Abstract

Turbulent flows are known to grow with downstream distance; think of a volcanic plume broadening as streamwise distance from the volcanic crater increases. This spreading occurs due to the transport, and mixing, of background fluid into the turbulent flow across the sharp interface demarcating the turbulent flow from the background in a process known as entrainment. In the special case where the background is non-turbulent this interface is known as the turbulent/non-turbulent interface and entrainment is known to be driven by viscous diffusion of the turbulent fluid into the background. This was first postulated by Corrsin and Kistler [1] and arises since the turbulent/non- turbulent interface is, in-effect, an isosurface of zero vorticity-magnitude to account for the fact that the background is irrotational whilst the vorticity is, by definition, non-zero in the turbulent portion of the flow. Accordingly the only non-zero source term at the turbulent/non-turbulent interface in the vorticity-magnitude transport equation is viscous diffusion. However, many (most) industrial and environmental flows exist within a turbulent background, for example wind-turbine wakes are exposed to atmospheric turbulence and gas-turbine blades are exposed to the turbulent outflow of the combustor. In such cases the intuition of Corrsin and Kistler [1] breaks down. Indeed, in the review paper of da Silva et al. [2] it was even suggested that when two streams of turbulence with comparable turbulence intensity are adjacent to one another the interface between them breaks down meaning that there is no discernible interface demarcating the adjacent streams of turbulence. In this seminar we prove the existence of a turbulent/turbulent interface [3] for a wake exposed to various degrees of freestream turbulence, including cases where the intensity of the freestream turbulence is greater than that within the wake. We will then explore the physics of the turbulent/turbulent interface which are different than those for turbulent/non-turbulent interfaces [4]. Finally, we will then examine how the presence of freestream turbulence affects the entrainment rate into the wake, considering the spatial evolution of the entrainment of mass, streamwise momentum, and kinetic energy [5]. Understanding these physics is important to being able to more accurately predict the spreading of turbulent flows exposed to freestream turbulence which is important for e.g. designing layouts for more efficient future wind farms.

References

[1] S. Corrsin and A. L. Kistler. Free-stream boundaries of turbulent flows. Technical Report NACA Tech. Rep. TN-1244, 1955.

[2] C. B. da Silva, J. C. R. Hunt, I. Eames, and J. Westerweel. Interfacial layers between regions of different turbulence intensity. Annual Review of Fluid Mechanics, 46(1):567–590, 2014.

[3] K. S. Kankanwadi and O. R. H. Buxton. Turbulent entrainment into a cylinder wake from a turbulent back- ground. Journal of Fluid Mechanics, 905:A35, 2020.

[4] K. S. Kankanwadi and O. R. H. Buxton. On the physical nature of the turbulent/turbulent interface. Journal of Fluid Mechanics, 942:A31, 2022.

[5] O. R. H. Buxton and J. Chen. The relative efficiencies of the entrainment of mass, momentum, and kinetic energy from a turbulent background. Journal of Fluid Mechanics, 977:R2, 2023.