The effect of data assimilation of large-scale eddies on small-scale eddies in turbulence is studied by direct numerical simulations (DNSs) of Navier-Stokes turbulence with Taylor microscale Reynolds numbers up to 179. The DNSs show that even if the data of small-scale eddies are lost at some initial instant, they can be regenerated from the data of large-scale eddies under the condition that Fourier modes with wave number less than a critical wave number k(*) are continuously assimilated, where k(*) approximately 0.2eta(-1) with eta identical with(nu(3)/epsilon)(1/4), epsilon the mean energy dissipation rate, and nu the viscosity.
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Yoshida et al. (2005) studied this question.