TIDAL HYDRODYNAMICS
Bruce Parker
Center for Maritime Systems/Davidson Laboratory,
Stevens Institute of Technology, Hoboken, NJ, USA
Definition
Tidal hydrodynamics refers to the physics of vertical and
horizontal water movement caused by the tidal forces of
the moon and sun.
Introduction
In most estuaries, the dominant forces that cause the water
to move are produced by the gravitational effects of the
moon and sun on the oceans. These astronomical forces
cause the water to move vertically (the tide) and horizontally (the tidal current), the entire phenomenon usually
referred to as the tides. Tidal motion is actually the motion
of extremely long waves generated in the deep ocean,
which propagate over the shallower continental shelf and
up into even shallower estuaries where their size is usually
amplified.
Although it is astronomical factors 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. It is the hydrodynamics (determined by the
dimensions of the ocean, continental shelves, bays, and
rivers) that determines how large the tide range (height difference between high water and low water) will be and
when the high and low waters will occur. It is the hydrodynamics that determines how fast the tidal currents will
flow and when slack waters will occur, and it is the hydrodynamics that determines how significant the diurnal tidal
signal will be compared with the usually dominant semidiurnal tidal signal.
Only the oceans are large enough for the tidegenerating forces to directly produce a tide of significant
size (see Tides, and also Parker, 2007). The tides in an
estuary are forced at the estuary entrance by the tide wave
from the deep ocean (having been modified to some
degree by propagating over the shallower continental
shelf). When we speak of the tidal hydrodynamics of estuaries, we are essentially speaking of shallow-water tides,
which are significantly different than open-ocean tides in
a number of ways, including having much larger tidal
ranges and faster tidal currents. In shallow water the tidal
wavelength is shorter, which is one factor leading to larger
tidal amplitudes when the tide wave reflects from the head
of an estuary. In estuaries, full and partial reflections of
these very long tidal waves, the nearness of basin lengths
to resonance for particular tidal frequencies, continuity
effects, frictional damping, and advective/inertial effects
all affect the tide and tidal currents. In shallow water the
hydrodynamics also transfers tidal energy, through various nonlinear processes, to new frequencies. These new,
so-called shallow-water tidal constituents can be larger
than many of the astronomically generated tidal
constituents. Some shallow-water constituents (called
overtides) are higher harmonics of particular astronomical
constituents, which distort the simple sinusoidal shape of
tide and tidal current curves that are found in the open
ocean, often causing asymmetry in the tidal cycle. These
same nonlinear processes also lead to interactions between
the tide and other nontidal phenomena such as windinduced changes (e.g., storm surges) and river discharge.
Brief astronomical background
Tidal hydrodynamics deals with the forced oscillations
caused by the astronomical tide-producing forces. The
tides are the most predictable phenomenon in estuaries
because of this astronomical forcing, which varies due to
the well-known periodic motions resulting from the revolution of the Earth around the sun, the revolution of the
moon-Earth system, and the rotation of the Earth on its
axis (see Tides, and also Parker, 2007). These periodic
motions determine that in any physical data set from an
estuary (e.g., water level, currents, salinity, and water temperature), the tidal energy will be found at numerous very
precisely defined tidal frequencies, whose amplitudes and
phases can easily be calculated by harmonically analyzing
that data set. There are dozens of these so-called tidal constituents, each constituent representing some aspect of
the relative astronomical motions of the Earth, moon,
and sun. These constituents tend to fall into bands. In the
semidiurnal band, constituents produce two high waters
(and two low waters) per day. In the diurnal band, constituents produce one high water (and one low water) per day.
There are also other less important bands, including higher
harmonics caused by shallow-water nonlinear effects,
which will be discussed later in this entry. Tidal hydrodynamics modifies the amplitude and phases of these tidal
constituents.
For the purposes of this entry, only the five most important tidal constituents will be mentioned until the shallowwater constituents are discussed (for more constituents see
Parker, 2007, Table A, which includes 149 tidal constituents). These five larger constituents are named M 2 , S 2 ,
N 2 , K 1 , and O 1 , the first three being semidiurnal and the
last two diurnal. M 2 , the main lunar semidiurnal constituent, represents the Earth turning under a slowly revolving
moon with 2 cycles (and two high waters) in each
24.8412-h lunar day. It thus has a period of 12.4206 h
and a frequency (1/tidal period) of 1.9323 cycles per
(solar) day. S 2 , the main solar semidiurnal constituent, represents the Earth turning under the sun with 2 cycles (and
two high waters) in each 24.00-h solar day. It thus has
a period of 12.00 h and a frequency of 2.00 cycles per
(solar) day. When the moon and sun are in alignment at
new and full moons, their tidal forces work together to
produce larger tide ranges (called spring tides). When
the moon and sun are out of alignment, at first and third
quarters, their tidal forces work against each other to produce smaller ranges (called neap tides). N 2 , with a period
of 12.6583 h, represents the effect of the elliptical
686
TIDAL HYDRODYNAMICS
Bruce Parker
Center for Maritime Systems/Davidson Laboratory,
Stevens Institute of Technology, Hoboken, NJ, USA
Definition
Tidal hydrodynamics refers to the physics of vertical and
horizontal water movement caused by the tidal forces of
the moon and sun.
Introduction
In most estuaries, the dominant forces that cause the water
to move are produced by the gravitational effects of the
moon and sun on the oceans. These astronomical forces
cause the water to move vertically (the tide) and horizontally (the tidal current), the entire phenomenon usually
referred to as the tides. Tidal motion is actually the motion
of extremely long waves generated in the deep ocean,
which propagate over the shallower continental shelf and
up into even shallower estuaries where their size is usually
amplified.
Although it is astronomical factors 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. It is the hydrodynamics (determined by the
dimensions of the ocean, continental shelves, bays, and
rivers) that determines how large the tide range (height difference between high water and low water) will be and
when the high and low waters will occur. It is the hydrodynamics that determines how fast the tidal currents will
flow and when slack waters will occur, and it is the hydrodynamics that determines how significant the diurnal tidal
signal will be compared with the usually dominant semidiurnal tidal signal.
Only the oceans are large enough for the tidegenerating forces to directly produce a tide of significant
size (see Tides, and also Parker, 2007). The tides in an
estuary are forced at the estuary entrance by the tide wave
from the deep ocean (having been modified to some
degree by propagating over the shallower continental
shelf). When we speak of the tidal hydrodynamics of estuaries, we are essentially speaking of shallow-water tides,
which are significantly different than open-ocean tides in
a number of ways, including having much larger tidal
ranges and faster tidal currents. In shallow water the tidal
wavelength is shorter, which is one factor leading to larger
tidal amplitudes when the tide wave reflects from the head
of an estuary. In estuaries, full and partial reflections of
these very long tidal waves, the nearness of basin lengths
to resonance for particular tidal frequencies, continuity
effects, frictional damping, and advective/inertial effects
all affect the tide and tidal currents. In shallow water the
hydrodynamics also transfers tidal energy, through various nonlinear processes, to new frequencies. These new,
so-called shallow-water tidal constituents can be larger
than many of the astronomically generated tidal
constituents. Some shallow-water constituents (called
overtides) are higher harmonics of particular astronomical
constituents, which distort the simple sinusoidal shape of
tide and tidal current curves that are found in the open
ocean, often causing asymmetry in the tidal cycle. These
same nonlinear processes also lead to interactions between
the tide and other nontidal phenomena such as windinduced changes (e.g., storm surges) and river discharge.
Brief astronomical background
Tidal hydrodynamics deals with the forced oscillations
caused by the astronomical tide-producing forces. The
tides are the most predictable phenomenon in estuaries
because of this astronomical forcing, which varies due to
the well-known periodic motions resulting from the revolution of the Earth around the sun, the revolution of the
moon-Earth system, and the rotation of the Earth on its
axis (see Tides, and also Parker, 2007). These periodic
motions determine that in any physical data set from an
estuary (e.g., water level, currents, salinity, and water temperature), the tidal energy will be found at numerous very
precisely defined tidal frequencies, whose amplitudes and
phases can easily be calculated by harmonically analyzing
that data set. There are dozens of these so-called tidal constituents, each constituent representing some aspect of
the relative astronomical motions of the Earth, moon,
and sun. These constituents tend to fall into bands. In the
semidiurnal band, constituents produce two high waters
(and two low waters) per day. In the diurnal band, constituents produce one high water (and one low water) per day.
There are also other less important bands, including higher
harmonics caused by shallow-water nonlinear effects,
which will be discussed later in this entry. Tidal hydrodynamics modifies the amplitude and phases of these tidal
constituents.
For the purposes of this entry, only the five most important tidal constituents will be mentioned until the shallowwater constituents are discussed (for more constituents see
Parker, 2007, Table A, which includes 149 tidal constituents). These five larger constituents are named M 2 , S 2 ,
N 2 , K 1 , and O 1 , the first three being semidiurnal and the
last two diurnal. M 2 , the main lunar semidiurnal constituent, represents the Earth turning under a slowly revolving
moon with 2 cycles (and two high waters) in each
24.8412-h lunar day. It thus has a period of 12.4206 h
and a frequency (1/tidal period) of 1.9323 cycles per
(solar) day. S 2 , the main solar semidiurnal constituent, represents the Earth turning under the sun with 2 cycles (and
two high waters) in each 24.00-h solar day. It thus has
a period of 12.00 h and a frequency of 2.00 cycles per
(solar) day. When the moon and sun are in alignment at
new and full moons, their tidal forces work together to
produce larger tide ranges (called spring tides). When
the moon and sun are out of alignment, at first and third
quarters, their tidal forces work against each other to produce smaller ranges (called neap tides). N 2 , with a period
of 12.6583 h, represents the effect of the elliptical
686
TIDAL HYDRODYNAMICS