Homogeneous isotropic turbulence in a triply periodic box is the canonical setting for studying the universal small-scale statistics of turbulent flow, and direct numerical simulation (DNS) is the only method that resolves every excited scale without a closure model. It is also the right idealisation for mixed-phase clouds: at the scales that govern how droplets and ice particles cluster, grow and collide, cloud turbulence is locally homogeneous and isotropic, and those are the scales a DNS can afford to resolve.
I am developing a suite of Julia packages for simulating isotropic turbulence, written for the GPU as the main computational unit; once mature, the suite is to replace the CPU-targeted code used in NAISS 2026/3-574. GBGIsotropicTurbulence.jl is the head package: a pseudo-spectral DNS of an incompressible velocity field and an optional passive scalar, each optionally forced, with Lagrangian tracers sampling the fields along their trajectories. It rests on GBGPeriodicFields.jl, which carries the field mathematics, and on GBGStreamingStatistics.jl, which accumulates statistics in memory without ever storing the flow. They will be joined by GBGCloudPhysics.jl for mixed-phase clouds, where the tracer machinery becomes inertial droplets and ice particles. The same source runs on CPU arrays, CUDA and ROCm; the documentation is published at https://grigorysarnitsky.github.io/GBGIsotropicTurbulence.jl. The solver already reproduces the statistics of the independent DNS code TurTLE at a matched physics point, agreeing to within two per cent in the Taylor-scale Reynolds number.
GBGIsotropicTurbulence.jl is in its final development stage and needs extensive testing in a cluster environment. That testing is meant to produce new results, not only to reproduce known ones. Its first target is the interpolation used for Lagrangian tracking. The established schemes were designed for fields dealiased by the 2/3 rule. This code uses phase-shift dealiasing, which reaches a given resolution on a smaller grid. That trades arithmetic for memory, a bargain that suits a GPU. The resulting field is rougher at the grid scale than those schemes assume, which hurts traditional interpolation schemes. GBGCloudPhysics.jl is mid-development, and its testing will establish whether it reaches results of the kind sought in NAISS 2026/3-574 at a lower computational cost.