where U and L are the velocity and length scale of the motion, and v is the viscosity. The Reynolds number is the ratio of the inertial force to the viscosity force. When Re is small, the friction force is important, i.e., it is comparable with the inertial force, and the flow is laminar. When Re is large, the frictional force is less important, i.e., it is much smaller than the inertial force, so that the frictional effect is confined within very thin boundary layers near the solid boundary of the flow field. The flow under a large Reynolds number is turbulent.
The Richardson number is the ratio of the stratification and the square of the vertical velocity shear. A strong stratification can inhibit the instability, but a strong velocity shear is in favor of the instability; thus, the Richardson number is widely used as an index for instability. A necessary condition for instability is Ri < 1/4. However, this does not necessarily mean that instability will actually occur.
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