Reynolds Stress tensor
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.
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.
vec2scal, subaverf, statf.
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