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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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Institute of Oceanogphy Gdańsk University

Jan Jędrasik

The Hydrodynamic Model of the Southern Baltic Sea

The hydrodynamic model

  • Based on Princeton Ocean Model (Blumberg and Mellor 1987)

  • Vertical mixing processes are parameterized by the scheme of second order turbulence closure (Mellor and Yamada 1982)

  • In order to apply the model for the Baltic Sea some modifications were done (Kowalewski 1997)

Description of the hydrodynamic model m3d ug equations and boundary cionditions
Descriptionof the hydrodynamic modelM3D_UG Equations and boundary cionditions

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.

At the sea surface

Heat fluxes

Energy fluxes

Kinematic condition at the surface

At the bottom z = H

Parametrised as

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

Initial conditions

T = T(x,y,z), S = S(x,y,z).

Application of the model

Rotational criterium

where: , angular velocityof Earth; , geographical latitude

Horizontal diffusivity criterium

where: AH, horizontal diffusivity coefficient

Courant-Fridrichs-Levy’s condition

where: C velocity of fundamental mode, Umax , maxime current velocity; or Ct = 2Ci + umax, Ci , velocity of fundamental internal mode, umax , maxime advection velocity.

Radiation condition

Sigma coordinates (x*, y*, , t*),

x* = x,    y* = y,    ,   t* = t,

where: D = H + , dla z =  = 0,

for z = -H  = -1

The modelled areas

  • The inflows from 85 rivers

  • The fields of wind speed over the sea surface were taken from 48-hours ICM forecast model

Area I

Area II

Area III

Numerical grids

Vertical grid

  • based on -transformation defined as:

Horizontal grid

  • Model allows to define subareas with different grid density

Temporal and spatial steps in the modelled areas