A DATA ASSIMILATION STUDY FOR THE IDENTIFICATION OF SCALES GOVERNING GRID TURBULENCE DECAY

Abstract

The decay of incompressible homogeneous isotropic turbulence (HIT), which can be studied via grid turbulence experiments, is among the most important issue in turbulence theory, since isotropic turbulence is the framework in which the deepest investigations of nonlinear features o f turbulence can be performed. Even though numerous studies have been devoted to HIT since about one century, many questions remain open. Among them, the identification of scales which govern the decay of HIT still deserves further investigations. Although there is consensus that the turbu lent kinetic energyK, after a possible transient relaxation phase, follows an algebraic law, i.e. K(t) ∝ tnK , the question of the dependence of the exponent nK to some specific features of the initial condition has raised some controver sies. However, the most recent works indicate that there is no universal regime and that the decay rate is definitely governed by the details of the initial condition. Indeed, it is generally stated in the literature that the exponent nK is related to the asymptotic large-scale behavior of the longi tudinal velocity correlation functionf (r, t = 0) in physical space, or equivalently, to the asymptotic behavior of the ki netic energy spectrumE(k, t = 0) in spectral space. But it is worth keeping in mind that, due to technological limitations, the exact behavior of the velocity correlation function, or that of the energy spectrum, at scales much larger than the integral scale escapes both experimental and numerical investigation at the present time. Besides, the con cept of large-scale asymptotic behavior is hard to reconcil e with real-life turbulent flows, which are bounded in space and can be observed over finite times only. It is also interesting to note that the Comte-Bellot Corrsin theory, which proves to be effective in predicting the value of the exponentnK , relies on a single length scale which is the integral scale.