Evidence of an inverse cascade in a plane wall jet through large-scale forcing.

The present work focuses on understanding the scale interactions within a turbulent boundary layer through large-scale, large-perturbation forcing. A plane wall jet (PWJ), the model flow field, was subject to acoustic forcing. The streamwise wavelengths of the forcing $\lambda_{ex}$, were larger than the local integral length scale $\delta(x)$, where $x$ is the streamwise direction. When the forcing wavelength $\lambda_{ex}$ was larger than the wavelengths of the naturally occurring outer large-scales of the unperturbed jet $\lambda_{n}$, the forcing energy was transferred to scales smaller than $\lambda_{ex}$ in a forward cascade. As the PWJ develops downstream, the local integral length scale $\delta(x)$ gets larger due to the spreading of the PWJ. Hence, as the PWJ develops at downstream locations where $\lambda_{ex}<\lambda_n$, the forcing energy was transferred to scales larger than $\lambda_{ex}$ indicating an inverse cascade. This transfer was accompanied by a transfer of momentum away from the near-wall region to the outer region of the plane wall jet and reduction of the friction velocity for all $\lambda_{ex}$ considered.