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Books on the topic 'Vortex instability'

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Author: Grafiati
Published: 6 September 2023

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1

Hall, Philip. On the Gortler vortex instability mechanism at hypersonic speeds. Hampton, Va: ICASE, 1989.

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2

Hall, Philip. On the Goertler vortex instability mechanism at hypersonic speeds. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1989.

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3

Otto, S. R. On the secondary instability of the most dangerous Gortler vortex. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1993.

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4

P, Bassom Andrew, and Institute for Computer Applications in Science and Engineering., eds. On the instability of Görtler vortices to nonlinear travelling waves. Hampton, Va: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1990.

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5

Otto, S. R. On the secondary instability of the most dangerous Go rtler vortex. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.

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6

Denier, James P. The effect of wall compliance on the Gortler vortex instability. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1990.

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7

Hall, Philip. The inviscid secondary instability of fully nonlinear longitudinal vortex structures in growing boundary layers. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1990.

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8

Michalke, Alfons. A note on the instability of a vortex sheet leaving a semi-infinite plate. Koln: DFVLR, 1987.

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9

Arbic, Brian K. Generation of mid-ocean eddies: The local baroclinic instability hypothesis. Cambridge, Mass: Massachusetts Institute of Technology, 2000.

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10

Arbic, Brian K. Generation of mid-ocean eddies: The local baroclinic instability hypothesis. Cambridge, Mass: Massachusetts Institute of Technology, 2000.

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11

Philip, Hall, and Langley Research Center, eds. Effects of Görtler vortices, wall cooling and gas dissociation on the Rayleigh instability in a hypersonic boundary layer. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1991.

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12

Philip, Hall, and Langley Research Center, eds. Effects of Görtler vortices, wall cooling and gas dissociation on the Rayleigh instability in a hypersonic boundary layer. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1991.

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13

National Aeronautics and Space Administration (NASA) Staff. Initiation of Long-Wave Instability of Vortex Pairs at Cruise Altitudes. Independently Published, 2019.

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14

Vortex instabilities in 3D boundary layers: The relationship between Görtler and crossflow vortices. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1990.

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15

Zeitlin, Vladimir. Instabilities in Cylindrical Geometry: Vortices and Laboratory Flows. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0011.

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Vortex solutions in cyclo-geostrophic equilibrium are described and their geostrophic and ageostrophic barotropic and baroclinic instabilities are studied along the lines of Chapter 10. Special attention is paid to centrifugal instability which, as the inertial instability of jets, is due to modes trapped in the anticyclonic shear in the vortex, and has asymmetric counterparts. Saturation of this instability is shown to exhibit some specific patterns. Instabilities of intense hurricane-like vortices are analysed and shown to be sensitive to fine details of the vortex profile. Nonlinear saturation of such instabilities exhibits typical secondary meso-vortex structures, and leads to intensification of the vortex. Special attention is paid to instabilities in laboratory flows in rotating cylindrical channels. Classification of these instabilities is given, and their nature, in terms of resonances between different wave modes, is established. Rigid-lid and free-surface configuration with topography are considered and compared with experiments.
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16

Zeitlin, Vladimir. Rotating Shallow-Water model with Horizontal Density and/or Temperature Gradients. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0014.

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The derivation of rotating shallow-water equations by vertical averaging and columnar motion hypothesis is repeated without supposing horizontal homogeneity of density/potential temperature. The so-called thermal rotating shallow-water model arises as the result. The model turns to be equivalent to gas dynamics with a specific equation of state. It is shown that it possesses Hamiltonian structure and can be derived from a variational principle. Its solution at low Rossby numbers should obey the thermo-geostrophic equilibrium, replacing the standard geostrophic equilibrium. The wave spectrum of the model is analysed, and the appearance of a whole new class of vortex instabilities of convective type, resembling asymmetric centrifugal instability and leading to a strong mixing at nonlinear stage, is demonstrated.
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17

Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator is studied using an example by Trefethen et al. The integrable models (KdV, Hasimoto’s vortex soliton) and their hamiltonian formalism are studied. Delving into deeper mathematics, geodesics on Lie groups are studied: first using the Lie algebra and then using Milnor’s approach to the curvature of the Lie group. Arnold’s deep idea that Euler’s equations are the geodesic equations on the diffeomorphism group is then explained and its curvature calculated. The next three chapters are an introduction to numerical methods: spectral methods based on Chebychev functions for ODEs, their application by Orszag to solve the Orr–Sommerfeld equation, finite difference methods for elementary PDEs, the Magnus formula and its application to geometric integrators for ODEs. Two appendices give an introduction to dynamical systems: Arnold’s cat map, homoclinic points, Smale’s horse shoe, Hausdorff dimension of the invariant set, Aref ’s example of chaotic advection. The last appendix introduces renormalization: Ising model on a Cayley tree and Feigenbaum’s theory of period doubling.
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