Analysis 02: OWF Effect on the Ocean - On the Effect of Offshore Wind Farms on the Atmosphere and Ocean Dynamics - page 67

Such processes are defined for horizontal and vertical exchanges comprising the
exchange of momentum, heat, mass, and salinity. They can be summarized under
advection and diffusion. The exchange processes are based on local gradients,
which are strengthened by turbulent motion.
In hydrology, advection means the transport of solved or suspended material in
water with the flow, thus with the mean speed and direction of the ocean flow
(Rubin and Atkinson 2001 ). In the vertical, salinity and heat transport, as well as the
one of momentum, is related to the vertical velocity component w .
Diffusion is defined as a transport of molecules along a concentration gradient
(Jones 2010 ); as intensified, the gradient is as stronger as diffusion.
The different terms regarding advection and diffusion in HAMSOM were
switched on and off by manipulating the source code to evaluate their impact
factor. Therefore, some explanations about HAMSOM details are necessary. The
following description is in accordance with Backhaus ( 1985 ) and Pohlmann ( 2006 ).
HAMSOM s diffusion and advection terms are bounded in the equation of

motion, the transport equation of temperature, respectively salinity. While the
diffusion terms, the vertical shear stress and the terms determining the surface
gravity waves are formulated implicitly, all other terms are formulated explicitly
(Pohlmann 2006 ). The advective terms in the momentum equation and the transport
equation for temperature and salinity are solved explicitly, with the exception of the
vertical advective term. Advection and diffusion of temperature and salinity in
HAMSOM follow a method related to the difference scheme of second order
accuracy from Lax and Wendroff ( 1960 ). That second order advective scheme
was implemented in HAMSOM in combination with a superbee flux limiter (Roe
1986 ) by Hein ( 2013 ) and is able to simulate the diffusion more realistically, and
the mixing processes are fully controlled by physical processes. The use of the flux
limiter avoids spurious oscillation due to shock waves, contact with surfaces, or
discontinuous derivatives across any characteristics (Roe 1986 ). Fick

'

' s laws

describe the diffusion itself.
At this point, two important coefficients of the model HAMSOM must be
introduced—the vertical eddy viscosity coefficient A vc and the vertical eddy diffu-
sion coefficient A dc .
The coefficient A vc is used because small-scale vortices or eddies in the motion
cannot be resolved at the mesoscale. To consider such vortices, the large-scale
motion is calculated with eddy viscosity that characterizes the transport and dissi-
pation of energy in the smaller scale flow. So A vc is linked with the transfer of
momentum caused by turbulent eddies and is linked to the molecular exchange in
the vertical because the vertical eddy diffusion coefficient A dc in the prognostic
equation of temperature is calculated via A vc . In an equation, this subject matter is
described as follows.
A vc can be separated into different applications, into the usage in surface mixed
layer, the bottom mixed layer, and the interior, which is under laminar conditions.
In the case of the laminar part, the coefficient A vc is defined as 0.0134 cm 2 /s. In the
case of the turbulent part, the coefficient A vc is defined by