35 
Appendix 
The circulation model is used to calculate currents in shallow surface waters which are 
influenced by bottom topography, wind, inflows and outflows of water, earth gravitation, 
and rotation. Baroclinie and thermodynamic processes (heat fluxes) are also taken into 
account. 
MOMENTUM EQUATIONS 
Equations of motion for the components of current velocity are derived from the classical 
form of conservation of momentum. It is reasonable to cast the equations in spherical 
co-ordinates. Since we are concerned with large-scale flow on the globe, the common 
hydrostatic approximation is applied. Thus we are left with two momentum equations for 
the horizontal components of velocity. Also the Boussinesq approximation is used. In 
addition, we make use of Reynolds’ decomposition into mean current (m,v) and 
fluctuation (u',v'). By inserting and averaging we obtain the standard equations for the 
velocities (eastward, northward) of mean horizontal flow: 
du u du v du du tan cp _ 1 1 dp 
— + - + — + w —uv= 2cosm<pv— — 
dt R cos tp dA R dtp dz R p R cos (p dA 
1 
R cos (p dA 
(;u'u') - 
l d , —r-,. d ——- tan cp —— 
(cos cp u v ) (u w ) + —M V 
R cos <p dep dz R 
dv u dv v dv , dv tan <p . 1 1 dp 
— + + — +w— + —uu= - 2co sin (pu-- — 
dt R cos <p dA R dtp dz R p R dtp 
1 
R cos (p dA 
(mV) 
1 d — d — • tan (p—r~, 
(cos tpv v ) (v w ) —M M 
R cos q.y dtp dz R 
where 
u,v,w: components of velocity (eastward, northward, upward) 
_ dA n d(p dz 
u = R cos (p — ,v = R — ,w = -— 
dt dt dt 
R : radius of the earth 
t : time 
A,tp : geographical longitude and latitude 
a : angular velocity of the earth rotation 
p : water pressure 
p : density of sea water 
CLOSURE MODEL 
To close the equations, we use a simple turbulence model at diagnostic level, i.e. without 
any additional evolution equation for, e.g., turbulent kinetic energy.