the nonlinear tidal hydrodynamics causing an asymmetry
within the tidal cycle. This can be due not only to
shallow-water effects but even more importantly to
nonlinear lateral inertia effects (that do not need shallow
water). Such tidally induced residual current effects are
discussed below, as one of the many phenomena that
appear in tidal currents but not in the tide.
Special aspects of tidal currents (compared with
the tide)
The tide is a scalar quantity, with a one-dimensional
movement, that is, simply moving up or down. The tidal
current, however, is a vector quantity, representing the
horizontal water flow in two dimensions, and because it
is a vector quantity, its movements are more complicated
than the tide (but still very predictable because it has the
same astronomical forcing).
There are situations where the tidal current flow can
look approximately one dimensional, namely, when the
estuary or waterway is very narrow. In this case, a plot
of changing tidal current looks like a tide curve except
the sine curve is above and below a zero speed line. This
is called a reversing tidal current. In one tidal cycle, the
current goes from its maximum positive value
(maximum flood) through the zero current speed (slack
water) to the maximum negative value (maximum ebb)
and back again through slack water to maximum flood.
The slacks are usually referred to as slack before flood
(SBF) and slack before ebb (SBE). [Alternative names
for the above include flood strength, ebb strength, slack
flood begins (SFB), and slack ebb begins (SEB)].
Most tidal currents, however, are rotary tidal currents,
that is, the direction of flow rotates 360
o (around the compass) over one tidal cycle. This rotation is due to both the
Earth’s rotation and certain geographic conditions.
Because the tidal current speed varies as this rotation takes
place, the shape that the tip of the current vector traces out
can be an ellipse of various widths or even almost a circle
(in the open ocean) when the speed remains approximately
the same throughout the cycle (Figure 8). Within an estuary that has a more complicated geography, for example,
those with islands and various channels, the shape can
even be more complicated (such as the shape shown in
the fourth plot in Figure 8). Because of the elliptical shape,
one can still use the terms flood current (for the tidal current
flow into and up an estuary) and ebb current (for the tidal
flow down and out of an estuary). However, there will not
be a true slack water, because for that brief time, the flow
will be cross-channel, so we use the terms minimum before
flood (MBF) and minimum before ebb (MBE).
Dramatic spatial variation in tidal
currents: vertically
The spatial variation of tidal currents, both horizontally
(i.e., geographically) and vertically in the water column,
is much more complex than the spatial variation of tides.
The tide, being the one-dimensional movement of the
water surface, does not have a variation with depth
(although the vertical tidal movement of different water
density layers does change considerably with depth).
However, tidal currents vary considerably from the surface to the bottom. Bottom friction is a major cause of this
variation. The tidal current is slowest near the bottom and
faster nearer to (but usually not right at) the water surface.
Usually the tidal current will turn (from flooding to
ebbing, or vice versa) earlier near the bottom than near
the water surface, so there will be times when the tidal current is going in the opposite direction at one depth than at
another depth. One example of the variation in tidal current speed across a cross section of Chesapeake Bay is
shown in Figure 9. In this figure, one sees the current
flooding (i.e., flowing up the bay) in the deeper depths
and ebbing (i.e., flowing down the bay) near the water’s
surface (except on the west side, where it is still flooding).
There are also other effects that can make the tidal current vary vertically. Tidal currents can be modified by
baroclinic effects, that is, by density differences vertically
along the water column, due to salinity differences
(in estuaries that are not well mixed) or temperature differences (offshore in the coastal ocean), which allow the
propagation of internal tide waves. Such baroclinic effects
on tidal currents are often seen in the middle of a stratified
water column, but not near the bottom or near the water
surface, where frictionally caused mixing takes place.
Dramatic spatial variation in tidal
currents: horizontally
Horizontally (i.e., geographically), the tide varies quite
smoothly due to the hydrodynamic effects of such things
as changing depths and widths, resonance, and Coriolis
force. Such variations can often be reproduced or
predicted with even simple analytical models. Although
tidal currents are also affected by these same hydrodynamic effects and can change in similar ways, there are
other hydrodynamic effects which can make tidal currents
change dramatically in the horizontal direction, often over
surprisingly short distances. One example is the tidal current in a navigation channel compared with the tidal current in the nearby shallows. The tidal current is much
faster in the deeper channel than in the shallows, and the
times of slacks and of maximum floods and ebbs can be
quite different than those in the nearby shallows.
One does not require a dramatic change in depth to see
differences in the tidal currents. Even in a wide bay,
changes in bathymetry will affect the tidal currents. Not
only will current speeds vary with horizontal distance
(as mentioned above), but the bathymetry will steer the
current. Also, currents within a channel or constricted portion of bathymetry will tend to be more reversing than currents in a more open and flat part of the bay, where a more
rotary tidal current will be possible.
In Figure 9, where vertical variation in the tidal currents
was seen, there was also horizontal variation along the
width of the bay. Bottom friction is often the main reason
for the horizontal variation in tidal current, due to the
TIDAL HYDRODYNAMICS
697
within the tidal cycle. This can be due not only to
shallow-water effects but even more importantly to
nonlinear lateral inertia effects (that do not need shallow
water). Such tidally induced residual current effects are
discussed below, as one of the many phenomena that
appear in tidal currents but not in the tide.
Special aspects of tidal currents (compared with
the tide)
The tide is a scalar quantity, with a one-dimensional
movement, that is, simply moving up or down. The tidal
current, however, is a vector quantity, representing the
horizontal water flow in two dimensions, and because it
is a vector quantity, its movements are more complicated
than the tide (but still very predictable because it has the
same astronomical forcing).
There are situations where the tidal current flow can
look approximately one dimensional, namely, when the
estuary or waterway is very narrow. In this case, a plot
of changing tidal current looks like a tide curve except
the sine curve is above and below a zero speed line. This
is called a reversing tidal current. In one tidal cycle, the
current goes from its maximum positive value
(maximum flood) through the zero current speed (slack
water) to the maximum negative value (maximum ebb)
and back again through slack water to maximum flood.
The slacks are usually referred to as slack before flood
(SBF) and slack before ebb (SBE). [Alternative names
for the above include flood strength, ebb strength, slack
flood begins (SFB), and slack ebb begins (SEB)].
Most tidal currents, however, are rotary tidal currents,
that is, the direction of flow rotates 360
o (around the compass) over one tidal cycle. This rotation is due to both the
Earth’s rotation and certain geographic conditions.
Because the tidal current speed varies as this rotation takes
place, the shape that the tip of the current vector traces out
can be an ellipse of various widths or even almost a circle
(in the open ocean) when the speed remains approximately
the same throughout the cycle (Figure 8). Within an estuary that has a more complicated geography, for example,
those with islands and various channels, the shape can
even be more complicated (such as the shape shown in
the fourth plot in Figure 8). Because of the elliptical shape,
one can still use the terms flood current (for the tidal current
flow into and up an estuary) and ebb current (for the tidal
flow down and out of an estuary). However, there will not
be a true slack water, because for that brief time, the flow
will be cross-channel, so we use the terms minimum before
flood (MBF) and minimum before ebb (MBE).
Dramatic spatial variation in tidal
currents: vertically
The spatial variation of tidal currents, both horizontally
(i.e., geographically) and vertically in the water column,
is much more complex than the spatial variation of tides.
The tide, being the one-dimensional movement of the
water surface, does not have a variation with depth
(although the vertical tidal movement of different water
density layers does change considerably with depth).
However, tidal currents vary considerably from the surface to the bottom. Bottom friction is a major cause of this
variation. The tidal current is slowest near the bottom and
faster nearer to (but usually not right at) the water surface.
Usually the tidal current will turn (from flooding to
ebbing, or vice versa) earlier near the bottom than near
the water surface, so there will be times when the tidal current is going in the opposite direction at one depth than at
another depth. One example of the variation in tidal current speed across a cross section of Chesapeake Bay is
shown in Figure 9. In this figure, one sees the current
flooding (i.e., flowing up the bay) in the deeper depths
and ebbing (i.e., flowing down the bay) near the water’s
surface (except on the west side, where it is still flooding).
There are also other effects that can make the tidal current vary vertically. Tidal currents can be modified by
baroclinic effects, that is, by density differences vertically
along the water column, due to salinity differences
(in estuaries that are not well mixed) or temperature differences (offshore in the coastal ocean), which allow the
propagation of internal tide waves. Such baroclinic effects
on tidal currents are often seen in the middle of a stratified
water column, but not near the bottom or near the water
surface, where frictionally caused mixing takes place.
Dramatic spatial variation in tidal
currents: horizontally
Horizontally (i.e., geographically), the tide varies quite
smoothly due to the hydrodynamic effects of such things
as changing depths and widths, resonance, and Coriolis
force. Such variations can often be reproduced or
predicted with even simple analytical models. Although
tidal currents are also affected by these same hydrodynamic effects and can change in similar ways, there are
other hydrodynamic effects which can make tidal currents
change dramatically in the horizontal direction, often over
surprisingly short distances. One example is the tidal current in a navigation channel compared with the tidal current in the nearby shallows. The tidal current is much
faster in the deeper channel than in the shallows, and the
times of slacks and of maximum floods and ebbs can be
quite different than those in the nearby shallows.
One does not require a dramatic change in depth to see
differences in the tidal currents. Even in a wide bay,
changes in bathymetry will affect the tidal currents. Not
only will current speeds vary with horizontal distance
(as mentioned above), but the bathymetry will steer the
current. Also, currents within a channel or constricted portion of bathymetry will tend to be more reversing than currents in a more open and flat part of the bay, where a more
rotary tidal current will be possible.
In Figure 9, where vertical variation in the tidal currents
was seen, there was also horizontal variation along the
width of the bay. Bottom friction is often the main reason
for the horizontal variation in tidal current, due to the
TIDAL HYDRODYNAMICS
697