We examine how the presence of active galactic nuclei (AGN) correlates with location in large-scale cosmic structures using the Galaxy and Mass Assembly (GAMA) survey across the G09, G12, and G15 fields. Our sample contains 18 927, 9 273, and 1 148 galaxies for highly dense filaments, moderately dense tendrils, and highly underdense voids, respectively. AGN are identified among emission-line galaxies using Baldwin-Phillips-Terlevich (BPT) diagnostic diagrams based on [NII], [SII], and [OI]. We compare AGN fractions across filament, tendril, and void regions and as a function of distance from the nearest filament centreline. Our results reveal a mild excess in filaments compared to voids when using [SII]- and [NII]-based classifications, while no significant environmental dependence is found for [OI]-based classifications. Overall, we find a weak environmental trend with AGN activity, which suggests that the local environment does not always dominate AGN activity; instead, secular processes are likely to be at play. Our findings are consistent with previous studies reporting only marginal preferences for overdense environments for AGN.

We compute the optimal response of the turbulent Couette mean flow to initial conditions, harmonic and stochastic forcing at Re = 750. The equations for the coherent perturbations are linearized near the turbulent mean flow and include the associated eddy viscosity. The mean flow is found to be linearly stable but it has the potential to amplify steamwise streaks from streamwise vortices. The most amplified structures are streamwise uniform and the largest amplifications of the energy of initial conditions and of the variance of stochastic forcing are realized by large-scale streaks having spanwise wavelengths of 4.4h and 5.2h respectively. These spanwise scales compare well with the ones of the coherent large-scale streaks observed in experimental realizations and direct numerical simulations of the turbulent Couette flow. The optimal response to the harmonic forcing, related to the sensitivity to boundary conditions and artificial forcing, can be very large and is obtained with steady forcing of structures with larger spanwise wavelength (7.7h). The optimal large-scale streaks are furthermore found proportional to the mean turbulent profile in the viscous sublayer and up to the buffer layer.