The particle paths of the Arnold-Beltrami-Childress (ABC) flows \[ u = (A \sin z+ C \cos y, B x + A z, y x). \] are investigated both analytically and numerically. This three-parameter family spatially periodic provides a simple steady-state solution Euler's equations. Nevertheless, streamlines have complicated Lagrangian structure which is studied here with dynamical systems tools. In general, there set closed (on torus, T3) helical streamlines, each surrounded by finite region KAM...

The linear stability of convection in a rapidly rotating sphere studied here builds on well established relationships between local and global theories appropriate to the small Ekman number limit. Soward (1977) showed that disturbance marginal theory necessarily decays with time due process phase mixing (where spatial gradient frequency is non-zero). By implication, critical Rayleigh smaller than true value by an O (1) amount. complementary view mode cannot be embedded consistent WKBJ...

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes data from experiments, measurements, and large-scale simulations at multiple spatiotemporal scales. Machine learning (ML) offers a wealth techniques to extract ...Read More

The correct asymptotic theory for the linear onset of instability a Boussinesq fluid rotating rapidly in self-gravitating sphere containing uniform distribution heat sources was given recently by Jones et al. (2000). Their analysis confirmed established picture that at small Ekman number corrections due to suction outer boundary. All analytic predictions both stress-free and rigid (no-slip) boundaries compare favourably with our full numerics (always Prandtl unity), despite fact very numbers...

We describe a hydromagnetic dynamo utilizing Bénard convection between rotating parallel planes. The model is based upon an asymptotic expansion in two spatial scales valid for large Taylor number.Received 28 July 1972DOI:https://doi.org/10.1103/PhysRevLett.29.837©1972 American Physical Society

A hydromagnetic dynamo model is considered. Boussinesq, electrically conducting fluid confined between two horizontal planes and heated from below. The system rotates rapidly about the vertical axis with constant angular velocity. It supposed that instability first sets in as stationary convection characterized by a small length scale. In preliminary calculations Lorentz force neglected so magnetic induction equation of motion are decoupled. possibility motions occurring at onset may sustain...

Abstract The onset of instability for a self-gravitating, internally heated, fluid sphere radius, r∗0, at large Taylor number, [Ttilde] (a measure the rotation rate), is investigated. pioneering work Roberts (1968) and Busse (1970) has shown that convection concentrated in layer thickness, r∗0[Ttilde]−1/9, which forms cylindrical surface, coaxial with diameter parallel to angular velocity. Inside this layer, Rossby waves short length scale, r∗0 [Ttilde]− 1/6, propagate eastwards. For...

The existence of fast dynamos caused by steady motion an electrically conducting fluid is established consideration a two-dimensional spatially periodic flow: the velocity, which independent vertical coordinate z, finite and continuous everywhere but vorticity infinite at X-type stagnation points. A mean-field model developed using boundary-layer methods valid in limit large magnetic Reynolds number R. field confined to sheets, width order R−½. mean lies uniform on horizontal planes: its...

Abstract Mit Hilfe der Korrelationsapproximation zweiter Ordnung und einer neuen Technik (doppelte Fouriertransformation ‐entwicklung) wird eine Reihe von alten Ergebnissen in Theorie Elektrodynamik gemittelter Felder Magnetohydrodynamik durch systematische allgemeine Ableitung dargestellt. Sie werden Formen gebracht, die Rolle des Helicity‐Spektrums Induktionsprozessen neuem Licht erscheinen lassen. Die Situationen, denen Ergebnisse exakt gültig sind, angegeben. Neue Ausdrücke für...

An asymptotic analysis is made of the magnetic induction equation for certain flows characterized by a large Reynolds number R . A novel feature hybrid approach given to problem. Advantage taken combination Eulerian and Lagrange coordinates. Under conditions problem can be reduced solving pair coupled partial differential equations dependent on only two space coordinates (cf. Braginskii 1964 ). Two main cases are considered. First case examined, in which production azimuthal field from...

In this paper we study advection–diffusion of scalar and vector fields for the steady velocity field \[ (u, v, w) = \left(\frac{\partial \psi}{\partial y},-\frac{\partial\psi}{\partial x},K\psi\right),\quad \psi \sin x y + \delta \cos y. \] If δ > 0 streamlines ψ constant form a periodic array oblique cat's-eyes separated by continuous channels carrying finite fluid flux. problems treated, advection dominates diffusion, are transported both in thin boundary layers within channels. Effective...

Abstract An idealised α2ω-dynamo is considered in which the α-effect prescribed. The additional ω-effect results from a geostrophic motion whose magnitude determined indirectly by Lorentz forces and Ekman suction at boundary. As strength of increased, critical value α∗ c reached dynamo activity sets in; solution kinematic α2-dynamo problem. In neighbourhood magnetic field weak order E 1/4(μηρω)½ due to control suction; E(≪1) number. At certain values α∗, viscosity independent solutions are...

The stability of an electrically conducting Boussinesq fluid which is confined between two horizontal planes a distance d apart investigated. heated from below, cooled above and the whole system rotates rapidly with angular velocity Ωc about vertical axis. A weak non-uniform magnetic field, whose strength measured by Alfvén ΩM [[Lt ] Ωc, see (1.2)] permeates corresponds to flow uniform electric current parallel rotation When modified Rayleigh number R [see (2.1)] greater than zero q = κ/λ...

Abstract An axisymmetric αω‐dynamo model of the Galactic disc is investigated. The thin and its width, 2 h * , varies slowly with distance, ωT from axis symmetry. strength α linearly axialdistance, z while differential rotation, dΩ /dωT remains constant. Otherwise are arbitrary functions . results applied to special case oblate spheroid first investigated by S TIX (1976) later W HITE (1977). In limit small aspect ratio new agree those obtained confirm that dynamo numbers computed too small.

The problem of the inward solidification a spherical or cylindrical body molten material, initially at its uniform fusion temperature, when outside is suddenly cooled, considered. A complete asymptotic theory developed for case parameter A, which measures ratio latent heat to sensible substance, large. Uniformly valid approximations solution are found everywhere, all time t*, up instant t* = e ,at material completely frozen. Though many results have been obtained previously, treatment final...

The Petschek model for incompressible reconnexion has been put on a firm mathematical foundation in an earlier paper by Soward & Priest, who discovered ‘local’ similarity solution the process. present extends that analysis to compressible reconnexion, which previous Alfvén waves are replaced slow magneto-acoustic shocks of switch-off type. By contrast with suggestion, it is found unnecessary include intermediate standing ahead shocks. maximum rate typically half Petschek's stated value,...

Journal Article THE LINEAR STRABILITY OF FLOW IN NARROW GAP BETWEEN TWO CONCENTRIC ROTATING SPHERES Get access A. M. SOWARD, SOWARD School of Mathematics, The University, Newcastle upon Tyne Search for other works by this author on: Oxford Academic Google Scholar C. JONES Quarterly Mechanics and Applied Volume 36, Issue 1, February 1983, Pages 19–42, https://doi.org/10.1093/qjmam/36.1.19 Published: 01 1983 history Received: 21 August 1981 Revision received: 20 January 1982