In natural convection, the momentum equation includes a buoyancy term g beta(T - T_infinity) and a viscous term nu times the second derivative of velocity, balanced against inertia terms.
Nondimensionalizing by a characteristic length L, the buoyancy term scales as g beta Delta T, and the viscous term scales as nu u0/L^2. Comparing the buoyancy scale against the viscous scale produces the dimensionless group Gr = g beta Delta T L^3 / nu^2.
By convention, this is quoted and used as the ratio of buoyancy force to viscous force, exactly analogous to how Reynolds number is quoted as inertia force to viscous force.
\[ \boxed{\text{Grashof number} = \dfrac{\text{buoyancy force}}{\text{viscous force}}} \]