Vortex methods and vortex statistics

Conference · Sat May 01 00:00:00 EDT 1993

OSTI ID:10173312

Chorin, A J

Vortex methods originated from the observation that in incompressible, inviscid, isentropic flow vorticity (or, more accurately, circulation) is a conserved quantity, as can be readily deduced from the absence of tangential stresses. Thus if the vorticity is known at time t = 0, one can deduce the flow at a later time by simply following it around. In this narrow context, a vortex method is a numerical method that makes use of this observation. Even more generally, the analysis of vortex methods leads, to problems that are closely related to problems in quantum physics and field theory, as well as in harmonic analysis. A broad enough definition of vortex methods ends up by encompassing much of science. Even the purely computational aspects of vortex methods encompass a range of ideas for which vorticity may not be the best unifying theme. The author restricts himself in these lectures to a special class of numerical vortex methods, those that are based on a Lagrangian transport of vorticity in hydrodynamics by smoothed particles (``blobs``) and those whose understanding contributes to the understanding of blob methods. Vortex methods for inviscid flow lead to systems of ordinary differential equations that can be readily clothed in Hamiltonian form, both in three and two space dimensions, and they can preserve exactly a number of invariants of the Euler equations, including topological invariants. Their viscous versions resemble Langevin equations. As a result, they provide a very useful cartoon of statistical hydrodynamics, i.e., of turbulence, one that can to some extent be analyzed analytically and more importantly, explored numerically, with important implications also for superfluids, superconductors, and even polymers. In the authors view, vortex ``blob`` methods provide the most promising path to the understanding of these phenomena.

• Research Organization: Lawrence Berkeley Lab., CA (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 10173312
• Report Number(s): LBL-34124; CONF-9306196-1; ON: DE93016974; TRN: 93:017873
• Resource Relation: Conference: Les Houches Summer School of Theoretical Physics,Les Houches (France),28 Jun - 30 Jul 1993; Other Information: PBD: May 1993
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
HYDRODYNAMICS
NUMERICAL SOLUTION
VORTICES
THREE-DIMENSIONAL CALCULATIONS
IDEAL FLOW
TURBULENCE
TWO-DIMENSIONAL CALCULATIONS
INCOMPRESSIBLE FLOW
EQUATIONS OF MOTION
LAGRANGIAN FUNCTION
CONVERGENCE
STATISTICAL MECHANICS
SUPERFLUIDITY
QUANTUM FLUIDS
VORTEX FLOW
DIFFERENTIAL EQUATIONS
VISCOUS FLOW
665000
PHYSICS OF CONDENSED MATTER