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, P.G.: The instability ... of these rings andlead to their splitting into two or three parts [3].3 Oceanic Vortices 69flow exiting in the South Indian Ocean forms Teddies (throughflow eddies) and the Loop Current in the...

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, ... . 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 Hyperbolic Instability 46 2 .4 The Zigzag Instability ... 127 4. 4 Continuously Stratiﬁed Rectilinear Fronts . . . 128 4. 4.1 Lagrangian Approach in the Case of Continuous Stratiﬁcation 128 4. 4.2 Existence and Uniqueness of the Adjusted State in the Unbounded...

The Lecture Notes in Physics Part 2 pps

... reveal the turbulent region during the forcing by the spinning sphere and the more smoothdensity structure soon after the forcing is stopped. Vortices produced in this way(either with the spinning ... densityperturbation 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 not in balance with the radialdensity ... stratiﬁcation within the conﬁning cylinder, with a relatively sharp interfacebetween the upper and the lower layers. During the subsequent evolution of the vortex after removing the cylinder, this...

The Lecture Notes in Physics Part 3 ppsx

... 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 normalto the osculating ... Lamb–Oseen vortex. In the frame rotating with the vortex core, the strain field rotates at the angularspeed −ζ/2 and since the elliptic deformation is a mode m = 2, the fluid in the coreof the vortex ... vorticity, ζ, the streamlinesare hyperbolic as shown in Fig. 2.8 and the continuous stretching along the unsta-ble manifold of the stagnation point of the flow induces instability. The instabilityFig....

The Lecture Notes in Physics Part 5 ppsx

... version of these theorems was presented in Sect. 3.2.2. In the quasi-geostrophic framework, these theorems state that even in the presenceof diabatic heating and frictional or other forces, there ... g∇2h,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 pre-dictions, and in particular ... t)/(2πr)Therefore, the kinetic energy of the vortex K ∼v2rdr will be ﬁnite if the areaintegral of the barotropic vorticity of the vortex is null. This can be achieved in twoways: either...

The Lecture Notes in Physics Part 6 ppt

... to the continuity equation in (4. 1). Equation (4. 6) immediately givesv(x, t) + fX(x, t) = vI(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. The interaction of these vortexsheets ... found in Reznikand Zeitlin [19]. In rotating stratiﬁed ﬂuids the geostrophic balance (the “geostrophic wind” rela-tion) is to be combined with the hydrostatic balance giving the so-called thermalwind...

The Lecture Notes in Physics Part 7 pot

... 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 rewritethem 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 Approach in the Case of ContinuousStratification The ... g(ρ1h1+ ρ2h2). (4. 60) The fast motions in the linear approximation are internal inertia-gravity waves prop-agating along the interface between the layers. By linearizing about the rest stateh1=...

The Lecture Notes in Physics Part 8 pps

... 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 materialloop and therefore we can average (5. 14) by simply averaging the factors multiply-ing the mean line element dx. The ﬁrst term brings in the Lagrangian ... consists of zonal averaging,which is the typical setup in atmospheric wave–mean interaction theory. In this peri-odic case a material line traversing the domain in the zonal x-direction qualiﬁes...

The Lecture Notes in Physics Part 9 pptx

... of the time-integrated mean flow forcing andtherefore to a net lasting change in the mean flow. It is also clear that the net residualforcing 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 indeedpush the vortex to the left ... Longuet–Higgins in [32, 33]. In this theory the flow is periodic in the alongshore directionand, most importantly, the incoming wave forms a slowly varying wavetrain withconstant amplitude in the alongshore...

The Lecture Notes in Physics Part 10 ppsx

... increases the pseudomomentumof the wavepacket, because it compresses the wavepacket in the x-direction whilststretching 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 qLthat occur during dissipation. However, there ... Vertical mixing, energy, and the general circulation of the oceans.Annu. Rev. Fluid Mech. 36, 281–3 14 (20 04) . 141 44 . Zhu, X., Holton, J.: Mean ﬁelds induced by local gravity-wave forcing in the middle...

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