
Froude number—1. The nondimensional ratio of the inertial force to the force of gravity for a given fluid flow; the reciprocal of the Reech number. It may be given as where V is a characteristic velocity, L a characteristic length, and g the acceleration of gravity;
or as the square root of this number. 2. For atmospheric flows over
hills or other obstacles, a more useful form of the Froude number is where N_{BV} is the Brunt–Väisälä frequency of the ambient upstream environment, V is the wind speed component across the mountain, and L_{w} is the width of the mountain. Fr can be interpreted as the ratio of natural wavelength
of the air to wavelength of the mountain. Sometimes π will appear in
the numerator, and other times the ratio will be squared. When Fr = 1,
the natural wavelength of the air is in resonance with the size of the mountain and creates the most intense mountain waves, which can sometimes contain lenticular clouds and rotors
of reverse flow at the surface. For Fr < 1, some of the
lowaltitude upstream air is blocked by the hill, shortwavelength
waves separate from the top of the hill, and the remaining air at lower
altitudes flows laterally around the hill. For Fr > 1, very long
wavelengths form downwind of the hill, and can include a cavity of reverse flow just to the lee of the hill near the surface. Another form of the Froude number, using (z_{i} − z_{hill}) in place of L_{w}, is useful for diagnosing downslope windstorms and hydraulic jump, where z_{i} is the depth of the mixed layer above the base of the mountain, and z_{hill} is the height of the mountain.

