Triad interactions in a forced turbulence

Abstract

An analysis of the data of a direct numerical simulation of a forced incompressible isotropic turbulence at a high Reynolds number (Rλ≊180) is made to investigate the interaction among three Fourier modes of wave numbers that form a triangle. The triad interaction is classified into six types according to the direction of the energy transfer to each Fourier mode: (+,+,−), (+,−,+), (+,−,−), (−,+,+), (−,+,−), (−,−,+), where the + (or −) denotes the energy gain (or loss) of the modes of the largest, the intermediate, and the smallest wave numbers in this order. The last three types of the interaction are very few. In the first type of the interaction, a comparable amount of energy is exchanged typically among three modes of comparable magnitude of wave numbers. In the second and third types, the magnitudes of the larger two wave numbers are comparable and much larger than the smallest one, and a great amount of energy is exchanged between the former two. This behavior of the triad interaction agrees very well with the prediction due to various quasinormal Markovianized closure theories of turbulence, and was observed before for lower Reynolds number turbulence by Domaradzki and Rogallo [Phys. Fluids A 2, 413 (1990)]. The fact that the dominant triad interactions involve different scales of motion suggests that the statistics of the small-scale motions of turbulence may be directly affected by the large-scale motions. Nevertheless, Kolmogorov’s local energy cascade argument may hold at least partially because the energy is exchanged predominantly between modes of two comparable scales in the triad interaction.