A dimensionless number relating the ratio of buoyancy to inertial forces. In a stratified fluid with characteristic squared buoyancy frequency J,the bulk Richardson number is Ri = J/(U/L)^2 in which U and L are characteristic velocity and length scales. The gradient Richardson number is defined as a function of height for stratified parallel flows by Ri_g (z) = N^2(z)/(dU/dz)^2 in which U(z) is the mean horizontal velocity and N^2(z) is the squared buoyancy frequency as a function of height. The flux Richardson number is defined for stratified turbulent flows with perturbation horizontal and vertical velocity fields u' and w', respectively, by Ri_f = -(g/

ho_0)<

ho'w'>/((dU/dz) ) which is the ratio of the rate of conversion to potential energy by the vertical flux of perturbation density

ho' to the rate of extraction of mean kinetic energy from the background horizontal velocity U(z). The flux Richardson number is also called the mixing efficiency.