We present high-fidelity Direct Numerical Simulations (DNS) of idealized supraglacial channels, governed by the Boussinesq equations with a quadratic equation of state to model freshwater dynamics. The flow is driven by the competition between three forcing mechanisms, each quantified by a specific dimensionless control parameter: (i) a gravity-driven Poiseuille shear flow due to the channel slope, characterized by the friction Reynolds number ($Re_{\tau}$); (ii) boundary thermal forcing with fixed ice temperature at the bottom (Dirichlet) and atmospheric heat balance at the surface (Robin), controlled by an atmospheric Rayleigh number ($Ra_{air}$); and (iii) volumetric solar radiative heating, modeled via an 8-band spectral source term with bottom reflection, quantified by a radiative Rayleigh number ($Ra_{rad}$).

In the regime of interest (freshwater below $4^\circ$C), the density anomaly promotes a Rayleigh-Bénard-like instability: water heated at the surface and in the bulk becomes denser and sinks, interacting with rising cold water to form distinct convection cells. This convective circulation competes with the longitudinal shear flow, with both mechanisms contributing to the generation of turbulence. We specifically examine the resulting turbulent statistics, focusing on turbulence intensity and vertical profiles across the channel depth.

Through an exploration of the parameter space ($Re_{\tau}$, $Ra_{air}$, $Ra_{rad}$), we analyze the flow regimes and the transition between shear-dominated and buoyancy-dominated dynamics. Furthermore, we investigate the influence of the Prandtl number on these dynamics by comparing an idealized case ($Pr=1$) with a realistic freshwater scenario ($Pr=13$).