Nanda Nechingal Raghunathan

arXiv2026

Data Assimilation with Sparse Observations

Data assimilation by nudging (also called CDA) yields exponentially decaying errors and an infinite predictability horizon if the method parameter is large enough and the observations are frequent enough in time and dense enough in space. We consider the complementary case of moderate parameters and sparse and infrequent observations. We prove that assimilation with any data and any(positive) parameter strictly decreases errors and strictly increases the (now finite) predictability horizon.

math.NA↗

arXiv2026

Energy dissipation rates of ensemble eddy viscosity models of turbulence: the periodic box

Classical eddy viscosity models of turbulence add an eddy viscosity term based on the Kolmogorov-Prandtl parameterization by a turbulent length scale $l$ and a turbulent kinetic energy $k^{\prime }$. Approximations of the unknowns $l,k^{\prime }$ are typically constructed by solving multi-parameter systems of nonlinear convection-diffusion-reaction equations. Often these over-diffuse so additional fixes are added. Alternately, one can solve an ensemble of NSE's with perturbed data and simply compute directly $k^{\prime }$(without modeling). The question then arises: Does this ensemble eddy viscosity approach over-diffuse solutions? We prove herein that for turbulence in a periodic box it does not.

math.NA↗