Analysis 02: OWF Effect on the Ocean - On the Effect of Offshore Wind Farms on the Atmosphere and Ocean Dynamics - page 75

stronger gradient in momentum. The stronger gradient and an intense horizontal
velocity depend on the fact that the momentum cannot be transferred from the top
layer to the layers below. While advection triggers the magnitude of w , A vc also
controls the number of vertical cells. Additionally, the vertical cells, besides the two
main cells around the OWF, are caused by velocity gradients at the surface and are
suppressed in the case of normal vertical eddy viscosity coefficient A vc .
Summarizing, the vertical exchange triggers dimension and magnitude of the up-
and downwelling cells. The hydrographic conditions are influenced by the vertical
advection, which again affects the vertical motion. The vertical diffusion acts
especially at the thermocline and support an exchange within the OWF district.
The vertical eddy viscosity coefficient A vc affects the vertical exchange of momen-
tum and the vertical velocity component w due to variations in the form and the
magnitude of the wake in the velocity field. The flanks of the wake become more
important, and the v -component increases in direction from north to south. Also, the
wake is intensified, as well as the vertical velocity component w . As higher A vc is
stronger, the velocity components are reduced at the surface.

Horizontal Exchange
The horizontal exchange plays a secondary role for the OWF effect on the ocean
system in the vertical. The sensitivity runs regarding horizontal exchanges are listed
in Table 5.1 .

Figure 5.17 illustrates the extrema along the cross-section S-N through the OWF
for each sensitivity run regarding horizontal exchanges like diffusion, advection,
momentum, and a combination of any of them. Overall differences between the
various horizontal exchange modes exist, but the extrema do not strongly vary with
maximal discrepancies of 10 %, compared to the normal run (src50), with the

exception of src53 and additional src58 for the velocity components. Sensitivity run
src53 avoids horizontal TS diffusion, while src58 avoids Smagorinsky diffusion
and exchange of momentum.
The Smagorinsky diffusion describes a nonlinear diffusion acting horizontally,
depending on u - and v -components. The Smagorinsky diffusion coefficient K smg
includes the horizontal tension strain T hs and the horizontal shearing strain S hs .
In Cartesian coordinates, it can be written as follows:

u
∂

∂

!

t þ

Δ u ¼ ... þ K smag Δ u ð 5 : 5 Þ

v
∂

∂

!

t þ

v ¼ ... þ K smag Δ v ð 5 : 6 Þ

Δ

w
∂

∂

!

t þ

w ¼ ... þ ð : Þ

Δ 0 5 7

q

T hs þ

l s S hs ¼ ∂ u

∂

x ∂ v

¼ ∂ u
∂

y þ ∂ v

with K smag ¼

x .
The use of the Smagorinsky horizontal diffusion stabilizes the dynamical core
against horizontal shear instabilities.

and T , S

y

∂ ∂