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PIVMat 3.02

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PIVMat 3.02

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27 Apr 2006 (Updated )

A PIV Post-processing and data analysis toolbox

stresstensor (PIVMat Toolbox)
stresstensor (PIVMat Toolbox)
PIVMat Function Reference<< Prev | Next >> 
stresstensor
Reynolds Stress tensor

Description
T = stresstensor(V) returns a 3x3 matrix T containing the 6 components 
of the stress tensor computed from the 3-components velocity fields V 
(if V is a 2-components velocity field, T is a 2x2 matrix only). 
 
T is defined as:  T(i,j) = <u_i u_j>, where <.> denotes spatial and 
ensemble average (note that the minus sign in the usual definition is 
NOT included here). This definition assumes that the fields are 
statistically homogeneous (use vec2scal(V, 'uiuj') to obtain the 
spatial distribution of the stress tensor for non-homogeneous fields). 
 
Careful: this function does NOT substract the ensemble average. 
This has to be done before calling stresstensor: 
  T = stresstensor(subaverf(V,'e')); 
 
[T,B] = stresstensor(V) also returns the deviatoric tensor B, defined 
as B(i,j) = T(i,j)/trace(T) - delta(i,j)/C,  where delta(i,j) is the 
Kronecker (unity) tensor and C the number of components (2 or 3). 
For isotropic flow, all elements of B must be zero. 
 
Properties: 
  T is a symmetric matrix: T(i,j) = T(j,i). 
  The kinetic energy (per unit mass) is given by 2*trace(T). 
  For isotropic flow, T is proportional to the identity matrix. 
  For axisymmetric flow, T is diagonal with two identical elements. 
 
See Also
vec2scal, subaverf, statf. 
 
Published output in the Help browser 
   showdemo stresstensor 

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