Turbulence Transitions in Kelvin–Helmholtz Instability “Tube” and “Knot” Dynamics: Vorticity, Helicity, and Twist Waves

Abstract

We address the sources and dynamics of vorticity and helicity and their relations in transitions to turbulence arising due to Kelvin–Helmholtz instability (KHI) “Tube” and “Knot” (T&K) events. Such events are common in the atmosphere and oceans, and initial numerical simulations reveal that T&K dynamics significantly accelerate turbulence transitions and enhance KHI peak and mean energy dissipation rates. KHI T&K events arise where emerging KH billows exhibit varying wavelengths, phases, amplitudes, and/or discontinuities along their axes. As the KH billows intensify, these regions evolve roughly orthogonal billow cores and induced vortex tubes in close proximity. Their mutual advection as they intensify induces large-amplitude Kelvin vortex waves, or “twist waves”, that arise where locally uniform vortices are distorted by axial or radial advection. The twist waves propagate along, and fragment, the vortex tubes and billow cores, thus accounting for the emergence of helicity and the down-scale energy, enstrophy, and helicity fluxes within the turbulence inertial range. We describe the results of four direct numerical simulations (DNS) addressing KHI T&K dynamics in large and idealized small domains. The large-domain vorticity fields reveal the character and diversity of KHI T&K dynamics, the emergence of twist waves at larger and smaller scales, and their driving of turbulence transitions. Two small-domain DNS exhibit idealized KHI T&K events arising from KH billows that are mis-aligned and that exhibit phase variability along their axes. A third examines the interactions of two vortex tubes in close proximity. These reveal that twist waves drive the character and evolutions of the vorticity and helicity fields.