Excitation of surface waves in magnetohydrodynamics

1990 ◽  
Vol 43 (2) ◽  
pp. 183-188 ◽  
Author(s):  
Bhimsen K. Shivamoggi
Keyword(s):  
Magnetic Field ◽  
Gravitational Field ◽  
Asymptotic Behaviour ◽  
Pressure Distribution ◽  
Surface Waves ◽  
Initial Value Problem ◽  
Large Time ◽  
Far Field ◽  
Two Dimensional ◽  
Initial Value

A study is made of the transient development of two-dimensional linearized surface waves generated by a localized steady pressure distribution on the interface between a uniformly streaming, semi-infinite, infinitely conducting plasma subjected to a gravitational field and the confining vacuum magnetic field. The linearized equations associated with an initial-value problem are used to obtain the large-time asymptotic behaviour of the disturbance in the far field.

scholarly journals The influence of circulation on the stability of vortices to mode-one disturbances

1995 ◽  
Vol 451 (1943) ◽  
pp. 747-755 ◽  
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Initial Value Problem ◽  
Large Time ◽  
Asymptotic Methods ◽  
Two Dimensional ◽  
Initial Value ◽  
The Stability ◽  
Ultimate Fate ◽  
Solution Behaviour

The initial value problem for the two-dimensional inviscid vorticity equation, linearized about an azimuthal basic velocity field with monotonic angular velocity, is solved exactly for mode-one disturbances. The solution behaviour is investigated for large time using asymptotic methods. The circulation of the basic state is found to govern the ultimate fate of the disturbance: for basic state vorticity distributions with non-zero circulation, the perturbation tends to the steady solution first mentioned in Michalke & Timme (1967), while for zero circulation, the perturbation grows without bound. The latter case has potentially important implications for the stability of isolated eddies in geophysics.

Large-time behaviour of solutions of Burgers' equation

2002 ◽  
Vol 132 (4) ◽  
pp. 843-878 ◽  
Author(s):  
Daniel B. Dix
Keyword(s):  
Initial Data ◽  
Asymptotic Behaviour ◽  
Initial Value Problem ◽  
Large Time ◽  
Burgers Equation ◽  
Time Behaviour ◽  
Initial Value ◽  
Large Time Behaviour ◽  
Image Position ◽  
Sharp Error

The large-time asymptotic behaviour of real-valued solutions of the pure initial-value problem for Burgers' equation ut + uuxuxx = 0, is studied. The initial data satisfy u0(x) ~ nx as |x| , where n R. There are two constants of the motion that affect the large-time behaviour: Hopf considered the case n = 0 (i.e. u0L1(R)), and the case sufficiently small was considered by Dix. Here we completely remove that smallness condition. When n < 1, we find an explicit function U(), depending only on and n, such that uniformly in . When n 1, there are two different functions U() that simultaneously attract the quantity t12u(t12, t), and each one wins in its own range of . Thus we give an asymptotic description of the solution in different regions and compute its decay rate in L. Sharp error estimates are proved.

scholarly journals Transient development of gravity waves for two layered fluids

1992 ◽  
Vol 15 (2) ◽  
pp. 333-338 ◽  
Author(s):  
A. H. Essawy ◽  
M. S. Faltas
Keyword(s):  
Free Surface ◽  
Asymptotic Analysis ◽  
Gravity Waves ◽  
Initial Value Problem ◽  
Large Time ◽  
Generalized Functions ◽  
Incompressible Fluids ◽  
Initial Value ◽  
Wave Maker

The transient gravity waves generated by a harmonically oscillating wave maker immersed in two incompressible fluids, the upper fluid having a free surface, is considered. The resulting linearized initial value problem is solved using the method of generalized functions, and asymptotic analysis for large time and distance are given for the elevation.

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