Rossby Number

Rossby number, abbreviated as Ro, a dimensionless number, is used in fluid dynamics, meteorology, and oceanography to describe the relative importance of inertial forces to Coriolis forces in a rotating fluid system.

 Key Points about Rossby number

• Rotation vs. Inertia  -  The Rossby number describes the balance between the fluid's inertia and the Coriolis effect (caused by the Earth's rotation).  It quantifies whether the rotation is significant compared to the fluid's motion.
• Atmospheric and Oceanic Applications  -  The Rossby Number is widely used in meteorology and oceanography to assess the influence of Earth's rotation on various phenomena, including the development of weather systems, the behavior of ocean currents, and the formation of cyclones and anticyclones.
• Planetary Rossby Number  -  In some applications, a non-dimensional form of the Rossby Number known as the Planetary Rossby Number (Ro_p) is used, which incorporates the planetary vorticity.

Reynolds number Interpretation

• Ro < 1  -  The Coriolis forces dominate, and the flow is rotationally dominated.  This often occurs in large scale atmospheric and oceanic circulation patterns, such as trade winds and the jet stream.
• Ro > 1  -  The fluid's inertia dominates, and the flow is inertially dominated.  This regime is common in small scale fluid motions, like tornadoes and eddies.

The Rossby number is a crucial parameter for understanding the dynamics of rotating fluid systems on Earth and other celestial bodies with atmospheres or oceans.  It helps scientists and meteorologists study phenomena influenced by Earth's rotation, such as weather patterns, ocean circulation, and the behavior of planetary atmospheres.

 

Rossby number formula
\( Ro =  U \;/\; l_c \; f \)     (Rossby Number) \( U =  Ro \; l_c \; f \) \( l_c =  U \;/\; Ro \; f \) \( f =  U \;/\; Ro \; l_c \)
Symbol	English	Metric
\( Ro \) = Rossby number	\(dimensionless\)
\( U \) = characteristic velocity	\(ft\;/\;sec\)	\(m\;/\;s\)
\( l_c \) = characteristic length	\(in\)	\(mm\)
\( f \) = Coriolis frequency	\(rad\;/\;sec\)	\(rad\;/\;s\)