Differential approximation for Kelvin wa

This study explores the phenomenon of kelvulence, which involves the propagation of Kelvin waves on a thin vortex filament and its implications on turbulent cascades in superfluids near absolute zero. The objective is to provide a comprehensive understanding of the dynamics of these waves, particularly in relation to energy and wave action spectra. Utilizing a weak turbulence approach, the research derives a six-wave kinetic equation for weakly nonlinear Kelvin waves, allowing for the delineation of a concurrent direct energy cascade and inverse wave action cascade. The findings suggest that under high excitation levels, a –3 spectrum, associated with sharp angles and vortex line bending, may emerge, corroborated by recent numerical simulations. Furthermore, a transition to a –17/5 spectrum is observed at lower turbulence levels, indicating a shift from energy-dominating interactions to wave breaking effects. This dual cascade behavior underscores the complexity of turbulence in systems retaining two conserved quantities. The study’s results provide pivotal insights into the nature of turbalent dynamics in quantum fluids, thereby enhancing the broader understanding of wave interactions within superfluid systems.