Helicity dynamics in stratified turbulence in the absence of forcing

Abstract

A numerical study of decaying stably stratified flows is performed. Relatively high stratification (Froude number ≈ 10 −2 -10 −1 ) and moderate Reynolds (Re) numbers (Re ≈ 3-6 × 10 3 ) are considered and a particular emphasis is placed on the role of helicity (velocity-vorticity correlations), which is not an invariant of the nondissipative equations. The problem is tackled by integrating the Boussinesq equations in a periodic cubical domain using different initial conditions: a nonhelical Taylor-Green (TG) flow, a fully helical Beltrami [ArnoldBeltrami-Childress (ABC)] flow, and random flows with a tunable helicity. We show that for stratified ABC flows helicity undergoes a substantially slower decay than for unstratified ABC flows. This fact is likely associated to the combined effect of stratification and large-scale coherent structures. Indeed, when the latter are missing, as in random flows, helicity is rapidly destroyed by the onset of gravitational waves. A type of large-scale dissipative "cyclostrophic" balance can be invoked to explain this behavior. No production of helicity is observed, contrary to the case of rotating and stratified flows. When helicity survives in the system, it strongly affects the temporal energy decay and the energy distribution among Fourier modes. We discover in fact that the decay rate of energy for stratified helical flows is much slower than for stratified nonhelical flows and can be considered with a phenomenological model in a way similar to what is done for unstratified rotating flows. We also show that helicity, when strong, has a measurable effect on the Fourier spectra, in particular at scales larger than the buoyancy scale, for which it displays a rather flat scaling associated with vertical shear, as observed in the planetary boundary layer.

Absorption of waves by large-scale winds in stratified turbulence

“…The result indicates a preference towards an alignment of horizontal gradients of the vertical velocity with the mean flow, as there is an excess for +1 when compared with −1, and a deficit (compared with uniformly distributed angles) for the case in which the two fields are perpendicular. Interestingly, a preference of stratified flows towards developing one sign of velocity gradients (resulting in non-Gaussian PDFs) was reported before in [44].…”

Helicity, topology, and Kelvin waves in reconnecting quantum knots

“…It is linked to the growth of large scale magnetic fields in astrophysics and solar physics [1], the formation of supercell convective storms in meteorology [2], the decay rate of stratified turbulence [3], and the formation of large structures in rotating and stratified flows [4] among other problems. Helicity is a measure of the knottedness of field lines, which is conserved under appropriate conditions, and as such it has been called a "topological invariant" of many flows [5].…”

Backscatter in stratified turbulence

“…These fundamental features have been reported in several DNS and hyperviscosity simulations of stratified turbulence (e.g. [14,15,[17][18][19][20][23][24][25][26]). The importance of L b implies that LES of stratified turbulence does not require resolution of the smaller Ozmidov scale L o = 2π (ϵ/N 3 ) 1/2 , where ϵ is the kinetic energy molecular dissipation rate [10,22].…”