Session T02: Turbulence: DNS

Helical Turbulence - the Transition between 2D and 3D Turbulence

Based on vortex stretching, our theoretical understanding of 2D and 3D turbulence reveals fundamental differences. To gain further insights, we study helical-symmetric flows. The helical coordinate system (r, ζ, η) is given by r, ζ = az + bΦ and η = −bz + ar²Φ, where a, b = const, a² + b² > 0 and (r, Φ, z) are the common cylindrical coordinates. Helical symmetry implies, all dependent variables are independent of η. Helical flows differ whether they have a velocity u^η along the helix or not. In both cases, helical flows admit infinite classes of conservation laws and thus integral invariants exist. The central new invariants for helical turbulence are generalized helicity, when vortex stretching is present, and generalized enstrophy, without vortex stretching. The findings from 2D and 3D turbulence show that global invariants play a central role in turbulence and this is also expected for helical turbulence. Appropriate largescale simulations are conducted for this purpose. The helically reduced Navier-Stokes equations are discretized using high-order discontinuous Galerkin scheme. This numerical framework is utilized to study energy transport in helically symmetric flows for high Reynolds numbers.   

Direct numerical simulations of anisotropic homogeneous turbulence using parametric forcing

Turbulence modeling using RANS and LES are pragmatic alternatives to direct numerical simulations (DNS) for predicting complex turbulent flows. However, the predictive reliability of these modeling approaches is limited. Arguably, one of the reasons is that detailed data that could be used to inform such models is generally limited to simple canonical flows. The development of reliable generally applicable turbulence models will be facilitated by the accumulation of a rich set of data from a wide variety of complex turbulent flows. We propose to generate such a rich set of data using DNS in simple computational domains in which artificial forcing is applied to introduce turbulence complexity. As a first step in this direction, a family of anisotropic forcing formulations has been developed that introduce both component and scale anisotropy to homogeneous turbulence simulations. The forcing is formulated as a divergence-free anisotropic linear function of the fluctuating velocity that is applied to an anisotropically distributed set of large-scale Fourier modes. The anisotropy is controlled by four parameters that describe the anisotropy of the forcing and of the scales that are forced. Direct numerical simulations of turbulence with a wide range of anisotropies are being performed, and the resulting data is analyzed to characterize the turbulence anisotropy. The use of these data to inform anisotropic LES and RANS models will be discussed.   

Towards Validation of ANSYS Fluent for DNS Channel Flow

Direct Numerical Simulation (DNS) is an invaluable tool for visualizing turbulent structures down to the smallest length scales. Because of the large element count necessary to resolve these small structures, DNS is typically performed using high-order spectral methods. While these methods greatly ease the computational burden, they preclude the use of unstructured meshes, which are often a necessity to model complex geometry. Finite-volume methods enable the use of unstructured meshes at great computational cost. Existing literature has validated DNS using various finite-volume solvers, but the commercial solver ANSYS Fluent remains unvalidated. We demonstrate preliminary attempts to validate DNS of a low-Reynolds number (friction Reynolds number of 180) channel flow using ANSYS Fluent. Four meshes are examined with cell count from 8 million to 67 million elements. We compare energy spectra, Reynolds stress profiles, and Reynolds stress budgets, paying close attention to the aberrant “pile-up” of energy at large wavenumbers.   

Numerical study of Lagrangian velocity structure functions from a spatial-temporal perspective

Lagrangian intermittency in turbulence is generally known to be stronger than its Eulerian counterpart, but the underlying physical mechanisms are not as well understood.  A fundamental quantity for both physical understanding and modeling is the Lagrangian velocity increment $Delta_ au{mathbf u}(t)={mathbf u}^+(t+ au)-{mathbf u}^+(t)$, which is the difference between velocity fluctuations recorded at different time instants and different locations in space based on the instantaneous particle position. In this talk we discuss some physical insights that can be obtained by decomposing this increment into temporal and (randomized) spatial contributions, which bears resemblance to strong mutual cancellation between local and convective accelerations in the small $ au$ limit.  The correlation between the temporal and spatial relative velocities plays an important role in the second order Lagrangian structure function, which appears to approach  inertial range scaling at a time lag in less than 10 Kolmogorov time scales.  A DNS code that scales extremely well with respect to particle count has been used to obtain results in isotropic turbulence at Taylor-scale Reynolds number exceeding 1000.   

Turbulence simulations at grid resolution up to $32768^3$ enabled by Exascale computing

A GPU-enabled extreme scale turbulence simulations capability recently developed on the 1.1 Exaflop leadership-class supercomputer (named Frontier) is now available for computing homogeneous turbulence at very high resolution, with very favorable  performance characteristics.  This new simulation tool has been used to perform a series of new simulations  of forced isotropic turbulence, at grid resolutions from $2048^3$ to  $32768^3$. High Reynolds numbers up to 2500 based on the Taylor scale are reached by reducing viscosity along with progressive grid refinement.  Expected results will include energy spectra, velocity structure functions, and the statistics of highly intermittent fluctuations of the energy dissipation rate and enstrophy.   

Information-theoretic bounds in the prediction of extreme events and applications to turbulent flows

Predicting extreme events in turbulent flows, characterized by rare but intense fluctuations in flow properties, is of paramount importance due to their potential impact on the performance and reliability of a wide range of engineering systems. Various methods have been explored for predicting extreme events in turbulence; however, the theoretic bounds on the predictive accuracy of forecasting tools remain relatively unknown. Information theory, i.e., the science of message communication, offers a rigorous framework for investigating the fundamental limitations for the prediction and modeling of extreme events. Here, we leverage information-theoretic Fano-type inequalities to establish the bounds for predicting and modeling extreme events in turbulent flows. By investigating the inherent uncertainties and constraints that hinder predictive capabilities, Fano-type inequalities provide a lower bound on the probability of error over all the possible models. These bounds are universal and independent of the particular modeling tool employed. We demonstrate the application of the information-theoretic limits in the prediction of extreme events in a minimal turbulent channel flow. The time signals are defined as the energy contained in different Fourier modes of the three velocity components. The theoretical bounds on the errors are calculated for different variables and compared with actual models trained using numerical data. Our approach allows us to evaluate whether models are operating near their theoretical limits or whether further improvements are theoretically possible.