Editing Quantum turbulence (section)

=== Kelvin waves and vortex reconnections ===
[[File:Kelvin_waves_in_quantum_vortices.png|thumb|377x377px|Fig 4. Left: Schematic of a Kelvin wave with amplitude <math>A</math> and wavelength <math>\lambda</math>. Right: A straight vortex configuration that has been perturbed into a bent vortex configuration.]]
[[File:Vortex-reconnection-schematic.png|thumb|377x377px|Fig 5. Schematic of vortex reconnection of two vortices. The arrows on the vortices represent the direction of the vorticity in the vortex line. Left: Before the reconnection. Middle: The vortex reconnection is taking place. Right: after the reconnection.]]
Vortices in quantum fluids support Kelvin waves, which are helical perturbations of a vortex line away from its straight configuration that rotate at an angular velocity <math>\omega</math>, with

<math>\omega \approx \frac{\kappa k^2}{4 \pi}\ln{\left(\frac{1}{ka_0}\right)}</math>

Here <math>k=2\pi/\lambda</math> where <math>\lambda</math> is the wavelength and <math>k</math> is the wavevector.

Travelling vortices in quantum fluids can interact with each other, resulting in reconnections of vortex lines and ultimately changing the topology of the vortex configuration when they collide as suggested by Richard Feynman.<ref>{{cite book|author=R.P. Feynman|title=II. Progress in Low Temperature Physics|publisher=North-Holland Publishing Company|year=1955|volume=1|place=Amsterdam|chapter=Application of quantum mechanics to liquid helium}}</ref> At non-zero temperatures the vortex lines scatter thermal excitations, which creates a friction force with the normal fluid component (thermal cloud for atomic condensates). This phenomenon leads to the dissipation of kinetic energy. For example,  vortex rings will shrink, and Kelvin waves will decrease in amplitude.