TRR181 Seminar Series: 'Scale-dependent Error Growth in Navier...' by Dr. Nazmi Burak Budanur

October 25, 2022
"Scale-dependent Error Growth in Navier-Stokes Simulations", by Dr. Nazmi Burak Budanur (Max Planck Institute for the Physics of Complex Systems)

Abstract:

We estimate the maximal Lyapunov exponent at different resolutions and Reynolds numbers in large eddy (LES) and direct numerical simulations (DNS) of sinusoidally-driven Navier--Stokes equations in three dimensions. Independent of the Reynolds number when nondimensionalized by Kolmogorov units, the LES Lyapunov exponent diverges as an inverse power of the effective grid spacing showing that the fine scale structures exhibit much faster error growth rates than the larger ones. Effectively, i.e., ignoring the cut-off of this phenomenon at the Kolmogorov scale, this behavior introduces an upper bound to the prediction horizon that can be achieved by improving the precision of initial conditions through refining of the measurement grid.