The intrinsic depth of horizontal convection

The mainstream depth of a return flow can be viewed as an intrinsic depth of horizontal convection. By using a theoretical tube model combined with the application of the Maximum Entropy Production Principle (MaxEPP) in thermodynamics, the following statements can be made. Under fixed external forcing, the system chooses a particular depth as the mainstream depth of its return flow, the depth of which not only satisfies the maximum circulation rate and the maximum heat transport, but also satisfies the maximum entropy production rate. A comparison between this intrinsic depth and the container height leads to the definition of a relative partial and full-penetration pattern of the circulation. Moreover, this intrinsic depth is found to vary with the external forcing; the regulation of this variation is related to the Modified Rayleigh number.