Statistics of pressure Hessian quantities in well-resolved simulations at high Reynolds number.

The pressure Hessian, a second-order tensor that consists of second-derivatives of the pressure field, is known to have important effects on the evolution of velocity gradients following Lagrangian fluid particle trajectories in turbulence. Accurate characterization of the properties of this tensor at high Reynolds number is challenging due to strong intermittency, which also make accurate interpolation along particle trajectories a more demanding task. Nevertheless, access to almost the full power of the world's first exascale computer is expected to allow us to obtain reliable results at Reynolds numbers significantly higher than in previous results in the literature as well as recent work using machine learning. In particular, we will investigate both Eulerian and Lagrangian conditional averages of the pressure Hessian contracted with the velocity gradient tensor given the second and third-order invariants of the latter.

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