Fig. 2: Fluid flow and dynamics for membrane rotors.
From: Hyperuniformity and phase enrichment in vortex and rotor assemblies
A A representation of a membrane rotor—a disk rotating due to a torque τ in the plane of the membrane. B The velocity field due to a membrane rotor (solid line) which scales as a point vortex v ~ 1/r at small distances (dotted), r/λ ≪ 1, transitioning to a QG behavior at large distances v ~ 1/r2 (dashed). C Contour dynamics of an ellipse with radii ratios rl/rs ≤ 3, where rl (rs) is the major (minor) axis. Starting from the same contour, the dynamics differ according to the radius relative to the SD length. Blue is in the limit rl ≪ λ. In this limit, the ellipse is rotating as a rigid body, as predicted by Kelvin65 for an elliptic patch in an Euler fluid. Black is in the limit rl ≫ λ, no longer conserving its shape since the large distance flow is in the quasigeostrophic regime. D 200 point membrane rotors, blue is the initial random configuration, black is the final configuration. Solid line shows typical trajectory of an individual vortex. Note that the area did not change considerably since the system of vortices is self-bounding.
