PERTURBAZIONI OTTIMALI NON LINEARI ED EVENTI ESTREMI NEL FLUSSO IN UN CANALE

Understand the dynamics of wall turbulence is a challenging and difficult task but of key importance to improve flow control strategies and computational models. In this work, a nonlinear direct-adjoint method to compute optimal perturbations, i.e. perturbations with maximal kinetic energy at a given target time, is applied to the transitional and the turbulent channel flow. In the first part, perturbed Navier-Stokes equations are considered using the parabolic laminar profile as baseflow. The numerical code used for the optimizations is validated reproducing literature results on the transitional flow. Then, the assessment of the scaling exponent for the minimal transition energy is addressed in a small computational domain. The current computations are found in agreement with previous theoretical results and experimental findings. In the second part, the turbulent mean flow is used as baseflow in a Perturbative Reynolds-Averaged Navier-Stokes formulation (P-RANS). Theoretical profiles are used for the baseflow and an eddy viscosity model for the Reynolds stresses. Optimal perturbations in the turbulent flow are, thus, computed at two Reynolds number (Re=180 and Re=590), corroborating and extending previously published results. Visual inspection of the perturbations and the analysis of their premultiplied energy density spectra shows that the characteristic size of the optimal structures is proportional to the considered target time. Moreover, a varicose pattern of the velocity streaks is found at target time. Then, following recent literature, extreme dissipative events are sampled from DNS data at Re=180 and the neighbouring flow field is decomposed in eigenmodes by means of a Conditional Spatio-Temporal Proper Orthogonal Decomposition method (CST-POD). The symmetric and the antisymmetric parts of the flow field are separated before performing the CST-POD and it is shown that the first, associated to streaks instability of varicose type, is prevalent. This analysis is performed in four horizontal planes at different wall-normal positions. Therefore, a preliminary comparison is attempted between the extreme events leading modes and optimal perturbations constrained in a sub-domain of size comparable to the one used to sample the events. It is shown that perturbation shape, dissipation levels and quadrant distribution of the streamwise and wall-normal fluctuations are consistent between the two.