), it is said to have a balanced dynamics and, by implication, exhibits fewer temporal degrees of freedom than allowed by the m...

Ngày tải lên: 09/08/2014, 11:21

... 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 sensitive dependence of the solution ... (3.1 14) with KE(k) = 1 2 k 2 S, Ens(k) = 1 2 k 4 S = k 2 KE(k) . (3.115) The latter relations are a consequence of the spatial gradient of ψ having a Fourier transform equal to t...

Ngày tải lên: 09/08/2014, 11:21

... (4. 85) This can be verified by substituting (4. 85) into (4. 84) and by using (4. 83) to evaluate the time derivatives of u and h. The characteristic equation (4. 84) has a general solution, γ = Γ(ξ), for ... propaga- tion of a Kelvin wave along an eastern boundary (Fig. 4. 14) . The Kelvin 158 Rotating Shallow-Water and Wave Dynamics vorticity equation (4. 1 14) is R = βv u · ∇∇∇ζ ∼...

Ngày tải lên: 09/08/2014, 11:21

... (5. 64) the instability is equally strong for either sign of U (i.e., eastward or westward vertical shear). The smallest value for P(K) occurs when 0 = ∂P ∂K 4 = 4U 2 (K 4 − R 4 ) + 4U 2 K 4 , ... (K 2 + R −2 ) = β 2 R 4 + 4U 2 K 4 (K 4 − R 4 ) . (5. 64) Note that β tends to stabilize the flow because it acts to make P more positive and thus reduces the magnitude of Imag [...

Ngày tải lên: 09/08/2014, 11:21

... 135 o to the left of the interior wind. The oceanic layer (right) has a surface current, u o (z), directed 45 o to the right of the surface stress, τττ s (which itself is 45 o to the left of the interior ... 0 Fig. 5.18. Sketch of radiating Rossby waves from a zonal strip of transient forc- ing, F ∗ (x, y, t) (shaded area); the pattern of Rossby wave crests and troughs (i.e.,...

Ngày tải lên: 09/08/2014, 11:21

... 129, 131, 133, 173, 179, 189, 190, 207, 2 14, 2 24, 242 , 258, 2 74 streakline, 23 streamfunction, 34, 61, 67, 172, 244 , 247 , 2 64 streamline, 22, 61, 64, 2 64 stretching vorticity, 176 sub-mesoscale ... 129, 131, 133, 141 , 190, 2 14 roughness length, 241 salinity, 27, 37, 42 , 54 scale analysis, 24, 33, 50, 61, 75, 152, 218, 241 , 243 , 266, 270, 275 scale height, 47 second law...

Ngày tải lên: 09/08/2014, 11:21