There are many industrial and environmental situations where, at least transiently, a statically unstable density distribution occurs, with relatively dense fluid overlying less dense buoyant fluid in "narrow, tall" vertical channels of finite cross-section with high (length to width) aspect ratios. Examples include trickle chemical reactors and accidental releases of hazardous gases in vertical mineshafts. At sufficiently high Reynolds numbers, such flows become turbulent, with the dense fluid descending and mixing vigorously with the ascending buoyant fluid in the channel. Provided the aspect ratio is sufficiently large, the flow can be very well-described by a variant of Prandtl's mixing length theory, where the mixing length is given by the channel width, and the characteristic turbulent velocity is proportional to the product of the channel width and the square root of the local (statically unstable) buoyancy gradient. By comparison with laboratory experiments, where the evolution of the density distribution is tracked accurately using a non-invasive dye light-attenuation technique, I demonstrate that the evolution of the density distribution evolves in a self-similar fashion in two canonical situations: high aspect ratio Rayleigh-Taylor flow, where a layer of dense fluid is instantaneously released above another layer of buoyant fluid; and the constant buoyancy flux release of dense fluid into a narrow, tall channel. I show that the characteristic scalings of the flow evolution depend in a nontrivial manner on the boundary conditions, and in particular, that the assumption of a constant eddy viscosity, (independent of the present local value of the density gradient) is too simple to describe the time-dependent evolution of the flow appropriately.