Point-vortex approach in two-dimensional turbulence

Two-dimensional isotropic turbulent inflow conditions for vortex particle method

“…6] induced by the point vortices raises no problem when used as the singularity distribution on the domain boundaries and/or as the circulation carrier at each timestep. However, Esler and Ashbee [16], and Kuvshinov and Schep [21] showed, in their work on point vortices to realize a white noise signal, that there exists a problem when approximating the vorticity with delta functions (point vortices), i.e., infinite spikes, which is an associated singularity in the streamfunction and velocity field. This singularity appears when the distance to the point vortex becomes very small, |r − r | → 0: both streamfunction and velocity become very large; the first blows up logarithmically fast and the other like r −1 .…”

Decaying two-dimensional turbulence undergoes statistical heating

“…If the vortex merger paradigm found in Refs. [12][13][14] is accepted, these results appear to be in contradiction, and a key aim of this work is to resolve this apparent paradox.…”

“…In two-dimensional quantum turbulence (2DQT), in which there is no analog of merger events and opposite-signed vortex dipoles annihilate when their separation becomes small, it is established that ε > 0 because of "evaporative heating" [11] due to the annihilations. Evaporative heating can be understood using "punctuated equilibrium" point vortex models [12,13], which capture the essential dynamics of 2DQT in the limit where the vortex core (or healing length) is small compared to the vortex separation. In the conservative dynamics between dipole annihilation events, energy conservation requires that the formation of a dipole must be compensated by a tendency towards like-signed clustering elsewhere in the domain.…”

“…In contrast to 2DQT, most simple models of decaying 2DCT, e.g., the authors of Refs. [12][13][14], characterized the evolution of the 2DCT vortex field purely in terms of mergers of like-signed vortices. It is important to note that the numerical results found in Ref.…”

Explosion of relativistic electron vortices in laser plasmas

“…Now we assume ∂ t = 0, E θ = 0, v er = 0, Zn i = Zn i0 = 1, v i = 0 and neglect Eqs (20)-(21). Then Eqs (14), (16) and (19) become identities and from Eqs (15), (17) and (18) we obtain…”