# Froude number

## Froude number

- 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 aswhere*V*is a characteristic velocity,*L*a characteristic length, and*g*the acceleration of gravity; or as the square root of this number.

- For continuously stratified, nonrotating, dry, inviscid 2D flow over an obstacle of height
*h*, with incoming wind speed*U*, and upstream Brunt-väisälä frequency*N*, the quantity*U*/(*Nh*) yields a measure of whether there will be an upstream-propagating region of decelerated flow and, hence, is also sometimes referred to as the Froude number. For*U*/(*Nh*) >> 1, the flow ascends over the obstacle with no upstream deceleration. For*U*/(*Nh*) << 1, a region of upstream flow deceleration forms that may propagate continuously upstream with time. Note that referring to the above relation as the Froude number is not consistent with the classical definition of Fr (see definition 1 above). For consistency with the original definition of Fr, some advocate referring to the relation*Nh*/*U*(the inverse of Fr as it is defined herein) as the nondimensional mountain height.

*term edited 12 Dec 2014*

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact permissions@ametsoc.org. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.