Fundamentals of Geophysical Hydrodynamics

Dolzhanskii, F. V.; Gledzer, A. E.; Gledzer, E. B.; Khesin, Boris; Fröhlich, Jürg

doi:10.1007/978-3-642-31034-8

Cited by 30 publications

(28 citation statements)

References 11 publications

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“…computed by linearizing equation (1.4) around u s and calculating its stability with respect to perturbations including three dominant modes, of the stability analysis and the analytical expression for the neutral stability curve, similar in form to that in equation (4.1), can be found in Appendix B ofDolzhansky (2013). The critical Reynolds number Re c = min q Re n (q) and the corresponding critical wavenumber k c = κq c computed using the expression (4.1) can be compared with experimental observations.…”

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confidence: 99%

Bifurcations in a quasi-two-dimensional Kolmogorov-like flow

et al. 2017

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We present a combined experimental and theoretical study of the primary and secondary instabilities in a Kolmogorov-like flow. The experiment uses electromagnetic forcing with an approximately sinusoidal spatial profile to drive a quasi-two-dimensional (Q2D) shear flow in a thin layer of electrolyte suspended on a thin lubricating layer of a dielectric fluid. Theoretical analysis is based on a 2D model (Suri et al. 2014), derived from first principles by depth-averaging the full three-dimensional Navier-Stokes equations. As the strength of the forcing is increased, the Q2D flow in the experiment undergoes a series of bifurcations, which is compared with results from direct numerical simulations of the 2D model. The effects of confinement and the forcing profile are studied by performing simulations that assume spatial periodicity and strictly sinusoidal forcing, as well as simulations with realistic no-slip boundary conditions and an experimentally validated forcing profile. We find that only the simulation subject to physical no-slip boundary conditions and a realistic forcing profile provides close, quantitative agreement with the experiment. Our analysis offers additional validation of the 2D model as well as a demonstration of the importance of properly modelling the forcing and boundary conditions. arXiv:1601.00243v3 [physics.flu-dyn]

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confidence: 99%

Bifurcations in a quasi-two-dimensional Kolmogorov-like flow

et al. 2017

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“…In the Introduction we have noted the problem related to a difference by many orders in the helium-II viscosity coefficient, when using various methods of its measuring. Indeed, when helium-II flows through narrow slots and capillaries (when the flow velocity in the capillary with a diameter 10 -5 cm may be approximately several centimeters per second) the measured viscosity value does not exceed 10 -11 poise, and when we observe a decay velocity of the torsional axial oscillation of the disc in helium II we obtain the viscosity value variation from h (see [24,25]) when the value is extremely small for helium II.…”

Section: The Oscillation Of the Disc In Helium II And The Dcimentioning

confidence: 68%

“…Thereupon, in the second paragraph of the present paper it is offered to take into account the effects of the linear Eckman friction for interpretation of the vortex formation mechanism in the rotating helium-II on the basis of the DCI realization, that is considered in [4,14] and the first paragraph herein in connection with the cyclone-anticyclone asymmetry. At the same time, a consideration of the process of the vortex formation in the rotating helium -II, that is an alternative to the two-fluid theory, may be accepted, when it becomes reasonable to take into account even extremely low values of kinematic 6 viscosity coefficient  in helium -II, the order of magnitude of which is c см / 10 10   с for a certain rotation frequency range [24,25]. It should be also noted that paper [16] also shows the presence of a relationship between an effect of the linear (by a difference in velocities between the normal and the superfluid component) friction and the helium-II rotation frequency, where the friction is characterized by a coefficient proportional to the vessel rotation frequency 0  .…”

Section: Linear (Eckman) Friction In Rotating Superfluid Helium-iimentioning

confidence: 99%

Linear Eсkman friction in the mechanism of the cyclone-anticyclone vortex asymmetry and in a new theory of rotating superfluid

Chefranov¹

2014

Cardiometry

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The observed experimental and natural phenomenon of cyclone-anticyclone vortex asymmetry implies that a relatively more stable and showing a longer life, as well as a relatively more intense mode of rotation with an anticyclonic circulation direction (opposite to the direction of rotation of the medium as a whole) is realized as compared with an oppositely directed rotation of the cyclonic vortex mode. Until now, however, it was not a success to identify a universal triggering mechanism responsible for the formation of the corresponding breaking of chiral vortex symmetry, but, as the laboratory experiments show, such a mechanism should be closely interconnected with the presence of the rotation of the medium as a whole. In this paper we reveal the said linear universal instability mechanism of breaking of chiral symmetry in the sign of vortex circulation in the rotating medium in the presence of linear Eckman friction. Obtained is a condition for the linear dissipative -centrifugal instability (DCI), which leads (only when considering the external linear Eckman friction for an above-threshold value of rotation frequency of the underlying boundary surface of fluid) to the breaking of chiral symmetry in the Lagrangian fluid particle dynamics and the corresponding realization of the cyclone-anticyclone vortex asymmetry. The condition for the DCI is found by considering such a generalization of the Kármán classic solution where the effect of linear external friction is taken into account. A new non-stationary solution to the problem for the disc which carries out weak axial-torsional oscillations in fluid in connection with the experimental data on the rotating superfluid helium-II has been found.

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“…where g is the gravitational acceleration, V r and V ϕ are the velocity components of the fluid V = (V r , V ϕ ), S(r, ϕ, t) is the height of the free surface over a certain reference level, and H(r, ϕ, t) is the water depth. This set of equations conserves the potential vorticity (PV) [34]:…”

Section: Conditionsmentioning

confidence: 99%

Scattering of surface shallow water waves on a draining bathtub vortex

Churilov

Stepanyants

2019

Phys. Rev. Fluids

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In the linear approximation we study long wave scattering on an axially symmetric flow in a shallow water basin with a drain in the center. Besides of academic interest, this problem is applicable to the interpretation of recent laboratory experiments with draining bathtub vortices, description of wave scattering in natural basins, and also can be considered as the hydrodynamic analogue of scalar wave scattering on a rotating black hole in general relativity. The analytic solutions are derived in the lowfrequency limit to describe both pure potential perturbations (surface gravity waves) and perturbations with nonzero potential vorticity. For the moderate frequencies the solutions are obtained numerically and illustrated graphically. It is shown that there are two processes governing the dynamics of surface perturbations, the scattering of incident gravity water waves by a central vortex, and emission of gravity water waves stimulated by a potential vorticity. Some aspects of their synergetic actions are discussed.

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Fundamentals of Geophysical Hydrodynamics

Cited by 30 publications

References 11 publications

Bifurcations in a quasi-two-dimensional Kolmogorov-like flow

Bifurcations in a quasi-two-dimensional Kolmogorov-like flow

Linear Eсkman friction in the mechanism of the cyclone-anticyclone vortex asymmetry and in a new theory of rotating superfluid

Scattering of surface shallow water waves on a draining bathtub vortex

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