Statistical-mechanical approach to study the hydrodynamic stability of the stably stratified atmospheric boundary layer

Abstract

We study the hydrodynamic equilibrium properties of the stably stratified atmospheric boundary layer from measurements obtained in the Snow-Horizontal Array Turbulence Study (SnoHATS) campaign at the Plaine Morte Glacier in the Swiss Alps. Our approach is based on a combination of dynamical systems techniques and statistical analysis. The main idea is to measure the deviations from the behavior expected by a turbulent observable when it is close to a transition between different metastable states. We first assess the performance of our method on the Lorenz attractor, then on a turbulent flow. The results show that the method recognizes subtle differences among different stable boundary layers turbulence regimes and may be used to help characterise their transitions.

On reversals in 2D turbulent Rayleigh-Bénard convection: Insights from embedding theory and comparison with proper orthogonal decomposition analysis

“…In fact, contrary to Landau's conjecture [35], low dimensional descriptions of turbulent ow exist, providing that the right observable is embedded. This result also reinforces those found in [33] for the von Karman turbulent ow and in [58] for the turbulent atmospheric boundary layer. Moreover, the position on the reconstructed attractor can be used as a classier of the dierent phases of the dynamics.…”

Is Turbulence a State of Maximum Energy Dissipation?

“…In [46], only flow configurations with a single stationary state have been analysed and φ computed using the complete time series. To extend the results to the flow regimes featuring multistability, we use the strategy outlined in [49]. First of all, we reconstruct the dynamics by using the embedding methodology on the series of partial maxima of θ, denoted as θ i .…”

“…Since we are not dealing with a stationary process, we cannot compute a single φ for the full time series of θ. The method introduced in [49] consists of computing a value of φ i for each θ i , taking the 50 previous observations of the complete time series. The distribution of |φ| is shown in colorscale in Figure 11.…”

Statistical Investigation of Flow Structures in Different Regimes of the Stable Boundary Layer

“…Donda et al (2015) further found a strong sensitivity of the turbulence recovery to the timing and amplitude of added perturbations, thereby motivating the need for better characterisation of sub-mesoscale motions and their effect on turbulence. Statistical analyses of the hydrodynamical equilibrium properties of the SBL flow revealed that the very stable regime is prone to long-term memory effects in the turbulence dynamics, suggesting a dynamically unstable flow (Nevo et al, 2017). The long-term memory effects could be related to sub-mesoscale motions that can propagate for some time in very stable flow regimes due to weak turbulent mixing.…”

“…The long-term memory effects could be related to sub-mesoscale motions that can propagate for some time in very stable flow regimes due to weak turbulent mixing. Such memory properties in the turbulent observables suggest that very stable flow regimes need to be represented by high order closure models or stochastic processes (Nevo et al, 2017). A statistical characterisation of sub-mesoscale flow structures and their transport properties would greatly help defining such a stochastic process.…”