The Lecture Notes in Physics Part 2 pps
The Lecture Notes in Physics Part 2 pps
... corresponding with the density perturbation introduced in case 1, with the resultant circulation sketched in (b). The resulting cir- culation arising in case 2, in which the centrifugal force is initially ... stratification within the confining cylinder, with a relatively sharp interface between the upper and the lower layers. During the subsequent evolution of the vo...
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The Lecture Notes in Physics Part 3 ppsx
... > 2 and 2 < RO < 2/ 3orF < 2 and ( Ro < −2orRo > 2/ 3 ) . (2. 16) The instability growth rate is (Kerswell [20 ]) σ = ( 3Ro + 2 ) 2 F 2 − 4 16 F 2 (Ro + 1) 2 − 4Ro 2 . ... ζ, the streamlines are hyperbolic as shown in Fig. 2. 8 and the continuous stretching along the unsta- ble manifold of the stagnation point of the flow induces ins...
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The Lecture Notes in Physics Part 5 ppsx
... 65]. The (more recent) shallow-water version of these theorems was presented in Sect. 3 .2. 2. In the quasi-geostrophic framework, these theorems state that even in the presence of diabatic heating ... t) / (2 r) Therefore, the kinetic energy of the vortex K ∼ v 2 rdr will be finite if the area integral of the barotropic vorticity of the vortex is null. This can be...
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The Lecture Notes in Physics Part 8 pps
... unforced incompress- ible Euler equations in an unbounded domain conserve the impulse. The proof involves time-differentiating (5 .22 ) and using integration by parts together with an estimate of the ... rewriting the contour integral in (5.9) in terms of C, which mathemati- cally amounts to a variable substitution in the integrand. The only non-trivial step is the trans...
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The Lecture Notes in Physics Part 10 ppsx
... increases the pseudomomentum of the wavepacket, because it compresses the wavepacket in the x-direction whilst stretching it in the y-direction. At the same time, the Bretherton flow induced by the ... For instance, Coriolis forces were neglected throughout, but they can be incorporated both in GLM theory and in the other theoretical developments; this has been done...
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The Lecture Notes in Physics Part 1 doc
... co-rotating reference frame The Lecture Notes in Physics The series Lecture Notes in Physics (LNP), founded in 1969, reports new developments in physics research and teaching – quickly and informally, ... Shear Instability . . . . . 40 2. 2 In uence of an Axial Velocity Component . . . 41 2. 3 Instabilities of a Strained Vortex 43 2. 3.1 The Elliptic Instabilit...
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The Lecture Notes in Physics Part 4 potx
... and b = 1 2 Ro + 1 Ro 2 sin 2 θ + 1 Ro + 3 2 cos 2 θ. (2. 52) Parametric resonances occur when α = 1 4 j 2 , (2. 53) with j an integer, giving the formula (2. 14) discussed in Sect. 2. 3.1. References 1. ... resulting in the formation of so-called rings or synoptic eddies. These rings, and in particular the warm-core rings which are surface intensified, have l...
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The Lecture Notes in Physics Part 6 ppt
... vortex in QG models with a single active layer. In the 2D case, the jet breaks up in eddies while in the 1-1 /2 layer case, the jet is stable and long waves develop on the front and advect the vortex ... = r[sin(θ −t) − sin(θ)]=∇ 2 φ − γ 2 φ, where is the rotation rate of the mean flow and γ = 1/R d . The other part is due to the deformation of the vorte...
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The Lecture Notes in Physics Part 7 pot
... h 2 v 2 ) − ∂ ∂x h 1 u 2 1 + h 2 u 2 2 + g(ρ 2 − ρ 1 ) ρ 1 h 1 ∂h 2 ∂x = 0, (4.66) ∂h 2 ∂t + u 2 ∂h 2 ∂x + h 2 ∂u 2 ∂x = 0, (4.67) ∂v 2 ∂t + u 2 ∂v 2 ∂x + fu 2 = 0, (4.68) ∂v 1 ∂t + u 2 ∂v 1 ∂x + (u 1 − u 2 ) ∂v 1 ∂x + ... 131 | |X|,|Z|→∞ = f 2 X 2 2 + N 2 Z 2 2 . (4.1 12) This means that on some distant ellipse (which is a convex curve) f...
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The Lecture Notes in Physics Part 9 pptx
... [8]. Crucially, the Bretherton flow points backward, i.e. in the negative x-direction, at the vortex location above the wavetrain. Therefore the Bretherton flow does indeed push the vortex to the left ... lasting change in the mean flow. It is also clear that the net residual forcing points in the direction of p. So there is no intrinsic link between wave dissipation an...
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