“…Using innovative methods to stir the flow (to ensure that the turbulence does not decay), pseudo-spectral solvers for incompressible flows have been used to simulate HIT on boxes consisting of 12288 3 grid points to achieve a maximum Reynolds number Re λ = 1300 (where λ denotes the Taylor microscale) [6]. These DNS flow fields can then be used validate existing theories, and also inform the development of sub-grid models by exploring the general two-point, two-time, space-time velocity correlation, defined by R( x, t) = u i ( x, t)u j ( x + r, t + τ ) (1) where, u i , u j (i, j = 1, 2, 3) denotes the fluctuating velocity components, x + r = (x 1 + δx 1 , x 2 + δx 2 , x 3 + δx 3 ) denotes the distance between two points in the flow, τ denotes the temporal window, and . denotes the ensemble average.…”