In the framework of the generalized, nonlocal Gross-Pitaevskii (GP) model, we study numerically the pressure- and size-dependent mechanisms of roton emission and vortex nucleation by objects moving in superfluid ${}^4\mathrm{He}$. For each of several pressures in the range from 0 to the solidification pressure of $\approx 25\mathrm{bar}$, we chose the parameters of the interatomic interaction potential such that the resulting excitation spectrum for the generalized, nonlocal GP equation approximates fairly accurately the pressure-dependent dispersion curve determined experimentally by Godfrin et al. [Phys. Rev. B 103, 104516 (2021)]. In the two-dimensional approximation, for circular obstacles (disks) moving in quiescent ${}^4\mathrm{He}$, we calculated two critical velocities—one corresponding to the roton emission and the other to the nucleation of quantized vortices—as functions of pressure and the obstacle's size. We also comment briefly on three-dimensional simulations of the roton emission and vortex nucleation by moving spherical obstacles.

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• Vortices in superfluids
• Helium-4 superfluids
• Superfluids