🌊 Stokes Flow

The Reynolds number Re compares inertial forces to viscous forces in a fluid. The Re slider spans roughly 10^-4 to 5 on a log scale; at the low end, viscosity totally dominates and the flow is "creeping" — no turbulence, no inertia, every motion is instantly damped.

The field mode draws the exact closed-form Stokes solution for uniform flow past a sphere, which is derived assuming inertia is negligible entirely. That solution has no Re dependence built into the velocity field itself, so the streamline pattern only depends on flow speed and sphere size, not on Re — this is the "wow point" noted directly in the code.

Dye particles are stored at fixed base positions (r0, a0) inside an annulus, and their displayed position is computed by applying the CURRENT total accumulated shear to that base position. Because the shear-to-position mapping is exactly invertible, running shearTotal back down to zero snaps every particle back to precisely where it started, reproducing the classic Couette-cell dye experiment.

It states that a swimmer using a reciprocal stroke (one that looks identical played forwards or backwards) cannot generate net motion at low Reynolds number. The simulation models thrust as the area enclosed by the two arm angles in shape-space; a reciprocal stroke (phaseShift = 0) traces a loop with zero enclosed area, so net displacement stays at zero however fast you move.

With a 90-degree phase shift between the two arms, the shape-change cycle traces a closed loop in shape-space that encloses a nonzero area, and the code integrates that loop area (a times db/dt) directly into forward displacement (swimX). Set the phase shift to zero (Reciprocal button) and the loop collapses to a line with zero area, so the swimmer oscillates in place instead of advancing.