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Understanding and predicting turbulent flow phenomena remain a challenge for both theory and applications. The nonlinear and nonlocal character of small-scale turbulence can be comprehensively described in terms of the velocity gradients, which determine fundamental quantities like dissipation, enstrophy, and the small-scale topology of turbulence. The dynamical equation for the velocity gradient succinctly encapsulates the nonlinear physics of turbulence; it offers an intuitive description of a host of turbulence phenomena and enables establishing connections between turbulent dynamics, statistics, and flow structure. The consideration of filtered velocity gradients enriches this view to express the multiscale aspects of nonlinearity and flow structure in a formulation directly applicable to large-eddy simulations. Driven by theoretical advances together with growing computational and experimental capabilities, recent activities in this area have elucidated key aspects of turbulence physics and advanced modeling capabilities. 

The data is from a direct numerical simulation of forced isotropic turbulence on a 10243 periodic grid, using a pseudo-spectral parallel code. Time integration of the viscous term is done analytically using integrating factor. The other terms are integrated using a second-order Adams-Bashforth scheme and the nonlinear term is written in vorticity form1. The simulation is de-aliased using phase-shift and a 2√2 /3 truncation2,3. Energy is injected by keeping constant the total energy in modes such that their wave-number magnitude is less or equal to 2. After the simulation has reached a statistical stationary state, 5028 frames of data, which includes the 3 components of the velocity vector and the pressure, are generated and ingested into the database. The duration of the stored data is about five large-eddy turnover times.