Amplitude of Waves in the Kelvin-wave Cascade

Development of experimental techniques to study superfluid dynamics, in particular, application of nanomechanical oscillators to drive vortex lines, enables potential observation of the Kelvin-wave cascade on quantized vortices. One of the first questions that then arises in analysis of the experimental results is the relation between the energy flux in the cascade and the amplitude of the Kelvin waves. We provide such relation based on the L’vov—Nazarenko picture of the cascade. Remarkably, the dependence of the amplitude of the waves on the energy flux is extremely weak as a power law with an exponent of 1/10.