52
K. Myrberg and A. Lehmann
Fig. 2.8 The tilt of the sea
surface across the Great Belt
calculated according to the
sea level differences between
Korsör and Slipshavn and the
relation between the tilt and
the surface currents measured
at the lightship Halskov Rev
according to Dietrich et al.
(1963). From Leppäranta and
Myrberg (2009)
Consider the full horizontal equation of motion (2.3) for the combination of the
Ekman theory and the geostrophic theory. It is customary to assume that the resulting current velocity q = q E + q G is a linear superposition of the Ekman solution
q E and the geostrophic current q G . In a stationary regime and assuming that the
advection and horizontal friction can be omitted, Eq. (2.3) is reduced to
if (q E + q G ) = −
1
ρ
∇p + A v
∂ 2 (q E + q G )
∂z 2
.
(2.17)
If it is furthermore assumed that in the last term the influence of the geostrophic
flow is negligible, the Ekman equation and the geostrophic equation can simply be
summed up. As both the equations are linear, the solution of the resulting equation
is the sum of the Ekman and geostrophic solutions. Especially in the barotropic case
q G = const and thus ∂ 2 u G /∂z 2 = 0.