Institute of Oceanogphy Gdańsk University J an J ę drasik The Hydrodynamic Model of the Southern Baltic Sea. The hydrodynamic model. Based on Princeton Ocean Model (Blumberg and Mellor 1987).
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The Hydrodynamic Model of the Southern Baltic Sea
where: u, v, w,componentsof velocity prędkości;f, Coriolis parameter; , 0, density of sea water in situand reference density;
g, gravity acceleration; p, pressure; KM, AM, vertical and horizontal viscosity coefficients
where: patm, atmospheric preassure; , sea level elevations
where: T, temperatureof water; S, salinity; KH, AH,vertical and horizontal diffusivity coefficients; T, sourcesof heat
where: AC,,empirical coefficient; x, y, spatial steps in xand y direction.
where: q2, turbulent kinetic energy, turbulent macroscale; Kq, coefficient of vertical exchange of turbulent energy; , Karman‘s constant; H, sea depth; B1, E1, E2, empirical constants.
Kinematic condition at the surface
At the bottom z = H
Fluxes of energy at the bottom
Kinematic condition at the bottom
where: ox, oy, wind surface stresses; H0, heat fluxes from atmosphere; bx, by, bottom stresses; CD, drag coefficient (CD=0.0025); friction velocity; u, ub, v, vb, w, wb, components of velocity at the surface (no index) and at the bottom (with b index).
At the lateral boundary (rivers)
u(x,y,z) = 0, v(x,y,z) = 0, w(x,y,z) = 0
T = T(x,y,z), S = S(x,y,z).
Application of the model
where: , angular velocityof Earth; , geographical latitude
Horizontal diffusivity criterium
where: AH, horizontal diffusivity coefficient
where: C velocity of fundamental mode, Umax , maxime current velocity; or Ct = 2Ci + umax, Ci , velocity of fundamental internal mode, umax , maxime advection velocity.
Sigma coordinates (x*, y*, , t*),
x* = x, y* = y, , t* = t,
where: D = H + , dla z = = 0,
for z = -H = -1
Temporal and spatial steps in the modelled areas