Extremes, intermittency, and time directionality of atmospheric turbulence at the crossover from production to inertial scales

Abstract

The effects of mechanical generation of turbulent kinetic energy and buoyancy forces on the statistics of air temperature and velocity increments are experimentally investigated at the cross over from production to inertial range scales. The ratio of an approximated mechanical to buoyant production (or destruction) of turbulent kinetic energy can be used to form a dimensionless stability parameter ζ that classifies the state of the atmosphere as common in many atmospheric surface layer studies. Here, we assess how ζ affects the scale-wise evolution of the probability of extreme air temperature excursions, their asymmetry and time reversibility. The analysis makes use of high frequency velocity and air temperature time series measurements collected at z=5 m above a grass surface at very large frictional Reynolds numbers Re * = u * z/ν > 1 × 10 5 (u * is the friction velocity and ν is the kinematic viscosity of air). Using conventional higher-order structure functions, temperature exhibits larger intermittency and wider multifractality when compared to the longitudinal velocity component, consistent with laboratory studies and simulations conducted at lower Re * . Moreover, deviations from the classical Kolmogorov scaling for the longitudinal velocity are shown to be reasonably described by the She-Leveque vortex filament model that has no 'tunable' parameters and is independent of ζ. The work demonstrates that external boundary conditions, and in particular the magnitude and sign of the sensible heat flux, have a significant impact on temperature advection-diffusion dynamics within the inertial range. In particular, atmospheric stability affects both the buildup of intermittency and the persistent asymmetry and time irreversibility observed in the first two decades of inertial sub-range scales.

Visibility network analysis of large-scale intermittency in convective surface layer turbulence

“…the small-scale intermittency. Recently, Zorzetto, Bragg & Katul (2018) confirmed the nonlinear character of the system is responsible for the small-scale intermittency in the statistics of temperature increments. However, our results illustrate that the nonlinearity even affects the non-Gaussian characteristics of the single-point measurements of temperature fluctuations in highly convective conditions (i.e.…”

“…Similarly, in a highly convective ASL flow the ramp-cliff structures (slow rises followed by a sudden drop) in the T time series have been found to affect the small-scale and large-scale intermittency in such signals. In fact, while ramp-cliff structures are a signature of the presence of convective plumes inducing non-Gaussian temperature p.d.f.s (Chu et al 1996), thus contributing to large-scale intermittency, they have also been shown to impact the small-scale intermittency of temperature during highly convective conditions (Zorzetto et al 2018).…”

Experimental evidence of a phase transition in the multifractal spectra of turbulent temperature fluctuations at a forest canopy top

“…This statistically limited contribution of cliff structures to the intermittency of scalar fluctuations contrasts with the Zorzetto et al (2018) findings on the persistence of the signature of integral-scale ramp-cliff structures on θ fluctuations, well within the inertial convective subrange, explaining the larger intermittency of θ fluctuations. We suspect that the mixing-layer-type flow prevailing at the top of our canopy dampens the memory of the integral-scale eddy structures as opposed to shear-layer flow located far above surface roughness elements of Zorzetto et al (2018).…”

“…The squared turbulence intensity relative to the squared convection velocity varies from 0.04 in stable conditions up to 0.18 for the most unstable runs (table 1), reaching the limit of applicability of the Taylor hypothesis for these latter runs. To overcome this limitation, we normalized the time scale with L w (the integral scale of the vertical velocity w) (Zorzetto et al 2018), assuming that the distortion of the main advected eddies impacted similarly the time scale and L w , L w being much smaller than L u (table 1).…”

Fluctuation theorem and extended thermodynamics of turbulence

“…With these premises, the objective of this work is to illustrate that non-equilibrium thermodynamics and in particular the FT can be employed to describe the behaviour of the turbulent energy cascade. While the net transfer of energy from large to small scales is prevalent, it is shown here that back-scatter of energy, with its connection to time-scale irreversibility, obeys the statistics predicted by the FT [13,17–21]. To provide a physical context, a turbulent flow conceptually analogous to Joule’s original experiment is used, where work is done on the fluid system to generate, in a narrow band of scales, turbulent kinetic energy, which is then dissipated as heat.…”