Self-Similar Stochastic Excitations For Linear Models In Turbulent Channel Flow

A physics aware data-driven method is formulated to determine an optimal forcing structure for an eddy viscosity enhanced, linearised Navier-Stokes model of turbulent channel flow. By restricting the forcing to be white-in-time and spatially decorrelated, an optimisation problem is solved to determine the forcing spectra which drives the linear model's velocity spectra to match that of a high Reynolds direct numerical simulation. Through exploiting the self-similarity within the attached eddy hypothesis, this optimisation problem is further reduced to a single spanwise length scale, allowing a rapid approximation of the entire forcing spectra. By exploiting the linear nature of the model, the isolated effects of each of the forcing components and how they can be extrapolated to a global forcing structure is analysed. Continuing with the utilisation of linearity, the role of the amplification mechanisms in the linear model (Orr mechanism and lift-up effect) in mimicking the DNS velocity spectra is evaluated. Interestingly, the linear model can reproduce all qualitative features of the DNS spectra, with the scale-dependent contribution of either mechanism resembling the underlying physics of the attached eddies, as well as phenomenologically mimicking energy cascade features.