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Growth rates for the linearized motion of fluid interfaces away from equilibrium

Growth rates for the linearized motion of fluid interfaces away from equilibrium We consider the motion of a two‐dimensional interface separating an inviscid, incompressible, irrotational fluid, influenced by gravity, from a region of zero density. We show that under certain conditions the equations of motion, linearized about a presumed time‐dependent solution, are wellposed; that is, linear disturbances have a bounded rate of growth. If surface tension is neglected, the linear equations are well‐posed provided the underlying exact motion satisfies a condition on the acceleration of the interface relative to gravity, similar to the criterion formulated by G. I. Taylor. If surface tension is included, the linear equations are well‐posed without qualifications, whether the fluid is above or below the interface. An interesting qualitative structure is found for the linear equations. A Lagrangian approach is used, like that of numerical work such as (3), except that the interface is assumed horizontal at infinity. Certain integral equations which occur, involving double layer potentials, are shown to be solvable in the present case. © 1993 John Wiley & Sons, Inc. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications on Pure & Applied Mathematics Wiley

Growth rates for the linearized motion of fluid interfaces away from equilibrium

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References (35)

Publisher
Wiley
Copyright
Copyright © 1993 Wiley Periodicals, Inc., A Wiley Company
ISSN
0010-3640
eISSN
1097-0312
DOI
10.1002/cpa.3160460903
Publisher site
See Article on Publisher Site

Abstract

We consider the motion of a two‐dimensional interface separating an inviscid, incompressible, irrotational fluid, influenced by gravity, from a region of zero density. We show that under certain conditions the equations of motion, linearized about a presumed time‐dependent solution, are wellposed; that is, linear disturbances have a bounded rate of growth. If surface tension is neglected, the linear equations are well‐posed provided the underlying exact motion satisfies a condition on the acceleration of the interface relative to gravity, similar to the criterion formulated by G. I. Taylor. If surface tension is included, the linear equations are well‐posed without qualifications, whether the fluid is above or below the interface. An interesting qualitative structure is found for the linear equations. A Lagrangian approach is used, like that of numerical work such as (3), except that the interface is assumed horizontal at infinity. Certain integral equations which occur, involving double layer potentials, are shown to be solvable in the present case. © 1993 John Wiley & Sons, Inc.

Journal

Communications on Pure & Applied MathematicsWiley

Published: Oct 1, 1993

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