Reynolds stress closure in jet flows using wave models

Physics of Fluids, 2004

The structure of homogeneous turbulent shear flow is studied using data generated by Direct Numerical Simulations (DNS) and a linear analysis for both compressible and incompressible cases. At large values of the mean shear rate, the Rapid Distortion Theory (RDT) limit is approached. Analytical solutions are found for the inviscid compressible RDT equations at long times. The RDT equations are also solved numerically for both inviscid and viscous cases. The RDT solutions, confirmed by the DNS results, show that the even order transverse derivative moments of the dilatational and solenoidal velocity fields are anisotropic, with the dilatational motions more anisotropic than their solenoidal counterparts. The results obtained for the incompressible case are similar to those obtained for the solenoidal motions in the compressible case. The DNS results also indicate an increase in the anisotropy of the even order transverse derivative moments with the order of the moment, in agreement with the RDT predictions. Although the anisotropy decreases with Reynolds number, it is likely that for higher even order moments it will persist at large values of the Reynolds number, in contrast with the postulate of local isotropy. The RDT solutions also predict that the normalized odd order transverse derivative moments of the solenoidal velocity for the compressible case and of the velocity for the incompressible case should approach a constant different than zero at large times. This prediction is supported by the DNS data. For higher odd order normalized moments, the RDT analysis suggests that the anisotropy may persist at large values of the Reynolds number, in agreement with the experimental data. The amplification of the dilatational kinetic energy in the direction of the mean shear and the anisotropy of the dilatational dissipation tensor found in the DNS results are also consistent with the RDT analysis.

Physics of Fluids, 2013

Direct numerical simulation is used to evaluate the effect of plane strain on isotropic homogeneous turbulence. The subsequent return to isotropy after the removal of the strain is also investigated. Large, moderate, and small strain rates are computed at moderate turbulence Reynolds numbers. The initial turbulence is generated via mechanical mixing so that the large scale turbulence develops relatively naturally. Turbulence length scales, Reynolds numbers, decay rates, and anisotropy are computed over the range of the simulations, with the goal of quantifying how anisotropic decay behaves. The simulations indicate that large scale anisotropy may not decay to zero at very large times. In agreement with experimental data, the presence of a recovery region is discerned before the return process is observed. Trajectory crossing is observed on the anisotropy invariant map indicating that anisotropy itself is not sufficient to determine its time evolution. Model constants for classic return-to-isotropy models are determined from the data and shown to vary with time. The oriented-eddy collision model [M. B. Martell and J. B. Perot, "The oriented-eddy collision turbulence model," Flow, Turbul. Combust. 89(3), 335 (2012)], which includes turbulent structure information, is shown to predict the salient structure of the straining and return process. C 2013 AIP Publishing LLC. [http://dx.

Nature, 2006

Journal of Fluid Mechanics, 2014

Linear stability analysis is applied to the mean flow of an oscillating round jet with the aim to investigate the robustness and accuracy of mean flow stability wave models. The jet's axisymmetric mode is excited at the nozzle lip through a sinusoidal modulation of the flow rate at amplitudes ranging from 0.1 % to 100 %. The instantaneous flow field is measured via particle image velocimetry and decomposed into a mean and periodic part utilizing proper orthogonal decomposition. Local linear stability analysis is applied to the measured mean flow adopting a weakly nonparallel flow approach. The resulting global perturbation field is carefully compared to the measurements in terms of spatial growth rate, phase velocity, and phase and amplitude distribution. It is shown that the stability wave model accurately predicts the excited flow oscillations during their entire growth phase and during a large part of their decay phase. The stability wave model applies over a wide range of forcing amplitudes, showing no pronounced sensitivity to the strength of nonlinear saturation. The upstream displacement of the neutral point and the successive reduction of gain with increasing forcing amplitude is very well captured by the stability wave model. At very strong forcing (> 40%), the flow becomes essentially stable to the axisymmetric mode. For these extreme cases, the prediction deteriorates from the measurements due to an interaction of the forced wave with the geometric confinement of the nozzle. Moreover, the model fails far downstream in a region where energy is transferred from the oscillation back to the mean flow. This study supports previously conducted mean flow stability analysis of self-excited flow oscillations in the cylinder wake and in the vortex breakdown bubble and extends the methodology to externally forced convectively unstable flows. The high accuracy of mean flow stability wave models as demonstrated here is of great importance for the analysis of coherent structures in turbulent shear flows.

Journal of Fluid Mechanics, 1993

Intermittent bursting events, similar to those characterizing the dynamics of nearwall turbulence, have been observed in a low-dimensional dynamical model (Aubry et al. 1988) built from eigenfunctions of the proper orthogonal decomposition (Lumley 1967). I n the present work, we investigate the persistency of the intermittent behaviour in higher-but still of relatively low-dimensional dynamical systems. I n particular, streamwise variations which were not accounted for in an explicit way in Aubry et aL's model are now considered. Intermittent behaviour persists but can be of a different nature. Specifically, the non-zero streamwise modes become excited during the eruptive events so that rolls burst downstream into smaller scales. When structures have a finite length, they travel a t a convection speed approximately equal to the mean velocity at the top of the layer (y' 40). I n all cases, intermittency seems to be due to homoclinic cycles connecting hyperbolic fixed points or more complex (apparently chaotic) limit sets. While these sets lie in the zero streamwise modes invariant subspace, the connecting orbits consist of nonzero streamwise modes travelling downstream. Chaotic limit sets connected by quasitravelling waves have also been observed in a spatio-temporal chaotic regime of the Kuramoto-Sivashinsky equation (Aubry & Lian 1992 a). When the limit sets lose their steadiness, the elongated rolls become randomly active, as they probably are in the real flow. A coherent structure study in our resulting flow fields is performed in order to relate our findings to experimental observations. It is shown that streaks, streamwise rolls, horseshoe vortical structures and shear layers, present in our models, are all connected to each other. Finally, criteria to determine a realistic value of the eddy viscosity parameter are developed.