Publication Date:
2017-10-20
Description:
There is a long-standing debate in the literature of stratified flows over topography concerning the correct dimensionless number to refer to as a Froude number. Common definitions using external quantities of the flow include , , and , where and are, respectively, scales for the background velocity and buoyancy frequency, is the depth, and and are, respectively, height and width scales of the topography. It is also possible to define an internal Froude number , where , , and are, respectively, the characteristic velocity, reduced gravity, and vertical length scale of the perturbation above the topography. For the case of hydrostatic lee waves in a deep ocean, both and are insignificantly small, rendering the dimensionless number the only relevant dynamical parameter. However, although it appears to be an inverse Froude number, such an interpretation is incorrect. By non-dimensionalizing the stratified Euler equations describing the flow of an infinitely deep fluid over topography, we show that is in fact the square of the internal Froude number because it can identically be written in terms of the inner variables, . Our scaling also identifies as the ratio of the vertical velocity scale within the lee wave to the group velocity of the lee wave, which we term the vertical Froude number, . To encapsulate such behaviour, we suggest referring to as the lee-wave Froude number. © 2017 Cambridge University Press.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
Permalink
