Linear Navier-Stokes based model for turbulent channels with unstable stratification

Studies have shown that the linearized Navier-Stokes equations model the coherent large-scale structures in turbulent wall-bounded flows reasonably well. In the present work we aim to understand if this linear model can be extended to study the coherent large-scale structures that have been experimentally and numerically observed in turbulent Rayleigh--B{\'e}nard--Poiseuille flows [e.g., Chauhan et al., 2013, Pirozzoli et al., 2017]. In particular, we concentrate on two features of these structures. First, we look at the wall-normal coherence of the streamwise constant modes. And second, we study the inclination angle of the large-scale structures in these flows. These features are then compared to the available results from numerical and experimental studies. \\ \newline \underline{References} \\ K. Chauhan, N. Hutchins, J. Monty, and I. Marusic. Structure inclination angles in the convective atmospheric surface layer. \textit{Boundary-layer meteorol.}, 147(1):41--50, 2013. \\ S. Pirozzoli, M. Bernardini, R. Verzicco, and P. Orlandi. Mixed convection in turbulent channels with unstable stratification. \textit{J. Fluid Mech.}, 821:482--516, 2017.