Effective diffusivity of passive scalars in rotating turbulence

We use direct numerical simulations to compute turbulent transport coefficients for passive scalars in turbulent rotating flows. Effective diffusion coefficients in the directions parallel and perpendicular to the rotations axis are obtained by studying the diffusion of an imposed initial profile for the passive scalar, and calculated by measuring the scalar average concentration and average spatial flux as a function of time. The Rossby and Schmidt numbers are varied to quantify their effect on the effective diffusion. It is find that rotation reduces scalar diffusivity in the perpendicular direction. The perpendicular diffusion can be estimated from mixing length arguments using the characteristic velocities and lengths perpendicular to the rotation axis. Deviations are observed for small Schmidt numbers, for which turbulent transport decreases and molecular diffusion becomes more significant.Comment: 10 pages, 13 figures. Slightly modified version to address referees' comment

Inverse cascade behavior in freely decaying two-dimensional fluid turbulence

We present results from an ensemble of 50 runs of two-dimensional hydrodynamic turbulence with spatial resolution of 2048^2 grid points, and from an ensemble of 10 runs with 4096^2 grid points. All runs in each ensemble have random initial conditions with same initial integral scale, energy, enstrophy, and Reynolds number. When both ensemble- and time-averaged, inverse energy cascade behavior is observed, even in the absence of external mechanical forcing: the energy spectrum at scales larger than the characteristic scale of the flow follows a k^(-5/3) law, with negative flux, together with a k^(-3) law at smaller scales, and a positive flux of enstrophy. The source of energy for this behavior comes from the modal energy around the energy containing scale at t=0. The results shed some light into connections between decaying and forced turbulence, and into recent controversies in experimental studies of two-dimensional and magnetohydrodynamic turbulent flows.Comment: 7 pages, 6 figure

Turbulence comes in bursts in stably stratified flows

There is a clear distinction between simple laminar and complex turbulent fluids. But in some cases, as for the nocturnal planetary boundary layer, a stable and well-ordered flow can develop intense and sporadic bursts of turbulent activity which disappear slowly in time. This phenomenon is ill-understood and poorly modeled; and yet, it is central to our understanding of weather and climate dynamics. We present here a simple model which shows that in stably stratified turbulence, the stronger bursts can occur when the flow is expected to be more stable. The bursts are generated by a rapid non-linear amplification of energy stored in waves, and are associated with energetic interchanges between vertical velocity and temperature (or density) fluctuations. Direct numerical simulations on grids of 2048^3 points confirm this somewhat paradoxical result of measurably stronger events for more stable flows, displayed not only in the temperature and vertical velocity derivatives, but also in the amplitude of the fields themselves

Helicity dynamics in stratified turbulence in the absence of forcing

A numerical study of decaying stably-stratified flows is performed. Relatively high stratification and moderate Reynolds numbers are considered, and a particular emphasis is placed on the role of helicity (velocity-vorticity correlations). The problem is tackled by integrating the Boussinesq equations in a periodic cubical domain using different initial conditions: a non-helical Taylor-Green (TG) flow, a fully helical Beltrami (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. 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 non-helical 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