Predictions in the North Sea
Appendix C Residual (Horizontal) Circulation
Tidal Component
261
By convention, discrepancies between observed (or simulated) sea levels (or currents) and associated tidal predictions are referred to as 'residuals'. However, the
residual current components described here relate to longer term components associated with tidally-averaged values. In strongly tidal shallow seas, a substantial
residual originates from non-linear terms associated with tidal propagation (Nihoul
and Ronday, 1975). Three residual tidal components exist associated with: shallow
water, bed friction and advection. The latter is particularly pronounced near sharp
changes in bathymetry leading to pronounced gyres (Pingree and Maddock, 1980).
In shallow water, the other terms generate net circulations which are linked
together across the deeper areas by topographically steered streamlines (via the
pertaining geostrophic balance) (Fig. 13.3 ).
For barotropic tidal propagation in water depths greater than 50 m, 2D models
are generally adequate. In shallower water, the increasing importance of both bottom friction and effective vertical eddy viscosity requires fully 3D models (Prandle
1997a).
The net transport, Qr due to an osci1latory current O accompanying an oscillatory elevation ~ is
(CI)
where e is the phase lag between the two. Since the related net energy propagated,
QE is
(C2)
it follows that the propagation of tidal energy from ocean to shelf seas is accompanied by a related residual net transport.
Wind and Density Driven Components
In open seas, the observed steady state current, response R for a constant eddy
viscosity coefficient, E, follows from Ekman theory, (Prandle 1991b).
TW {bZ Eb }
R(z) =
bH e + k - 1
pEbe
(C3)
where
(C4)
T w is wind stress, p water density, f Coriolis parameter, H water depth, k bed friction coefficient and z height above the bed. In deep water (bH» 1) the first term
predominates and the current veers at 45° to the wind. In shallow water the second
Appendix C Residual (Horizontal) Circulation
Tidal Component
261
By convention, discrepancies between observed (or simulated) sea levels (or currents) and associated tidal predictions are referred to as 'residuals'. However, the
residual current components described here relate to longer term components associated with tidally-averaged values. In strongly tidal shallow seas, a substantial
residual originates from non-linear terms associated with tidal propagation (Nihoul
and Ronday, 1975). Three residual tidal components exist associated with: shallow
water, bed friction and advection. The latter is particularly pronounced near sharp
changes in bathymetry leading to pronounced gyres (Pingree and Maddock, 1980).
In shallow water, the other terms generate net circulations which are linked
together across the deeper areas by topographically steered streamlines (via the
pertaining geostrophic balance) (Fig. 13.3 ).
For barotropic tidal propagation in water depths greater than 50 m, 2D models
are generally adequate. In shallower water, the increasing importance of both bottom friction and effective vertical eddy viscosity requires fully 3D models (Prandle
1997a).
The net transport, Qr due to an osci1latory current O accompanying an oscillatory elevation ~ is
(CI)
where e is the phase lag between the two. Since the related net energy propagated,
QE is
(C2)
it follows that the propagation of tidal energy from ocean to shelf seas is accompanied by a related residual net transport.
Wind and Density Driven Components
In open seas, the observed steady state current, response R for a constant eddy
viscosity coefficient, E, follows from Ekman theory, (Prandle 1991b).
TW {bZ Eb }
R(z) =
bH e + k - 1
pEbe
(C3)
where
(C4)
T w is wind stress, p water density, f Coriolis parameter, H water depth, k bed friction coefficient and z height above the bed. In deep water (bH» 1) the first term
predominates and the current veers at 45° to the wind. In shallow water the second