Note on a class of exact solutions in magneto-hydrodynamics

LIN, C. C.

doi:10.1007/bf00298016

Cited by 99 publications

(44 citation statements)

References 1 publication

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“…I f steady-state flow is assumed, the equations reduce further to a set of ordinary non-linear differential equations. This was first shown by LIN (1958) in connection with the motion of an electrically conducting fluid in a magnetic field. Lin's development is equally applicable to geophysical problems where the Coriolis forces appear due to the earth's rotation.…”

Section: Introductionmentioning

confidence: 80%

The structure of the Ekman layer for geostrophic flows with lateral shear

Benton

Lipps

Tuann

1964

TellusA

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A generalized Ekman flow is obtained for the boundary layer of a semi-infinite, rotating homogeneous fluid with lateral variation in the horizontal velocity components far from the boundary surface. The fields of motion considered include uni-directional motion with lateral shear, symmetric and elongated eddies, and cols. A solution for the first of these cases is obtained to fifth order: for the others, t o second order. In all cases the magnitude of the vertical velocities induced by convergence in the boundary layer is greater for systems with negative relative vorticity than for systems with positive relative vorticity. The result differs substantially from first-order theory, for which the magnitude of the vertical velocity is proportional to the relative vorticity. A number of meteorological applications are considered.

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Section: Introductionmentioning

confidence: 80%

The structure of the Ekman layer for geostrophic flows with lateral shear

Benton

Lipps

Tuann

1964

TellusA

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“…In this article we concentrate only on this mode from now on by replacing A Ã 0 and É Ã 0 by A 0 sin and É 0 sin and address other possibilities in the future. Even though Lin (1958) suggested such solutions as a form of exact solution of the MHD equations, this has not previously been used for the reconnection problem, as far as we are aware. There are eight natural boundary conditions that we impose, namely, B ¼ v ¼ 0 at the origin and B ¼ B e and v ¼ v e at the external point ðR, , zÞ ¼ ð1, =2, 0Þ or, in terms of the flux function and stream function,…”

Section: Proposed New Solutionsmentioning

confidence: 94%

Exact Solutions for Spine Reconnective Magnetic Annihilation

Mellor

Priest

Titov

2002

Geophysical & Astrophysical Fluid Dynamics

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Solutions for spine reconnective annihilation are presented which satisfy exactly the three-dimensional equations of steady-state resistive incompressible magnetohydrodynamics (MHD). The magnetic flux function (A) and stream function ðÉÞ have the formin terms of cylindrical polar coordinates ðR, , zÞ. First of all, two non-linear fourth-order equations for A 1 and É 1 are solved by the method of matched asymptotic expansions when the magnetic Reynolds number is much larger than unity. The solution, for which a composite asymptotic expansion is given in closed form, possesses a weak boundary layer near the spine (R ¼ 0). These solutions are used to solve the remaining two equations for A 0 and É 0 . Physically, the magnetic field is advected across the fan separatrix surface and diffuses across the spine curve. Different members of a family of solutions are determined by values of a free parameter ðÞ and the components ðB Re , B ze Þ and ðv Re , v ze Þ of the magnetic field and plasma velocity at a fixed external point ðR, , zÞ ¼ ð1, =2, 0Þ, say.

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“…Let i2 be the constant angular velocity of the disk, wo the constant normal velocity of the fluid at the disk and Uo cos cot, the velocity of the oscillating free stream. Following Von Khrm~n [1] and Lin [13], the velocity components (u, v, w) and the pressure p are chosen in the form ] u = ~ 2 d71 yG(rl) + UoHl(rl)e ior, where I / = z (~2/v) 1/2 , r = 12t, 13 = 6o/~2. The physical quantities p and u are the density and kinematic coefficient of viscosity of the fluid.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…13, it is appropriate to expand the function in the form (hi, h 2 , f l , f 2 ) = ~ (i13)-n/2 (hln ' h2n, fln, f2n).…”

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confidence: 99%

Flow due to an oscillatory free stream past a porous rotating disk

Purushothaman

Rajagopalan

1983

J Eng Math

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The effects of constant suction or injection of a homogeneous viscous fluid on the oscillatory flow past a porous disk are studied. Due to the oscillatory free stream, a secondary flow with the tangential components of velocity alone is produced. Separate solutions for low and high frequencies of oscillation are obtained. The streamwise and crosswise components of the oscillatory flow are obtained by choosing suitable forms for the low-and high-frequency oscillations. Expressions for the correction to the shearing stress at the surface due to the secondary flow are presented.

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Note on a class of exact solutions in magneto-hydrodynamics

Cited by 99 publications

References 1 publication

The structure of the Ekman layer for geostrophic flows with lateral shear

The structure of the Ekman layer for geostrophic flows with lateral shear

Exact Solutions for Spine Reconnective Magnetic Annihilation

Flow due to an oscillatory free stream past a porous rotating disk

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