The conditions for dynamical similarity of motions of a frictionless perfect-gas atmosphere

✍ Scribed by G. K. Batchelor

• Publisher: John Wiley and Sons
• Year: 1953
• Tongue: English
• Weight: 775 KB
• Volume: 79
• Category: Article
• ISSN: 0035-9009
• DOI: 10.1002/qj.49707934004

✦ Synopsis

Abstract

The object of this paper is to show, in an elementary way, the general significance of the Richardson number for motions of a frictionless perfect gas of variable density subject to gravity. Dimensionless parameters like the Richardson number are important in relation to the concept of dynamical similarity of flow fields, and as a consequence the paper consists largely of discussions of the conditions for dynamical similarity of flow fields of specified kind. It is established that if the flow fields are such that the pressure and density everywhere depart by small fractional amounts only from the values for an equivalent atmosphere in adiabatic equilibrium and if the vertical length scale of the velocity distribution is small compared with the scale height of the atmosphere, the Richardson number is the sole parameter governing dynamical similarity. Various possible forms of the Richardson number are examined.