The Lecture Notes in Physics Part 3 ppsx

... Neglecting the torsion, the obtained flow is therefore similar to the one studied previously. Indeed, the normalto the osculating plane (so-called binormal) is precessing with respect to the z-axiswith ... Fig. 2.8 and the continuous stretching along the unsta-ble manifold of the stagnation point of the flow induces instability. The instabilityFig. 2.8 Flow around an hyperbolic fixed point50 J M. ... phasemode may be destabilized by the strain due to other vortices.1 Dynamics of Vortices in Rotating and Stratified Fluids 33 1 .3 Concluding Remarks In the preceding sections we have discussed...

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 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 ... For instance, Coriolis forces were neglected throughout, but they can beincorporated both in GLM theory and in the other theoretical developments; this hasbeen done in the quoted references. The ... beaches.J.FluidMech. 449, 31 3 33 9 (2001). 161, 165, 17015. Bühler, O., McIntyre, M.E.: On non-dissipative wave–mean interactions in the atmosphere oroceans. J. Fluid Mech. 35 4, 30 1 34 3 (1998). 141, 142,...

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, ... State in the Unbounded Domain . . 130 4.4 .3 Trapped Modes and Symmetric Instability in ContinuouslyStratiﬁedCase 133 4.5 Conclusions . . 136 References . 136 5 Wave–Vortex Interactions 139 O. ... 402.2 In uence of an Axial Velocity Component . . . 412 .3 Instabilities of a Strained Vortex 43 2 .3. 1 The Elliptic Instability . . 442 .3. 2 The Hyperbolic Instability 462.4 The Zigzag Instability...

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 ... 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 ... Beckers [1]. In these experiments the vorticeswere generated by the tangential-injection method, but now in the annular regionbetween two thin-walled cylinders, thus effectively increasing the steepness...

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 ... 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 ... instance, in the thermocline)and thus their identification and study have been more recent. 3. 1.1.1 Large Rings In general, wind-induced currents are intensified at the western boundaries ofthe...

The Lecture Notes in Physics Part 6 ppt

... shrinks with time,while the trailing front extends behind the vortex. The interaction of these vortexsheets with the vortex still needs mathematical modeling. 3. 3.5 Interaction Between a Vortex ... 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 ... isolated mass anomalies (the isopycnals do not pinch off). Therefore, theyentrain the surrounding fluid and the motion of this fluid must be taken into account. The surrounding fluid advected northward...

The Lecture Notes in Physics Part 7 pot

... 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= ... Plane-Parallel Case4 .3. 1.1 Governing Equations and General Properties of the ModelTo introduce the baroclinic effects in the dynamics in the simplest way we consider the two-layer rotating shallow water ... coor-dinates (M,θ)as independent variables in the Monge–Ampère equation was exten-sively used in the literature, in particular by Cullen and collaborators [5–7]. In (M,θ)coordinates, the thermal...

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 ... the intrinsic frequency ˆω = ω − U · k. It is the intrinsicfrequency that is relevant for the local fluid dynamics relative to the basic flow. In ray tracing only a single branch for the intrinsic ... region. If n = 3 then this fixes the impulse uniquely, but if n = 2then the value of the impulse depends on the location of the coordinate origin unless the net integral of ∇ × u, which is the total...

The Lecture Notes in Physics Part 9 pptx

... 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 ... [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 ... 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 link between wave dissipation and mean flow forcing butthere...

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