The Ekman number is a dimensionless number used in describing geophysical

Geophysics

Geophysics is the physics of the Earth and its environment in space; also the study of the Earth using quantitative physical methods. The term geophysics sometimes refers only to the geological applications: Earth's shape; its gravitational and magnetic fields; its internal structure and...

 phenomena in the oceans and atmosphere. It characterises the ratio of viscous

Viscosity

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

 forces in a fluid

Fluid

In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

 to the fictitious forces

Coriolis effect

In physics, the Coriolis effect is a deflection of moving objects when they are viewed in a rotating reference frame. In a reference frame with clockwise rotation, the deflection is to the left of the motion of the object; in one with counter-clockwise rotation, the deflection is to the right...

 arising from planet

Planet

A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

ary rotation

Rotation

A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...

. It is named after the Swedish oceanographer Vagn Walfrid Ekman

Vagn Walfrid Ekman

Vagn Walfrid Ekman was a Swedish oceanographer.Born in Stockholm to Fredrik Laurentz Ekman, himself an oceanographer, he became committed to oceanography while studying physics at the University of Uppsala and, in particular, on hearing Vilhelm Bjerknes lecture on fluid dynamics.During the...

.

More generally, in any rotating flow, the Ekman number is the ratio of viscous forces to Coriolis forces. When the Ekman number is small, disturbances are able to propagate before decaying owing to frictional effects. The Ekman number describes the order of magnitude for the thickness of an Ekman layer, a boundary layer

Boundary layer

In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface where effects of viscosity of the fluid are considered in detail. In the Earth's atmosphere, the planetary boundary layer is the air layer near the ground affected by diurnal...

 in which viscous diffusion is balanced by Coriolis effects, rather than the usual convective inertia.

Definitions

It is defined as:


- where D is a characteristic (usually vertical) length scale of a phenomenon; ν, the kinematic eddy viscosity; Ω, the angular velocity

Angular velocity

In physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per...

 of planet

Planet

A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

ary rotation

Rotation

A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...

; and φ, the 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...

. The term 2 Ω sin φ is the Coriolis frequency

Coriolis effect

In physics, the Coriolis effect is a deflection of moving objects when they are viewed in a rotating reference frame. In a reference frame with clockwise rotation, the deflection is to the left of the motion of the object; in one with counter-clockwise rotation, the deflection is to the right...

.
It is given in terms of the kinematic viscosity , the angular
velocity , and a characteristic lengthscale .

There do appear to be some differing conventions in the literature.

Tritton gives:


In contrast, the NRL Plasma Formulary gives:


NRL states that this latter definition is equivalent to the root of the ratio of 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...

 to Reynolds number. There are various definitions for the Rossby number as well.