Sustaining processes from recurrent flows in body-forced turbulence

Abstract

By extracting unstable invariant solutions directly from body-forced three-dimensional turbulence, we study the dynamical processes at play when the forcing is large scale and unidirectional in either the momentum or the vorticity equations. In the former case, the dynamical processes familiar from recent work on linearly stable shear flows – variously called the self-sustaining process (Waleffe, Phys. Fluids, vol. 9 (4), 1997, pp. 883–900) or vortex–wave interaction (Hall & Smith, J. Fluid Mech., vol. 227, 1991, pp. 641–666; Hall & Sherwin, J. Fluid Mech., vol. 661, 2010, pp. 178–205) – are important even when the base flow is linearly unstable. In the latter case, where the forcing drives Taylor–Green vortices, a number of mechanisms are observed from the various types of periodic orbits isolated. In particular, two different transient growth mechanisms are discussed to explain the more complex states found.