The Lecture Notes in Physics Part 4 potx

... 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 long since been identified in the vicinity ... Fluids. 3, 2 644 (1991). 44 , 53, 54 34. Miyazaki, T.: Elliptical instability in a stably stratified rotating fluid. Phys. Fluids 5, 2702 (1993). 44 , 45 35. Moore, D.W., Saffman,...

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... 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, ... . 40 2.2 In uence of an Axial Velocity Component . . . 41 2.3 Instabilities of a Strained Vortex 43 2.3.1 The Elliptic Instability . . 44 2.3.2 The Hyp...

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... reveal the turbulent region during the forcing by the spinning sphere and the more smooth density structure soon after the forcing is stopped. Vortices produced in this way (either with the spinning ... 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 f...

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... ensured by the choice of the axial velocity of the co-moving frame. Neglecting the torsion, the obtained flow is therefore similar to the one studied previously. Indeed, the normal to the osculating ... Lamb–Oseen vortex. In the frame rotating with the vortex core, the strain field rotates at the angular speed −ζ/2 and since the elliptic deformation is a mode m = 2,...

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... 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 and frictional or other forces, there ... g∇ 2 h, which is the gradient wind balance presented above (further details are available in [100]). The problem of separating these two types of motions in numerical weather p...

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... to the continuity equation in (4. 1). Equation (4. 6) immediately gives v(x, t) + fX(x, t) = v I (x) fx= M(x). (4. 8) By applying the chain differentiation rule to (4. 7) and injecting the result into ... around and behind the vortex: the gradient circling around the vortex forms a trapped zone which shrinks with time, while the trailing front extends behind the vortex. Th...

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... we consider (4. 94a), (4. 94b), (4. 94c), (4. 94d) and (4. 94e) taken between the flat top z = H and bottom z = 0. We rewrite them in the form (4. 107) and introduce the deviations of the particle positions ... centrifugal instability replaces the symmetric (inertial) instability in the axisymmetric case. 4. 4 Continuously Stratified Rectilinear Fronts 4. 4.1 Lagrangian Appro...

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... 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 transformation of the line element ... integration domain is now a mean material loop and therefore we can average (5. 14) by simply averaging the factors multiply- ing the mean line element dx. The first term...

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... of the time-integrated mean flow forcing and therefore to a net 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 ... [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...

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... 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 ... dissipate, then the wavepacket on the left in Fig. 5.9 would simply turn into the dual vortex couple on the right in terms of the structural changes in q L th...

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