Transient formation of the passive scalar spectrum at a turbulent interface

We consider the transport of a passive scalar through the turbulent-turbulent interface between two decaying isotropic turbulent flows with different kinetic energy. Although the concentration of a passive substance exhibits a complex behaviour that shows many phenomenological parallels with the turbulent velocity field, the statistical properties of passive scalar turbulence are in part decou­pled from those of the underlying velocity [1,2]. In our numerical experiment, the passive scalar is initially uniform in each of the two isotropic regions. The interaction of the two isotropic flows generates a high scalar variance region in the centre of the mixing layer and two intermittent scalar fronts arise at the margins of the mixing layer. The velocity field instead presents one front only which is placed in the part of the field where the kinetic energy is lower [3,4] or, in case the ener­gy is uniform but the correlation is varying, where the integral scale is lower [5]. In the central part of the mixing layer, between the two intermittent fronts, the spectrum of the scalar fluctuation shows a full range of scales just after one eddy turnover time (see figure below). Moreover, the scalar spectrum shows a more prominent inertial range region than the velocity spectrum - a wider range with a scaling exponent closer to -5/3 - a feature which has been observed also in ho­mogeneous flows at moderate Reynolds numbers, see [6,7]. This feature is preserved for about ten eddy turnover times, during which the scalar variance decays slower than the velocity fluctuatio

Intermittency layers associated to turbulent interfaces

In this study we focus on the transport across an interface which separates two regions with homogeneous and isotropic turbulence in absence of a mean shear. The turbulent transport resulting presents an internal structure. Indeed, in the case of turbulent self-diffusion, both experiments and simulations show that the fluid velocity field is marked by a high intermittency front located aside the interface, which is the source of turbulent bursts penetrating the low turbulence region. The presence of an inner structure inside a layer of turbulence self-transport highlights the different nature of the turbulent transport with respect to the Gaussian diffusion. By including other effects, for instance a passive scalar transport or a mass transport in presence of a density stratification, the phenomenology is much enriched. For instance, our preliminary numerical experiments on the passive scalar transport reveals the presence of two intermittency fronts, one on each side of the interface. As can be seen if the figure below, the intermittency level in the fronts is high. This is true both for the scalar and the scalr derivative statistics. A gradual decay in time is observed while they propagate toward the lateral isotropic regions of the flow. In the presence of a kinetic energy gradient across the interface, the locations and intensity of the intermittency fronts are no more symmetric to respect to the interface. The front on the high energy side of the mixing region penetrates deeper and exhibits stronger intermittency. Analogous features are observed also in two dimension

Cumulative distribution of the stretching of vortical structures in isotropic turbulence

By using a Navier-Stokes isotropic turbulent field numerically simulated in the box with a discretization of 1024^3 [Biferale et al. (2005)], we show that the probability of having a stretching-tilting larger than twice the local enstrophy is very small. This probability decreases if we try to filter out the large scales, while it increases filtering out the small scales. This is basically due to the suppression of the compact structures (blobs)

Energy and water vapor transport across a simplified cloud-clear air interface

We consider a simplified physics of the could interface where condensation, evaporation and radiation are neglected and momentum, thermal energy and water vapor transport is represented in terms of the Boussinesq model coupled to a passive scalar transport equation for the vapor. The interface is modeled as a layer separating two isotropic turbulent regions with different kinetic energy and vapor concentration. In particular, we focus on the small scale part of the inertial range as well as on the dissipative range of scales which are important to the micro-physics of warm clouds. We have numerically investigated stably stratified interfaces by locally perturbing at an initial instant the standard temperature lapse rate at the cloud interface and then observing the temporal evolution of the system. When the buoyancy term becomes of the same order of the inertial one, we observe a spatial redistribution of the kinetic energy which produce a concomitant pit of kinetic energy within the mixing layer. In this situation, the mixing layer contains two interfacial regions with opposite kinetic energy gradient, which in turn produces two intermittent sublayers in the velocity fluctuations field. This changes the structure of the field with respect to the corresponding non-stratified shearless mixing: the communication between the two turbulent region is weak, and the growth of the mixing layer stops. These results are discussed with respect to experimental results with and without stratification.Comment: 12 pages, 8 figure

Mixing of a passive scalar across a thin shearless layer: Concentration of intermittency on the sides of the turbulent interface

The advection of a passive scalar through an initial flat interface separating two different isotropic decaying turbulent fields is investigated in two and three dimensions. Simulations have been performed for a range of Taylors microscale Reynolds numbers from 45 to 250 and for a Schmidt number equal to 1. Different to the case where the transport involves the momentum and kinetic energy only and one intermittency layer is formed in the low-turbulent energy side of the system, in the passive scalar concentration field two intermittent layers are observed to develop at the sides of the interface. The layers move normally to the interface in opposite directions. The dimensionality produces different time scaling of the passive scalar diffusion, which is much faster in the two-dimensional case. In two dimensions, the propagation of the intermittent layers exhibits a significant asymmetry with respect to the initial position of the interface and is deeper for the layer which moves towards the high kinetic energy side of the system. In three dimensions, the two intermittent layers propagate nearly symmetrically with respect the centre of the mixing region. During the temporal decay, inside the mixing, which is both inhomogeneous and anisotropic but devoid of a mean velocity shear, the passive scalar spectra are computed. In three dimensions, the exponent in the scaling range gets in time a value close to that of the kinetic energy spectrum of isotropic turbulence (-5/3). In two dimensions, instead the exponent settles down to a value that is about one-half of the corresponding isotropic case. By means of an analysis based on simple wavy perturbations of the interface we show that the formation of the double layer of intermittency is a dynamic general feature not specific to the turbulent transport. These results of our numerical study are discussed in the context of experimental results and numerical simulations. © 2014 Taylor and Francis