Generation of Periodic Motions by a Disk Performing Torsional Oscillations in a Viscous, Continuously Stratified Fluid

Il'inykh, Yu. S.; Chashechkin, Yu. D.

doi:10.1023/b:flui.0000024820.93509.45

Cited by 4 publications

(1 citation statement)

References 6 publications

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“…A comprehensive list of references, especially for stratified fluids, can be found in Voisin (2003) and Voisin, Ermanyuk & Flór (2011). The case of the disk has been considered in numerous works, for steady displacements in a rotating fluid (Stewartson 1957;Moore & Saffman 1969; Vedensky & Ungarish 1994; Tanzosh & Stone 1995), for oscillating displacements in a stratified fluid (Il'inyhk & Chashechkin 2004;Bardakov, Vasil'ev & Chashechkin 2007;Davis & Llewellyn Smith 2010) or for more complicated surface fluctuations (Walton 1975;Kerswell 1995). The method of resolution is based on the use of the Hankel transform, which leads to a system of dual integral equations.…”

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Wave field and zonal flow of a librating disk

Dizès

2015

J. Fluid Mech.

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In this work, we provide a viscous solution of the wave field generated by librating a disk (harmonic oscillation of the rotation rate) in a stably stratified rotating fluid. The zonal flow (mean flow correction) generated by the nonlinear interaction of the wave field is also calculated in the weakly nonlinear framework. We focus on the low dissipative limit relevant for geophysical applications and for which the wave field and the zonal flow exhibit generic features (Ekman scaling, universal structures, etc.). General expressions are obtained which depend on the disk radius a * , the libration frequency ω * , the rotation rate Ω * of the frame, the buoyancy frequency N * of the fluid, its kinematic diffusion ν * and its thermal diffusivity κ * . When the libration frequency is in the inertia-gravity frequency interval (min(Ω * , N * ) < ω * < max(Ω * , N * )), the presence of conical internal shear layers is observed in which the spatial structures of the harmonic response and of the mean flow correction are provided. At the point of focus of these internal shear layers on the rotation axis, the largest amplitudes are obtained: the angular velocity of the harmonic response and the mean flow correction are found to be O(εE −1/3 ) and (ε 2 E −2/3 ) respectively, where ε is the libration amplitude and E = ν * /(Ω * a * 2 ) is the Ekman number. We show that the solution in the internal shear layers and in the focus region is at leading order the same as that generated by an oscillating source of axial flow localized at the edge of the disk (oscillating Dirac ring source).

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confidence: 99%

Wave field and zonal flow of a librating disk

Dizès

2015

J. Fluid Mech.

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A Regular System of Vortices in a Circular Stratified Flow Behind the Edge of a Rotating Disk

Bardakov

2018

Springer Geology

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Basic properties of free stratified flows

2006

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Results of analytical studies of the governing equations of stratified rotating fluids based on the unification of theories of continuous and discrete groups, perturbations and modern numerical visualizations are described. Symmetries of basic systems and their simplified versions, different approximations and constitutive turbulent models are compared. A new method to calculate discrete groups analytically, which does not need a preliminary search for continuous groups, is developed. As an example of the practical use of the developed algorithm, a complete classification of cellular and roll structures of Bénard convection is presented. A complete classification of 3D periodic motions in compressible viscous stratified and rotating fluids, including regular (wave) and singular elements, is performed by perturbation methods. In all cases, in a viscous fluid, besides waves there are two different periodic boundary layers. In a homogeneous fluid the split boundary layers are merged, thus forming a joint doubly-degenerate structure. Stratification and rotation reduce the degeneration of the 3D periodic boundary layers. Calculations of a 3D periodic wave beam emitted by an oscillating part of a sloping plane are visualized by a computer-graphics method. The existence of thin extended components on the edges of the 3D wave cone is demonstrated.

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Generation of Periodic Motions by a Disk Performing Torsional Oscillations in a Viscous, Continuously Stratified Fluid

Cited by 4 publications

References 6 publications

Wave field and zonal flow of a librating disk

Wave field and zonal flow of a librating disk

A Regular System of Vortices in a Circular Stratified Flow Behind the Edge of a Rotating Disk

Basic properties of free stratified flows

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