Vortex Mutual Friction, Orbital Inertia, and History-Dependent Textures in Rotating Superfluid ${}^3\mathrm{He}-\mathit{A}$

We have measured the resistive and reactive mutual friction coefficients in rotating superfluid ${}^3\mathrm{H}\mathrm{e}-A$ at $29.3\mathrm{bars}$ pressure. The results agree with those predicted from the equation of orbital hydrodynamics for two quantum continuous vortices if the previously measured value of the orbital viscosity is used. Our results put an upper limit on the orbital inertia of less than $0.005ħ$ per Cooper pair. We explain our observation of history-dependent textures by noting that the ease of formation of continuous vortices depends on the relative direction of $\mathbf{l}$ and the rotation axis.