A Lagrangian closure approximation for homogeneous isotropic turbulence

Abstract eng:
The closure problem of turbulence has been one of the most important subjects in fluid dynamics through many years. Now a large number of closure models, ranging from empirical to theoretical, are available. In this paper, we are interested in closure models which are compatible with Kolmogorov’s five-thirds law without any adjustable free parameter. From this point of view, there are few closure models [1, 2], which are originated in the Lagrangian direct-interaction approximation (DIA) proposed by Kraichnan [3]. Their closure equations yield the Kolmogorov constant, CK = 1.72. In this paper, a new closure approximation, which is completely different from the DIA, is proposed for homogeneous isotropic stationary turbulence in the Lagrangian description. A two-closed-equation set is derived without any adjustable free parameter. The Kolmogorov constant CK is evaluated to be 1.66. This value is close to 1.62, which is the mean value of numerous experimental data collected by Sreenivasan [4].

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