The path to the most efficient and effective solution leads to utilizing passive and natural effects to your advantage. This goes up against modern methods of stringent artificial control of everything. Solar and ground heat transfer are not going to change by leaps and bounds over the long-term. You can aid mother nature by optimizing flows and rates and ratios, but it is inherently a game of diminishing returns. The key here is to follow the laws and rules of the system you are building.
The questions you are presenting lead in a direction that not many people understand. The answers you seek involve calculus, physics, engineering, and a wizard who knows how to make sense of them. These wizards typically make large sums of money answering these questions and making the magic into a working design. Things like enthalpy, entropy, gradients, and fluid dynamics are rather fuzzy. Making comparisons and decisions is all about trade-offs. Controlled mayhem, so to speak. Finding specific answers that pertain to your specific set of conditions, configuration and expectations of performance is going to be difficult.
That being said, here you go:
Richardson number - Wikipedia, the free encyclopedia
On the critical Richardson number in stably stratified turbulence - Galperin - 2007 - Atmospheric Science Letters - Wiley Online Library
http://en.wikipedia.org/wiki/Boussin...tion_(buoyancy)
Combined forced and natural convection - Wikipedia, the free encyclopedia