Statistics – Computation
Scientific paper
Oct 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981rspsa.378..179l&link_type=abstract
Royal Society (London), Proceedings, Series A - Mathematical and Physical Sciences, vol. 378, no. 1773, Oct. 8, 1981, p. 179-205
Statistics
Computation
22
Barotropic Flow, Computational Fluid Dynamics, Equilibrium Flow, Flow Stability, Inviscid Flow, Steady Flow, Angular Momentum, Circulation, Energy Methods, Euler-Lagrange Equation, Kelvin-Helmholtz Instability, Perturbation Theory, Rotating Bodies, Variational Principles, Velocity Distribution, Vortices
Scientific paper
Theorems are proven which relate the equilibrium and stability of steady flows to the stationary nature of the energy for isocirculational perturbations at fixed angular momentum. Similar principles are also demonstrated for containers forced to rotate at fixed angular velocity. The invariant concepts of the load of a vortex line and the metage of a point on that line are introduced to define the surfaces of a constant load, and it is shown that the content of Kelvin's circulation theorem is contained in the conservation of a certain circular function. A Lagrangian for inviscid barotropic fluid mechanics is shown to yield the fluid equations in Clebsch's form. An energy functional yielding all steady flows as its stationary points is also derived, and its minimization is found to yield stable inviscid barotropic flows.
Katz Jonathan
Lynden-Bell Donald
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