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Register a new userExploring the turbulent velocity gradients at different scales from the perspective of the strain-rate eigenframe
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Expressing the evolution equations for the filtered velocity gradient tensor (FVGT) in the strain-rate eigenframe provides an insightful way to disentangle and understand various processes such as strain self-amplification, vortex stretching and tilting, and to consider their properties at different scales in the flow. Using data from Direct Numerical Simulation (DNS) of the forced Navier-Stokes equation, we consider the relative importance of local and non-local terms in the FVGT eigenframe equations across the scales using statistical analysis. The analysis of the eigenframe rotation-rate, that drives vorticity tilting, shows that the anisotropic pressure Hessian plays a key role, with the sub-grid stress making an important contribution outside the dissipation range, and the local spinning due to vorticity making a much smaller contribution. The results also show the striking behavior that the vorticity tilting term remains highly intermittent even at relatively large scales. We derive a generalization of the Lumley triangle that allows us to show that the pressure Hessian has a preference for two-component axisymmetric configurations at small scales, with a transition to a more isotropic state at larger scales. Correlations between the sub-grid stress and other terms in the eigenframe equations are considered, highlighting the coupling between the sub-grid and nonlinear amplification terms, with the sub-grid term playing an important role in regularizing the system. These results provide useful guidelines for improving Lagrangian models of the FVGT, since current models fail to capture a number of subtle features observed in our results.
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We present a new approach for constructing data-driven subgrid stress models for large eddy simulation of turbulent flows. The key to our approach is representation of model input and output tensors in the filtered strain rate eigenframe. Provided inputs and outputs are selected and non-dimensionalized in a suitable manner, this yields a model form that is symmetric, Galilean invariant, rotationally invariant, reflectionally invariant, and unit invariant. We use this model form to train a simple and efficient neural network model using only one time step of filtered direct numerical simulation data from a forced homogeneous isotropic turbulence simulation. We demonstrate the accuracy of this model as well as the models ability to generalize to previously unseen filter widths, Reynolds numbers, and flow physics using a priori and a posteriori tests.
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The integral length scale ($mathcal{L}$) is considered to be characteristic of the largest motions of a turbulent flow, and as such, it is an input parameter in modern and classical approaches of turbulence theory and numerical simulations. Its experimental estimation, however, could be difficult in certain conditions, for instance, when the experimental calibration required to measure $mathcal{L}$ is hard to achieve (hot-wire anemometry on large scale wind-tunnels, and field measurements), or in standard facilities using active grids due to the behaviour of their velocity autocorrelation function $rho(r)$, which does not in general cross zero. In this work, we provide two alternative methods to estimate $mathcal{L}$ using the variance of the distance between successive zero crossings of the streamwise velocity fluctuations, thereby reducing the uncertainty of estimating $mathcal{L}$ under similar experimental conditions. These methods are applicable to variety of situations such as active grids flows, field measurements, and large scale wind tunnels.
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