Decaying turbulence in the presence of a shearless uniform kinetic energy gradient

Abstract

The decay of turbulent kinetic energy in nearly isotropic grid turbulence has been studied extensively as a fundamental point of reference for turbulence theories and numerical simulations. Most studies have focused on nearly homogeneous turbulence characterised by power-law decay. Other studies have focused on so-called shearless mixing layers, in which two regions with the same mean velocity but distinctly different kinetic energy levels slowly diffuse into each other downstream thus providing information about spatial transport of turbulence. Here, we introduce and study another type of shearless turbulent flow. It has initially a nearly uniform spatial gradient of kinetic energy of the form k ∼ β(y − y₀), where y is the spanwise position. In the experiments, this gradient is generated with the use of an active grid and screens mounted upstream of the wind-tunnel’s test section, iteratively designed to produce a uniform gradient of turbulent kinetic energy without mean velocity shear. Data are acquired using X-wire thermal anemometry at different spanwise and downstream locations. Profile measurements are used to quantify the constancy of the mean velocity and the linearity of the initial profile of kinetic energy. Measurements show that at all spanwise locations, the decay in the streamwise direction follows a power-law but with exponents n(y) that depend upon the spanwise location. The results are consistent with a decay of the form k/⟨u⟩² = β(x/x_ref)^−n(y)(y − y₀)/M. Results for the development of integral length scale, and for velocity skewness and flatness factors are also presented. Significant deviations from Gaussianity are observed especially for the spanwise velocity component in the lower kinetic energy region. Future experiments will be needed including measurements of the dissipation rate ϵ at sufficient accuracy, in order to unambiguously partition the energy decay into dissipation and spatial diffusion.

Keywords:

• homogeneous turbulence
• isotropic turbulence

Acknowledgements

The authors would like to thank Dr M. Wilczek for constructive comments regarding this work, and Juliaan Bossuyt for his assistance with the active grid.

Additional information

Funding

The financial support from the National Science Foundation [CBET 1033942] is gratefully acknowledged.