direction it had been flowing (also due to its inertia), until
the bending shoreline forces that edge flow to bend to the
middle and meet the flow down the middle, creating
a rotating whirlpool.
The most famous tidal whirlpool is the one that was
once violent and dangerous in the Strait of Messina
(between Sicily and the southern tip of the Italian mainland), which Homer depicted in his Odyssey as the second
of two monsters, Scylla and Charybdis, faced by Ulysses.
Another dangerous tidal whirlpool is the Malström in the
narrow strait between two of the southern Lofoten Islands
off Norway, which was written about by both Jules Verne
and Edgar Allan Poe (Parker, 2012).
Nonlinear shallow-water effects on tidal currents
The shallow-water nonlinear processes that affect the tide
(as discussed earlier) also affect the tidal currents, and in
many situations those shallow-water effects are seen to
be more dramatic in the tidal current than in the tide. The
asymmetric tidal current can have (1) a shorter flood phase
with higher speeds and a longer ebb phase with slower
speeds (called flood dominance because of the higher
flood current speeds), (2) a shorter ebb phase with higher
speeds and a longer flood phase with slower speeds (ebb
dominance), or (3) equal flood and ebb phases, but where
one of the slacks can last for a couple of hours. Asymmetry in the tidal current is important in the transport of sediment and pollutants. The transport of coarse sediment
depends on the maximum speeds achieved and so might
be transported up an estuary with a flood-dominant situation. Fine sediment stays suspended except near slacks, so
the case with longer slacks before ebb might lead to deposition at that time. (See Speer et al., 1991, for more discussion on flood and ebb dominance.)
The distortion in tidal currents can be greatly enhanced
by a strictly linear superposition effect that, in fact, will
not similarly enhance the distortion in the tide. An extreme
example is in Ramshorn Creek, a small shallow channel
connecting the shallow Cooper and New Rivers, both part
of the Intracoastal Waterway in South Carolina and both
connected to the Atlantic Ocean (Parker, 1991). Two tide
waves, each distorted by shallow water, enter Ramshorn
Creek at opposite ends and cross, superimposing their
effects. The M 2 flood currents for the two waves are in
opposite directions, and so the superposition of the two
waves leads to a reduction in the M 2 tidal current. Each
tide wave is distorted to a different degree, because the
two waterways leading to Ramshorn Creek do not have
exactly the same width or depth. Thus, in each waterway
there is a different phase relationship between M 2 and
M 4 , so that when the M 4 tidal constituent waves are
superimposed the two waves add together (rather than
cancel each other out like the two M 2 constituent waves),
thus increasing the M 4 tidal current. The result is the very
unusual situation of a dominant quarter-diurnal tidal current, that is, the tidal current actually changes directions
eight times a day instead of four (namely, there are four
tidal current cycles per day instead of two, each cycle
being 6.21 h long). There are other waterways in the salt
marsh estuaries of South Carolina and Georgia that also
exhibit the effects of two tide waves entering from opposite ends and crossing each other. Most are not as extreme
as in Ramshorn Creek, but the result is still a very distorted
tidal current curve. (This superposition effect does not
lead to a dominant M 4 in the tide because the two M 2 tides
being scalars add positively at the crossover point, not
negatively as with the M 2 vector tidal currents.)
Summary
Although it is astronomical forcing (the gravitational
effects of the moon and sun on the oceans) that makes
the tides so predictable, it is the hydrodynamics (i.e., physics of the water movement) that determines the size and
timing of the tides. When we speak of the tidal hydrodynamics of estuaries, we are speaking of shallow-water
tides, which have much larger tidal ranges and faster tidal
currents than open-ocean tides. In shallow water, the
hydrodynamics also transfers tidal energy, through various
nonlinear processes, to new frequencies. These so-called
shallow-water tidal constituents include higher harmonics
of particular astronomical constituents (called overtides),
which distort the simple sinusoidal shape of the tide and
tidal current curves that are found in the open ocean, often
causing asymmetry in the tidal cycle in an estuary. These
same nonlinear processes also lead to interactions between
the tide and nontidal phenomena such as river discharge
and wind-induced changes (e.g., storm surges). In this
entry, we have explained how each of these mechanisms
work and the importance of tidal hydrodynamics in moving the water and affecting the processes in estuaries.
Bibliography
Parker, B. B., 1991. The relative importance of the various nonlinear
mechanisms in a wide range of tidal interactions. In Parker, B. B.
(ed.), Tidal Hydrodynamics. New York: John Wiley and Sons,
pp. 237–268.
Parker, B. B., 1998. The Coriolis effect: motion on a rotating planet.
Mariners Weather Log, 42(2), 1373. August 1998.
Parker, B. B., 2007. Tidal Analysis and Prediction. NOAA Special
Publication NOS CO-OPS 3, National Ocean Service, NOAA,
Department of Commerce, Silver Spring, MD.
Parker, B. B., 2012. The Power of the Sea. New York: PalgraveMacMillan.
Speer, P., Aubrey, D. G., and Friedrichs, C. T., 1991. Nonlinear
hydrodynamics of shallow tidal inlet/bay systems. In Parker,
B. B. (ed.), Tidal Hydrodynamics. New York: Wiley,
pp. 321–340.
Cross-references
Mean Sea Level
Tidal and Nontidal Oscillations
Tidal Asymmetry
Tidal Datum
Tidal Hydrodynamics
Tidal Ranges
Tides
700
TIDAL HYDRODYNAMICS
the bending shoreline forces that edge flow to bend to the
middle and meet the flow down the middle, creating
a rotating whirlpool.
The most famous tidal whirlpool is the one that was
once violent and dangerous in the Strait of Messina
(between Sicily and the southern tip of the Italian mainland), which Homer depicted in his Odyssey as the second
of two monsters, Scylla and Charybdis, faced by Ulysses.
Another dangerous tidal whirlpool is the Malström in the
narrow strait between two of the southern Lofoten Islands
off Norway, which was written about by both Jules Verne
and Edgar Allan Poe (Parker, 2012).
Nonlinear shallow-water effects on tidal currents
The shallow-water nonlinear processes that affect the tide
(as discussed earlier) also affect the tidal currents, and in
many situations those shallow-water effects are seen to
be more dramatic in the tidal current than in the tide. The
asymmetric tidal current can have (1) a shorter flood phase
with higher speeds and a longer ebb phase with slower
speeds (called flood dominance because of the higher
flood current speeds), (2) a shorter ebb phase with higher
speeds and a longer flood phase with slower speeds (ebb
dominance), or (3) equal flood and ebb phases, but where
one of the slacks can last for a couple of hours. Asymmetry in the tidal current is important in the transport of sediment and pollutants. The transport of coarse sediment
depends on the maximum speeds achieved and so might
be transported up an estuary with a flood-dominant situation. Fine sediment stays suspended except near slacks, so
the case with longer slacks before ebb might lead to deposition at that time. (See Speer et al., 1991, for more discussion on flood and ebb dominance.)
The distortion in tidal currents can be greatly enhanced
by a strictly linear superposition effect that, in fact, will
not similarly enhance the distortion in the tide. An extreme
example is in Ramshorn Creek, a small shallow channel
connecting the shallow Cooper and New Rivers, both part
of the Intracoastal Waterway in South Carolina and both
connected to the Atlantic Ocean (Parker, 1991). Two tide
waves, each distorted by shallow water, enter Ramshorn
Creek at opposite ends and cross, superimposing their
effects. The M 2 flood currents for the two waves are in
opposite directions, and so the superposition of the two
waves leads to a reduction in the M 2 tidal current. Each
tide wave is distorted to a different degree, because the
two waterways leading to Ramshorn Creek do not have
exactly the same width or depth. Thus, in each waterway
there is a different phase relationship between M 2 and
M 4 , so that when the M 4 tidal constituent waves are
superimposed the two waves add together (rather than
cancel each other out like the two M 2 constituent waves),
thus increasing the M 4 tidal current. The result is the very
unusual situation of a dominant quarter-diurnal tidal current, that is, the tidal current actually changes directions
eight times a day instead of four (namely, there are four
tidal current cycles per day instead of two, each cycle
being 6.21 h long). There are other waterways in the salt
marsh estuaries of South Carolina and Georgia that also
exhibit the effects of two tide waves entering from opposite ends and crossing each other. Most are not as extreme
as in Ramshorn Creek, but the result is still a very distorted
tidal current curve. (This superposition effect does not
lead to a dominant M 4 in the tide because the two M 2 tides
being scalars add positively at the crossover point, not
negatively as with the M 2 vector tidal currents.)
Summary
Although it is astronomical forcing (the gravitational
effects of the moon and sun on the oceans) that makes
the tides so predictable, it is the hydrodynamics (i.e., physics of the water movement) that determines the size and
timing of the tides. When we speak of the tidal hydrodynamics of estuaries, we are speaking of shallow-water
tides, which have much larger tidal ranges and faster tidal
currents than open-ocean tides. In shallow water, the
hydrodynamics also transfers tidal energy, through various
nonlinear processes, to new frequencies. These so-called
shallow-water tidal constituents include higher harmonics
of particular astronomical constituents (called overtides),
which distort the simple sinusoidal shape of the tide and
tidal current curves that are found in the open ocean, often
causing asymmetry in the tidal cycle in an estuary. These
same nonlinear processes also lead to interactions between
the tide and nontidal phenomena such as river discharge
and wind-induced changes (e.g., storm surges). In this
entry, we have explained how each of these mechanisms
work and the importance of tidal hydrodynamics in moving the water and affecting the processes in estuaries.
Bibliography
Parker, B. B., 1991. The relative importance of the various nonlinear
mechanisms in a wide range of tidal interactions. In Parker, B. B.
(ed.), Tidal Hydrodynamics. New York: John Wiley and Sons,
pp. 237–268.
Parker, B. B., 1998. The Coriolis effect: motion on a rotating planet.
Mariners Weather Log, 42(2), 1373. August 1998.
Parker, B. B., 2007. Tidal Analysis and Prediction. NOAA Special
Publication NOS CO-OPS 3, National Ocean Service, NOAA,
Department of Commerce, Silver Spring, MD.
Parker, B. B., 2012. The Power of the Sea. New York: PalgraveMacMillan.
Speer, P., Aubrey, D. G., and Friedrichs, C. T., 1991. Nonlinear
hydrodynamics of shallow tidal inlet/bay systems. In Parker,
B. B. (ed.), Tidal Hydrodynamics. New York: Wiley,
pp. 321–340.
Cross-references
Mean Sea Level
Tidal and Nontidal Oscillations
Tidal Asymmetry
Tidal Datum
Tidal Hydrodynamics
Tidal Ranges
Tides
700
TIDAL HYDRODYNAMICS