Abstract
The dynamics of the forward vortex cascade in 2D turbulence in a superfluid film is investigated using analytic techniques. The cascade is formed by injecting pairs with the same initial seperation (the stirring code) at a constant rate. They move to smaller scales with constant current under the action of frictional forces, finally reaching the core size separation, where they annihilate and the energy is removed by a thermal bath. On switching off the injection, the pair distribution first decays starting from the initial stirring scale, with the total vortex density decreasing linearly in time at a rate equal to the initial injection rate. As pairs at smaller scales decay, the vortex density then falls off as a power law, the same power law found in recent exact solutions of quenched 2D superfluids.
Highlights
In this paper we show that analytic techniques can be used to study the dynamics of the growth and decay of the forward vortex cascade
We find that the decay of the vortex density is initially linear in time, but switches at longer times to a power-law decay with an exponent identical to that found in our recent exact solutions of quenched 2D superfluids [12]
We consider an incompressible superfluid film connected to a thermal bath at a temperature of 0.1 TKT, where TKT is the critical Kosterlitz-Thouless temperature where thermally excited vortex pairs drive the superfluid density to zero
Summary
In this paper we show that analytic techniques can be used to study the dynamics of the growth and decay of the forward vortex cascade. More recently two numerical simulations of the Gross-Pitaevskii model at high vortex densities found instead a forward energy cascade with a k−5/3 spectrum [8, 9].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
