Analysis 02: OWF Effect on the Ocean - On the Effect of Offshore Wind Farms on the Atmosphere and Ocean Dynamics - page 63

of the baroclinic model to barotropic model is done by
absence of baroclinic components. In the case of here used HAMSOM simulation
T012ug08 TS01HD60F01_BT (BT) , barotropic means negligence of the baroclinic
pressure component and the nonprognostic calculation of temperature and salinity.
A better treatment of temperature and salinity and further eliminations of baroclinic
components are not possible due to model design.
In this context, it must be mentioned that HAMSOM uses a semi-implicit
numerical scheme. The pressure component only is separated into internal
(baroclinic) and external (barotropic) components. Referred to Backhaus ( 1985 ),
the separation of barotropic and baroclinic pressure components is indicated in
following relation:

The simplification

' '

g Z 0

P 0 ðÞþ

z ϱ 0 d z int

Pz ðÞ¼ ð g

ϱ 1 ζ

Þ ext þ ð : Þ

5 1

with

atmospheric pressure at sea level; P 0 (

P ( ζ ): ¼ ζ ): ¼ atmospheric pressure anomaly at

sea level;
ˁ 1 : ¼ actual density of layer;

ˁ 0 : ¼ˁ 1 - ˁ 0 , ˁ 0 as reference density;

g : ¼ acceleration due to gravity;

ζ ¼

: surface elevation;

¼

ext : external component (barotropic);

int : ¼ internal component (baroclinic).

Based on explanations by Backhaus ( 1985 ), the atmospheric pressure P ( ζ ) is put
into the internal pressure component because it does not need to enter the implicit
scheme for the external pressure variations, which involves the sea surface eleva-
tion at the first layer. In the case of the internal component, the atmospheric
pressure enters as a pressure anomaly P (

ζ 0 ) due to the approximation of the internal
pressure gradients. That approximation obtains a high accuracy when it depends
entirely upon anomalies (Backhaus 1985 ).
The variations in the temperature and salinity field and thus in the density field
occur at much lower frequencies than the oscillation of the free surface. Hence, they
are solved by means of an explicit scheme, and therefore HAMSOM can only
simulate temporal and spatial changes of the large baroclinic fields. But the use of
implicit and explicit system components ends in the fact that a barotropic mode
during the implicit scheme strongly influences the temperature and the salinity
being treated in the explicit scheme. This means that the advection velocities
derived from the solution of the primitive equations are centered in time between
the adjacent time levels for heat and salinity because they are defined half a time
step apart from these. Finally, a constant temperature and salinity field gives the
barotropic conditions for the hydrography.