Ekman velocity

In oceanography, Ekman velocity – also referred as a kind of the residual ageostropic velocity as it derivates from geostrophy – is part of the total horizontal velocity (u) in the upper layer of water of the open ocean. This velocity, caused by winds blowing over the surface of the ocean, is such that the Coriolis force on this layer is balanced by the force of the wind. In oceanography, Ekman velocity – also referred as a kind of the residual ageostropic velocity as it derivates from geostrophy – is part of the total horizontal velocity (u) in the upper layer of water of the open ocean. This velocity, caused by winds blowing over the surface of the ocean, is such that the Coriolis force on this layer is balanced by the force of the wind. Typically, it takes about two days for the Ekman velocity to develop before it is directed at right angles to the wind. The Ekman velocity is named after the Swedish oceanographer Vagn Walfrid Ekman (1874–1954). Through vertical eddy viscosity, winds act directly and frictionally on the Ekman layer, which typically is the upper 50–100m in the ocean. The frictional surface flow (u) is at an angle to the right of the wind (45 degrees if viscosity is uniform in the vertical z-direction). This surface flow then modifies the flow slightly beneath it, which then is slightly more to the right, and finally the exponentially-weaker-with-depth flow vectors die down at around 50–100 meters, and finally form a spiral, called the Ekman spiral. The angle of each successive layer as we move downward through the spiral depends on the strength and vertical distribution of the vertical eddy viscosity. When the contributions from all the vertical layers are added up – the integration of the velocity over depth, from the bottom to the top of the Ekman layer – the total 'Ekman transport' is exactly 90 degrees to the right of the wind direction in the Northern Hemisphere and left in the Southern Hemisphere. Suppose geostrophic balance is achieved in the Ekman layer, and wind stress is applied at the water surface: where ϕ = p / ρ 0 , {displaystyle phi =p/ ho _{0},,} τ {displaystyle {oldsymbol { au }}} is the applied stress divided by ρ 0 {displaystyle ho _{0},} (the mean density of water in the Ekman layer)； z ^ {displaystyle {hat {oldsymbol {z}}}} is the unit vector in the vertical direction (opposing the direction of gravity). The definition of Ekman velocity is the difference between the total horizontal velocity ( u {displaystyle {oldsymbol {u}}} ) and the geostrophic velocity ( u g {displaystyle {oldsymbol {u}}_{g}} ): As the geostropic velocity ( u g {displaystyle {oldsymbol {u}}_{g}} ) is defined as