Efficient Generation of High-Reynolds-Number Homogeneous Turbulence by Disturbances Composed of Two Frequency Components Available to Purchase

We attempted to determine the number of frequency components required for efficient turbulence generation using a multi-fan type wind tunnel where 99 fans were driven to generate turbulence. In a previous study, a random-phase mode was applied, where an input signal composed of forty frequency components was fed to each fan with quasi-random phases. Using this driving mode, we achieved high-Reynolds-number homogeneous turbulence of Re_λ ∼ 750 in a relatively short distance. In the present study, in order to understand the elementary process of the evolution, one single frequency or two frequencies were used, instead of forty. When using the single frequency, initial dominant spectral peaks remain at lower frequencies over the tunnel length. In the case of two frequencies, f₁ and f₂ (f₁ = n₁f₀ and f₂ = n₂f₀; n₁ < n₂), where n₁ and n₂ are integers, and f₀ is defined as the reciprocal of a basic input data period, the turbulence characteristics depend on the relation between n₁ and n₂. When n₁ and n₂ are not coprime (i.e., n₂ can be divided by n₁), dominant spectral peaks remain over the tunnel length as in the case of using a single frequency, but when coprime (i.e., n₂ cannot be divided by n₁), the spectral shape becomes relatively smooth with the initial dominant peaks disappearing. However, it was found that the development of turbulence is much slower for the two-frequency case than for the forty-frequency case.