ensure that the fluid will continue to flow as long as the reactor is hotter than the heat sink, even when power cannot be supplied to the pumps. Notable examples are the S5G and S8G United States Naval reactors, which were designed to operate at a significant fraction of full power under natural circulation, quieting those propulsion plants. The S6G reactor cannot operate at power under natural circulation, but can use it to maintain emergency cooling while shut down. By the nature of natural circulation, fluids do not typically move very fast, but this is not necessarily bad, as high flow rates are not essential to safe and effective reactor operation. In modern design nuclear reactors, flow reversal is almost impossible. All nuclear reactors, even ones designed to primarily use natural circulation as the main method of fluid circulation, have pumps that can circulate the fluid in the case that natural circulation is not sufficient. Mathematical models of convection A number of dimensionless terms have been derived to describe and predict convection, including the Archimedes number, Grashof number, Richardson number, and the Rayleigh number. In cases of mixed convection (natural and forced occurring together) one would often like to know how much of the convection is due to external constraints, such as the fluid velocity in the pump, and how much is due to natural convection occurring in the system. The relative magnitudes of the Grashof number and the square of the Reynolds number determine which form of convection dominates. If , forced convection may be neglected, whereas if , natural convection may be neglected. If the ratio, known as the Richardson number, is approximately one, then both forced and natural convection need to be taken into account. Onset The onset of natural convection is determined by the Rayleigh number (Ra). This dimensionless number is given by where is the difference in density between the two parcels of material that are mixing is the local gravitational acceleration is the characteristic length-scale of convection: the depth of the boiling pot, for example is the diffusivity of the characteristic that is causing the convection, and is the dynamic viscosity. Natural convection will be more likely and/or more rapid with a greater variation in density between the two fluids, a larger acceleration due to gravity that drives the convection, and/or a larger distance through the convecting medium. Convection will be less likely and/or