= Solution
Let the mean streamwise <velocity> be $U(y)$ and set $S=dU/dy>0$. The relevant covariance is $\overline{u'v'}<0$ on this half of the channel. The work of the <Reynolds stress> against the mean <shear rate> gives
$$
\boxed{\mathcal P=-\overline{u'v'}\frac{dU}{dy}.}
$$
The <eddy viscosity> relation is $-\overline{u'v'}=\nu_T S$, so
$$
\boxed{\nu_T=\frac{-\overline{u'v'}}{dU/dy},\qquad\mathcal P=\nu_T\left(\frac{dU}{dy}\right)^2.}
$$
These are the kinematic-stress conventions, with the covariance measured per unit mass; inserting a stress measured in force per area would require division by <mass density>.
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