Ensemble transient growth in turbulent channel flow

In state space, turbulence at sufficiently high Reynolds numbers may well be viewed as an chaotic attractor, where the sensitivity of initial condition prevents one to explore the evolution of small perturbations for a longer time scale. However, in the statistical state space, where the ensemble-averaged dynamics of turbulence is considered instead, the turbulent attractor becomes a stable fixed point. In this presentation, we present an approach to compute an optimal tansient growth of a small perturbation added to turbulent channel flow. In the past, this has been computed using the linearised Navier-Stokes equations with a simple eddy viscosity model that acccunts for the effect of background turbulence (Reynolds & Hussain 1972, J. Fluid Mech. 54(2): 263-288). Here, without using such an ad-hoc model, we present a novel data-driven approach, where a low-dimensional form of the linearised operator governing the perturbation evolution is identified using a series of ensemble-averaged evolutions of initial conditions. We report some non-trivial differences between the predictions by the previous model and the present data-driven approach, and highlight the role of background turbulence on the perturbation evolution.