Ekman Layer
Abstract:
The Ekman layer is the layer of fluid near a fluid boundary
(can be a rigid boundary or an interface between two fluids)
that is affected by a viscous drag due to the no-slip
boundary condition, the Coriolis effect (in a rotating
frame), and the pressure gradient force. It is common for
the Ekman boundary layer to form in both fluids at an
interface, such as the region of air above the ocean and in
the ocean below the air, as well in a fluid at a rigid
bottom boundary, such as at the bottom of a rotating tank.
In this layer, an opposing flow forms due to the viscous
drag forces at the boundary. The resulting flow is then
forced sideways due to the nature of the Coriolis effect and
formed into a spiral, lovingly called the Ekman spiral. It
may be noted that this resulting flow is in the horizontal
plane only, however the this horizontal flow can be
divergent, resulting in vertical transport in incompressible
fluids (and compressible to a lesser degree).
Ekman transport is thought to be the mechanism for a
majority of atmospheric and oceanic mixing due the the
vertical velocity associated with Ekman pumping. In the
oceanic coastal areas, nutrients and even fish are pulled up
from deeper and brought closer to the surface. The
consistent atmospheric flows, such as the trade winds near
the equator, cause a net oceanic transport toward or away
from the equator serving to mix temperature toward the polar
directions. Ocean gyres are attributed to Ekman transport as
well, through the Coriolis effect.
On much smaller scales, the convergence of tea leaves in
the bottom of a stirred teacup is one of the best
visualizations of Ekman pumping. The flow of tea in the cup
has vorticity and drags at the bottom of the cup, causing a
converging horizontal flow in the Ekman layer. The
converging flow in the horizontal direction must be
accompanied with an upward vertical flow to maintain
incompressibility but the tea leaves stay at the bottom do
their density relative to the water. See the visualization
examples or try it yourself if you have not seen it!
- Derivation and Mathematical
Formulation
- Historical Observations
- Visualization and Experimental
Observations
- Resources