SEDLOB and PATLOB
131
3.1
Formulation of PATLOS
PATLOB uses the same approximation for the settling velocity, w s ' the critical
shear velocities of bed load (v em,b) and suspension load (vern), and the critical
velocity vem,d for a final deposition of the parcels found in SEDLOB. Furthermore, the critical velocities are updated by the bottom slope.
The new location of every particle is calculated from the old position (Goldstein 1985; Kurz 1977):
dF _
-=V.
dt
(31)
For the 3-D submodel the equation above is written in Cartesian coordinates as
rx,n+l = rx,n + u r At
ry,n+l = ry,n + vr At
rz n+l = rz n + Wg At,
,
,
r
and for the 2-D submodel as
rbot,x,n+l = rbot,x,n + Ubot,r At
rbot,y,n+l = rbot,y,n + Vbot,r At,
(32)
(33)
where r is used for the location interpolated inside of the numerical grid and n
for the time step. This means that the velocity components provided by the
OGCM are interpolated to the current position of the Lagrangian particle from
nearby points on the Eulerian numerical grid.
4
The vertical convection in SEDLOB and PAlLOB
SEDLOB and PATLOB take into account vertical convection. This is an important
feature because convection does not transport water and sediment in the same
way as advection does. Tracers are advected by currents, whereas convection due
to hydrostatic instability mixes water, sediments, and the tracers vertically in
"turbulent" water columns or "chimneys" (Fig. 12). The convection due to hydrostatic instability determines the depth of vertical mixing in the ocean. In the
model, the convection depth indicates how many layers participate in mixing,
that is to which layer a particle entering such a turbulent water column is propelled within the chimney. We use different techniques to introduce this mixing
into the two models. In SEDLOB, the sediment concentrations of vertical grid
boxes affected by the convection depth are mixed to obtain a homogenous sediment distribution in every time step. In PATLOB, a parcel entering a chimney at
the top is propelled downward to the base of the chimney and vice versa. This is
equivalent to the reflection of every particle around the middle depth of a con-
131
3.1
Formulation of PATLOS
PATLOB uses the same approximation for the settling velocity, w s ' the critical
shear velocities of bed load (v em,b) and suspension load (vern), and the critical
velocity vem,d for a final deposition of the parcels found in SEDLOB. Furthermore, the critical velocities are updated by the bottom slope.
The new location of every particle is calculated from the old position (Goldstein 1985; Kurz 1977):
dF _
-=V.
dt
(31)
For the 3-D submodel the equation above is written in Cartesian coordinates as
rx,n+l = rx,n + u r At
ry,n+l = ry,n + vr At
rz n+l = rz n + Wg At,
,
,
r
and for the 2-D submodel as
rbot,x,n+l = rbot,x,n + Ubot,r At
rbot,y,n+l = rbot,y,n + Vbot,r At,
(32)
(33)
where r is used for the location interpolated inside of the numerical grid and n
for the time step. This means that the velocity components provided by the
OGCM are interpolated to the current position of the Lagrangian particle from
nearby points on the Eulerian numerical grid.
4
The vertical convection in SEDLOB and PAlLOB
SEDLOB and PATLOB take into account vertical convection. This is an important
feature because convection does not transport water and sediment in the same
way as advection does. Tracers are advected by currents, whereas convection due
to hydrostatic instability mixes water, sediments, and the tracers vertically in
"turbulent" water columns or "chimneys" (Fig. 12). The convection due to hydrostatic instability determines the depth of vertical mixing in the ocean. In the
model, the convection depth indicates how many layers participate in mixing,
that is to which layer a particle entering such a turbulent water column is propelled within the chimney. We use different techniques to introduce this mixing
into the two models. In SEDLOB, the sediment concentrations of vertical grid
boxes affected by the convection depth are mixed to obtain a homogenous sediment distribution in every time step. In PATLOB, a parcel entering a chimney at
the top is propelled downward to the base of the chimney and vice versa. This is
equivalent to the reflection of every particle around the middle depth of a con-