THE EKMAN SPIRAL
- Let's use the first-order closure ideas that we just studied to solve the
equations for boundary layer motion.
- We will need to make many assumptions:
- the flow is in steady state, i.e,
- the boundary layer is horizontally homogeneous, i.e.,
- the boundary layer is statically neutral, i.e.,
- the boundary layer is barotropic, i.e., Ug
and Vg are
constant with height
- there is no subsidence, i.e., W
after making these assumptions, the equations of motion become:
can we solve equation set (1)?
let's define the magnitude of the geostrophic wind, G
by G = [U2g
also assume that the geostrophic wind is parallel to the X axis, thus:
also use first-order local closure K-theory, assuming a constant Km
to eliminate the flux terms.
Substituting (2) into (1) gives:
we have a set of two partial differential equations...., how to solve?????
we need to specify the boundary conditions:
= 0 at z = 0
= 0 at z = 0
--> G as z -->
large (get above the boundary layer)
--> 0 as z --> large (the geostrophic flow above the boundary
layer is parallel to the X axis)
- The solution to (3) using the above boundary conditions is:
velocity vectors for this solution are shown to the right.
that the velocity vectors trace out a spiral shape with height...., this is
called the Ekman Spiral
What is a physical interpretation of (4), graphically shown in the figure to
the right? ANSWER
flow around a low, the winds converge radially into the low as a
result. This inflow into the low induces upward vertical motion.
process for inducing vertical motion is called Ekman