Free-surface image of a force dipole

Reflecting a force dipole's position and normal orientation component across a flat clean free surface produces an image whose superposition enforces no penetration and zero tangential traction. Its flow at the swimmer causes both normal drift and reorientation.

For equal stresslets with height $h$ and axial separation $\ell \gg h$, the neighbour image doubles the leading axial repulsion. Its normal contribution is smaller than own-image attraction by order $(h/\ell {)}^3$, so leading height dynamics are unchanged. The approximation also neglects weak neighbour-induced orientation corrections.

A positive-strength parallel point stresslet below a flat shear-free impermeable plane is attracted by its identical reflected image. Its height satisfies $\dot{h}=-S/(32\pi \mu h^2)$ and formally reaches zero in finite time. Negative strength reverses the drift. Finite-body near-contact physics lies outside this singularity prediction.