= Solution
During a small incompressible displacement $u_i=v_i\Delta t$, pure advection changes the polar field by
$$
\delta p_i=-u_k\nabla_kp_i-\Omega_{ij}[u]p_j+\xi D_{ij}[u]p_j.
$$
The free-energy change is $\delta F=\int h_i\delta p_i,d\mathbf r$, where $h_i=\delta F/\delta p_i$. Integrating the translational term by parts and separating the antisymmetric and symmetric parts of $\nabla_i u_j$ identifies the <order-parameter stress>. Up to an arbitrary isotropic pressure, its three contributions obey
$$
\boxed{\nabla_i\Sigma_{ij}^{(1)}=-p_i\nabla_jh_i},
$$
$$
\boxed{\Sigma_{ij}^{(2)}=\frac12(p_ih_j-p_jh_i)},
\qquad
\boxed{\Sigma_{ij}^{(3)}=\frac\xi2(p_ih_j+p_jh_i)}.
$$
The first term is the distortion or Ericksen force density, the second transfers antisymmetric rotational torque, and the third is the symmetric <flow alignment of a polar order parameter> contribution.
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