Variational principles of fluid mechanics and electromagnetism: imposition and neglect of the Lin constraint

Thesis/Dissertation · Thu Jan 01 04:00:00 EST 1987

OSTI ID:6967062

Allen, Jr, R R

The Lin constraint has been utilized by a number of authors who have sought to develop Eulerian variational principles in both fluid mechanics and electromagnetics (or plasmadynamics). This dissertation first reviews the work of earlier authors concerning the development of variational principles in both the Eulerian and Lagrangian nomenclatures. In the process, it is shown whether or not the Euler-Lagrange equations that result from the variational principles are equivalent to the generally accepted equations of motion. In particular, it is shown in the case of several Eulerian variational principles that imposition of the Lin constraint results in Euler-Lagrange equations equivalent to the generally accepted equations of motion, whereas neglect of the Lin constraint results in restrictive Euler-Lagrange equations. In an effort to improve the physical motivation behind introduction of the Lin constraint, a new variational constraint is developed based on teh concept of surface forces within a fluid. Additionally, it is shown that a quantity often referred to as the canonical momentum of a charged fluid is not always a constant of the motion of the fluid; and it is demonstrated that there does not exist an unconstrained Eulerian variational principle giving rise to the generally accepted equations of motion for both a perfect fluid and a cold, electromagnetic fluid.

• Research Organization: Utah State Univ., Logan (USA)
• OSTI ID: 6967062
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
640430 -- Fluid Physics-- Magnetohydrodynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FLUID MECHANICS
HYDRODYNAMICS
LAGRANGE EQUATIONS
MAGNETOHYDRODYNAMICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
SURFACE FORCES
VARIATIONAL METHODS