A data-driven approach to modeling turbulent decay at non-asymptotic Reynolds numbers

Dynamic modeling of turbulent processes away from asymptotic parameter limits is an active area of turbulence research. This study considers the transient modeling of the kinetic energy dissipation rate, an important component for turbulence closure models like $k-\epsilon$. While asymptotic analysis of the turbulent dissipation process effectively calibrates the model parameters at high and low Reynolds numbers, these calibrations are inaccurate at intermediate Reynolds with strong dependence on large-scale turbulence properties. In intermediate regimes, model tuning via data-driven regression has a leading-order effect on accuracy such that a purely data-driven approach is sensible. Here, we model the kinetic energy dissipation rate in decaying isotropic turbulence using a NeuralODE, a continuous-depth neural network which models continuous-time processes. After training a model using direct numerical simulations (DNSs) over a range of Reynolds numbers and large-scale turbulence initial conditions, we show that a purely data-driven approach to modeling turbulent dynamics via NeuralODEs provides an attractive solution to turbulence closure in non-idealized parameter regimes.