In atmospheric dynamics and physical oceanography

Oceanography

Oceanography , also called oceanology or marine science, is the branch of Earth science that studies the ocean...

, the Rossby radius of deformation is the length scale at which rotational effects become as important as buoyancy

Buoyancy

In physics, buoyancy is a force exerted by a fluid that opposes an object's weight. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the...

 or gravity wave

Gravity wave

In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media which has the restoring force of gravity or buoyancy....

 effects in the evolution of the flow

Flow

-Relating to the movement of material:* Fluid dynamics, or fluid flow, the motion of a gas or liquid* Environmental flow, the amount of water necessary in a watercourse to maintain a healthy ecosystem* Flow chemistry, a chemical reaction run in a continuous stream...

 about some disturbance.

For a barotropic

Barotropic

In meteorology, a barotropic atmosphere is one in which the pressure depends only on the density and vice versa, so that isobaric surfaces are also isopycnic surfaces . The isobaric surfaces will also be isothermal surfaces, hence the geostrophic wind is independent of height...

 ocean

Ocean

An ocean is a major body of saline water, and a principal component of the hydrosphere. Approximately 71% of the Earth's surface is covered by ocean, a continuous body of water that is customarily divided into several principal oceans and smaller seas.More than half of this area is over 3,000...

:

, where is the gravitational acceleration

Gravitational acceleration

In physics, gravitational acceleration is the acceleration on an object caused by gravity. Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate relative to the center of mass....

, is the water depth, and is the Coriolis parameter at the reference latitude

Latitude

In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...

.

For baroclinic flow:

, where is the Brunt–Väisälä frequency and is the scale height

Scale height

In various scientific contexts, a scale height is a distance over which a quantity decreases by a factor of e...

.

The associated dimensionless parameter is the Rossby number

Rossby number

The Rossby number, named for Carl-Gustav Arvid Rossby, is a dimensionless number used in describing fluid flow. The Rossby number is the ratio of inertial to Coriolis force, terms v\cdot\nabla v\sim U^2 / L and \Omega\times v\sim U\Omega in the Navier–Stokes equations, respectively...

. Both are named in honor of Carl-Gustav Rossby.
Chelton et al. evaluated its geographic variability.