Small scale anisotropy in turbulent shearless mixing

We have imagined a numerical experiment to explore the onset of turbulent intermittency associated with a spatial perturbation of the correlation length. We place two isotropic regions, with different integral scales, inside a volume where the turbulent kinetic energy is initially uniform and leave them to interact and evolve in time. The different length scales produce different decay rates in the two regions. Since the smaller-scale region decays faster, a transient turbulent energy gradient is generated at the interface between the two regions. The transient is characterized by three phases in which the kinetic energy gradient across the interface grows, peaks and then slowly decays. The transient lifetime is almost proportional to the initial ratio of the correlation lengths. The direct numerical simulations also show that the interface width grows in time. The velocity moments inside this interaction zone are seen to depart from their initial isotropic values and, with a certain lag, the anisotropy is seen to spread to small scales. The longitudinal derivative moments also become anisotropic after a few eddy turnover times. This anisotropic behaviour is different from that observed in sheared homogeneous turbulent flows, where high transverse derivative moments are generated, but longitudinal moments almost maintain the isotropic turbulence values. Apart from the behaviour of the energy gradient transients, the results also show the timescaling of the interface diffusion width, and data on the anisotropy of the large and small scales, observed through one-point statistics determined inside the intermittency sublayer, which is associated with the interaction zone. Supplemental Material Online: http://prl.aps.org/supplemental/PRL/v107/i19/e19450

Self-similarity of the turbulent mixing with a constant in time macroscale gradient

In the absence of kinetic energy production, we consider that the influence of the initial conditions is characterized by the presence of an energy gradient or by the concurrency of an energy and a macroscale gradient on turbulent transport. Here, we present a similarity analysis that interprets two new results on the subject recently obtained by means of numerical experiments on shearless mixing (Tordella & Iovieno, 2005). In short, the two results are: i -- The absence of the macroscale gradient is not a sufficient condition for the setting of the asymptotic Gaussian state hypothesized by Veeravalli and Warhaft (1989), where, regardless of the existence of velocity variance distributions, turbulent transport is mainly diffusive and the intermittency is nearly zero up to moments of order four. In fact, it was observed that the intermittency increases with the energy gradient, with a scaling exponent of about 0.29; ii -- If the macroscale gradient is present, referring to the situation where the macroscale gradient is zero but the energy gradient is not, the intermittency is higher if the energy and scale gradients are concordant and is lower if they are opposite. The similarity analysis, which is in fair agreement with the previous experiments, is based on the use of the kinetic energy equation, which contains information concerning the third order moments of the velocity fluctuations. The analysis is based on two simplifying hypotheses: first, that the decays of the turbulences being mixed are almost nearly equal (as suggested by the experiments), second, that the pressure-velocity correlation is almost proportional to the convective transport associated to the fluctuations (Yoshizawa, 2002

Pre-unstable set of multiple transient three-dimensional perturbation waves and the associated turbulent state in a shear flow

In order to understand whether, and to what extent, spectral representation can effectively highlight the nonlinear interaction among different scales, it is necessary to consider the state that precedes the onset of instabilities and turbulence in flows. In this condition, a system is still stable, but is however subject to a swarming of arbitrary 3D small perturbations. These can arrive any instant, and then undergo a transient evolution which is ruled out by the initial-value problem associated to the Navier-Stokes linearized formulation. The set of 3D small perturbations constitutes a system of multiple spatial and temporal scales which are subject to all the processes included in the perturbative Navier-Stokes equations: linearized convective transport, linearized vortical stretching and tilting, and the molecular diffusion. Leaving aside nonlinear interaction among the different scales, these features are tantamount to the features of the turbulent state. We determine the exponent of the inertial range of arbitrary longitudinal and transversal perturbations acting on a typical shear flow, i.e. the bluff-body wake. Then, we compare the present results with the exponent of the corresponding developed turbulent state (notoriously equal to -5/3). For longitudinal perturbations, we observe a decay rate of -3 in the inertial range, typically met in two-dimensional turbulence. For purely 3D perturbations, instead, the energy decreases with a factor of -5/3. If we consider a combination of longitudinal and transversal perturbative waves, the energy spectrum seems to have a decay of -3 for larger wavenumbers ([50, 100]), while for smaller wavenumbers ([3,50]) the decay is of the order -5/3. We can conclude that the value of the exponent of the inertial range has a much higher level of universality, which is not necessarily associated to the nonlinear interaction.Comment: Proceedings of the 17th Australasian Fluid Mechanics Conference, 5-9 December 2010, Auckland, New Zealan

Dimensionality influence on passive scalar transport

We numerically investigate the advection of a passive scalar through an interface placed inside a decaying shearless turbulent mixing layer. We consider the system in both two and three dimensions. The dimensionality produces a different time scaling of the diffusion, which is faster in the two-dimensional case. Two intermittent fronts are generated at the margins of the mixing layer. During the decay these fronts present a sort of propagation in both the direction of the scalar flow and the opposite direction. In two dimensions, the propagation of the fronts exhibits a significant asymmetry with respect to the initial position of the interface and is deeper for the front merged in the high energy side of the mixing. In three dimensions, the two fronts remain nearly symmetrically placed. Results concerning the scalar spectra exponents are also presente