Seminar 16th April 2013 noon Building 54, Room 5025
Nonlinear Waves and Quantized Vortex Dynamics in Superfluids
Hayder Salman
Cambridge
- Categories
- Complex Systems
- Submitter
- Luke Goater
In this talk we discuss two distinct but related problems arising in the context of quantized vortex motion in superfluids and Bose-Einstein condensates. We model the phenomena we describe using the cubic Nonlinear Schrodinger equation, also known as the Gross-Pitaevskii (GP) equation. In the first part of the talk we show that, on hydrodynamic length scales, quantized superfluid vortices can be modelled as a system of coreless point vortices in 2D. We consider the asymptotic regimes under which point vortex dynamics is recovered from the GP equation. We show that the regime under which this occurs corresponds to the so-called Lighthill regime for evaluating the acoustic radiation in a classical fluid. We, therefore, formulate a corresponding theory of radiation that specifies the sound emitted by the motion of quantized vortices in the limit of low Mach number or equivalently large inter-vortex separation. We demonstrate our theoretical predictions with numerical simulations of the GP equation. We argue that the asymptotic results presented here allows one to recover the Biot-Savart law that governs the motion of vortex filaments in 3D from the GP equation.
In the second part of the talk, we focus on excitations on 3D superfluid vortex filaments. It is well known that quantized superfluid vortices can support excitations in the form of helical Kelvin waves. These Kelvin waves play an important role in the dynamics of these vortices and their interactions are believed to be the key mechanism for transferring energy in the ultra low temperature regime of superfluid turbulence in 4He. Kelvin waves can be ascribed to low amplitude excitations on vortex filaments. In this talk I will show that larger amplitude excitations of the vortices can be attributed to solitons propagating along the vortex filament. I will review the different class of soliton solutions that can arise as determined analytically from a simplified vortex model based on the localized induction approximation. I will show, through numerical simulations, that these solutions persist even in more realistic models based on a vortex filament model and the Gross-Pitaevskii equation. As a generalisation of these soliton solutions, I also consider the breathe r solutions on a vortex filament and illustrate how, under certain conditions, large amplitude excitations that are localized in space and time can emerge from lower amplitude Kelvin wave like excitations. The results presented are quite generic and are believed to be relevant to a wide class of systems ranging from classical to superfluid vortices. I will also interpret our results on these nonlinear vortex excitations in the context of the cross-over regime of scales in superfluid turbulence.