Accession Number : AD0902388

Title :   The Deformation of a Turbulent Field by an Inviscid, Mean Fluid Motion with Application to the Flow Around a Body.

Descriptive Note : Technical rept.,

Corporate Author : NAVAL UNDERWATER SYSTEMS CENTER NEWPORT RI

Personal Author(s) : Massey, Alan T. ; Goodman, Louis

Report Date : 01 AUG 1972

Pagination or Media Count : 36

Abstract : It is shown that for the steady, incompressible fluid motion around an arbitrarily shaped body the contravariant components of the velocity within the deformed region around the body are linearly related to the contravariant velocity components within the undeformed region far from the body; or equivalently, that if the motion is considered as a change of coordinates the velocity components follow the law for transformation of the contravariant components of a vector. From the Cauchy vorticity formula, the contravariant components of the vorticity covariance tensor for a turbulent field, superimposed on and advected and rapidly deformed by the mean motion around the body, are found to be linearly related to the vorticity covariance components for the undeformed field of turbulence. Finally, it is shown that a similar relationship applies to the contravariant components of the turbulent velocity covariance tensor. The transformation coefficients are found to be equal to the coefficients relating the spatial and material descriptions of the motion. The transformation coefficients are calculated for the two-dimensional problem of a source in a uniform stream. (Author)

Descriptors :   (*FLOW FIELDS, GEOMETRIC FORMS), (*CYLINDRICAL BODIES, FLOW FIELDS), BODIES OF REVOLUTION, INCOMPRESSIBLE FLOW, TURBULENCE, VISCOSITY, VORTICES, VELOCITY, TWO DIMENSIONAL FLOW, PARTIAL DIFFERENTIAL EQUATIONS, DEFORMATION, TRANSFORMATIONS(MATHEMATICS), COMPUTER PROGRAMS, FLOW VISUALIZATION, EQUATIONS OF MOTION, MATHEMATICAL MODELS, NUMERICAL METHODS AND PROCEDURES, AERODYNAMIC CONFIGURATIONS, INTEGRAL EQUATIONS.

Subject Categories : Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE