text: In order to derive the properties of an Ekman spiral a look is taken at a uniform, horizontal geostrophic interior flow in a homogeneous fluid. This flow will be denoted by , where the two components are constant because of uniformity. Another result of this property is that the horizontal gradients will equal zero. As a result, the continuity equation will yield, . Note that the concerning interior flow is horizontal, so  at all depths, even in the boundary layers. In this case, the Navier-Stokes momentum equations, governing geophysical motion can now be reduced to:
  Where  is the Coriolis parameter,  the fluid density and  the eddy viscosity, which are all taken as a constant here for simplicity. These parameters have a small variance on the scale of an Ekman spiral, thus this approximation will hold. A uniform flow requires a uniformly varying pressure gradient. When substituting the flow components of the interior flow,  and , in the equations above, the following is obtained:
  Using the last of the three equations at the top of this section, yields that the pressure is independent of depth.
   and   will suffice as a solution to the differential equations above. After substitution of these possible solutions in the same equations,   will follow. Now,   has the following possible outcomes:
  Because of the no-slip condition at the bottom and the constant interior flow for , coefficients  and  can be determined. In the end, this will lead to the following solution for :
  Here, . Note that the velocity vector will approach the values of the interior flow, when the  takes the order of . This is the reason why  is defined as the thickness of the Ekman layer. A number of important properties of the Ekman spiral will follow from this solution: 
  *When , it appears that the flow has a transverse component with respect to the interior flow, which differs 45 degrees to the left on the northern hemisphere, , and 45 degrees to the right on the southern hemisphere, . Note that, in this case, the angle between this flow and the interior flow is at its maximum. It will decrease for increasing . 
  *When  takes the value of , the resulting flow is in line with the interior flow, but will be increased with , with respect to the interior flow. 
  *For higher values of , there will be a minimal transverse component in the other direction as before. The exponential term will go to zero for , resulting in . Because of these properties, the velocity vector of the flow as a function of depth will look like a spiral.