hi pf!
i had an easy question on how to calculate the reynolds stress from the RANS equations. Reynold's Stress is defined as ##\rho \langle v_i v_j \rangle## where ##v_i## is the residual velocity measurement in the ##i## direction.
my question is, how is the reynolds stress actually calculated? for example, suppose we measure velocity only in the x and y directions. let's say we take 4 measurements and find that ##v_1 = 1,2,3,4## and ##v_2=4,5,6,7##.
is the following correct: $$ \langle v_i v_j \rangle = \left| \begin{array}{ccc}
\langle v_1 v_1 \rangle & \langle v_1 v_2 \rangle \\
\langle v_2 v_1 \rangle & \langle v_2 v_2 \rangle \end{array} \right|$$
where ##\langle v_1 v_2 \rangle## would be ##1*4+2*5+3*6+4*7## and hence ##\langle v_1 v_2 \rangle = \langle v_2 v_1 \rangle##
i appreciate all help!
i had an easy question on how to calculate the reynolds stress from the RANS equations. Reynold's Stress is defined as ##\rho \langle v_i v_j \rangle## where ##v_i## is the residual velocity measurement in the ##i## direction.
my question is, how is the reynolds stress actually calculated? for example, suppose we measure velocity only in the x and y directions. let's say we take 4 measurements and find that ##v_1 = 1,2,3,4## and ##v_2=4,5,6,7##.
is the following correct: $$ \langle v_i v_j \rangle = \left| \begin{array}{ccc}
\langle v_1 v_1 \rangle & \langle v_1 v_2 \rangle \\
\langle v_2 v_1 \rangle & \langle v_2 v_2 \rangle \end{array} \right|$$
where ##\langle v_1 v_2 \rangle## would be ##1*4+2*5+3*6+4*7## and hence ##\langle v_1 v_2 \rangle = \langle v_2 v_1 \rangle##
i appreciate all help!
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