|Introduction| | |Tide Generating Forces and tidal constituents| |

“The word 'tides' is a generic term used to define the alternating rise and fall in sea level with respect to the land, produced by the gravitational attraction of the moon and the sun.” ( Our Restless Tides). Tides contribute greatly to variability in velocity, density and pressure (or sea level). This is particularly true for sea level, which is largely tidal.

Barotropic tidal currents are the periodic water motions accompanying the tidal changes in sea level. Tidal currents flowing over topography in a stratified ocean can give rise to tidal period oscillations in isopycnals, known as internal, or baroclinic, tides. Internal tidal currents cause flow to be in different directions at different depths. The upper part of the following schematic of a two-layer ocean depicts a barotropic wave; the lower part depicts a baroclinic wave. The direction of flow and the relative velocities of the two layers are shown at the crests and troughs.

In some regions, the currents associated with internal tides may be much stronger than the currents associated with the surface, or barotropic, tide. The internal tidal currents may not be in phase with the barotropic tidal currents. Because of this it may not always be true that surface currents are flowing toward shore during rising, or flood tides, and conversely surface currents may not always be flowing out towards deeper water during falling, or ebb, tides.

Tidal currents contribute to mixing, in some cases dominating it, and thus influence distribution of water properties including sound speed. The variations in depth in coastal areas can result in variations in tidal mixing which can lead to formation of fronts. Residual, or mean, circulations can be generated through interaction of tides with topography.

Keep in mind that there are nonastronomical factors that may affect height and timing of sea level. These include configuration of the coastline; bathymetry; atmospheric pressure (inverted barometer effect); land-sea breeze cycle; and sustained high winds from a constant direction (set-up or storm surge).

A 1 mb change in atmospheric pressure causes approximately a 1 cm change in sea level. This is equivalent to "(for stationary lows, a change of roughly 15.4 mb results in about 0.5 foot change in water height)." From JMTAC CD

Naval Significance:

- navigation
- amphibious landings
- search and rescue
- mine drift
- flooding
- dispersal of pollutants
- construction of piers
- docks
- channels

At the center of the earth, the centripetal acceleration provided by the gravitational attraction between the moon and the earth exactly equals the centrifugal acceleration due to the rotation about the common center of mass, which lies inside the earth. The period of rotation about this common center of mass is 27.32 days, a sidereal month.

Everywhere else on the earth, there is an imbalance between the centripetal (inward) and centrifugal (outward) accelerations. The centrifugal acceleration is the same everywhere on the earth, but the gravitational force due to the moon varies over the surface of the earth.

This results in the **tide-generating force, TGF,** since on the side of the earth toward the moon the gravitational force exceeds the centrifugal acceleration and on the side of the earth away from the moon the centrifugal acceleration exceeds the gravitational force. At the spot on the earth exactly under the moon (sub-lunar point, or zenith) and the spot on the earth exactly opposite that (the antipode, or nadir), the TGF is in the same direction as earth’s gravity, and so has little effect since it is so much less in magnitude than g. The “sideways” forces, or horizontal component, of the TGF is called the **tractive force**.

The **equilibrium tide** is that which would result from the TGFs if the earth were completely covered by water and responded instantly to the changing forces (i.e. no inertia) and there were no friction. As a result of the tractive forces, the equilibrium tide, has two bulges, one on either side of the earth. Thus you see 2 highs and 2 lows per lunar day. This is known as the **semidiurnal** lunar tidal constituent. It has a period of 12.42 hours and is denoted by the symbol **M _{2}**.

The **lunar day** (also known as a **tidal day**), 24.84 hrs, exceeds the solar day (24 h) since the moon is revolving around the earth with a period of 27.32 days.

The moon's orbit, and hence the tidal bulges, are tilted relative to the earths equator, resulting in the 2 high waters per lunar day not being equal to each other.
This is known as the **diurnal inequality** of the lunar semidiurnal tide, and gives rise to the diurnal tides.
The principal lunar diurnal constituent, ** K _{1}** has a period of 23.93 hours.
The shape of the ocean basin is a major factor in determining whether the tide in a particular area is more semidiurnal in nature, more diurnal (as in the Gulf of Mexico) or a mixture of the two. These different tidal regimes, as well as the concepts of range, amplitude and period, are illustrated in the following figure.

A depiction of the three primary kinds of tides. From the top panel downward they are semidiurnal, mixed, and diurnal. Standard tidal terminology is used to describe the various aspects of the tides. The zero on these graphs is illustrative of the relationship of the tides to Mean Sea Level (MSL). From NOS Tidal Datums pub.

One also needs to consider the tides due to the sun. This gives rise to another semidiurnal constituent, S2, with a period of 12 hours.
The interaction or summation, known as beating, between the lunar and solar semidiurnal tides produces a fortnightly modulation with a period of 14.79 days
(=1/(*w _{M2} - w_{S2}*),
where

Various other parameters of the moon's orbit around the earth and the earth's orbit around the sun give rise to other tidal frequencies, or constituents, and add complexity to the tidal signal.
The amplitude of the equilibrium tide for each tidal constituent is known for any point on the earth.
To predict the actual tidal variations in sea level at any location, the amplitude and phase, also known as the tidal constants, for the **tidal constituents**, or components, must be known. These can be determined from a long (best if greater than 1 year) time series of measured sea level, or alternatively from a numerical model.

Each tidal constituent is designated by a name and a symbol. Tidal constituents are generally grouped by their period and fall into one of four categories:

- Overtides: these have periods shorter than 9 hours and are caused by nonlinear interactions of the other tidal constituents and bathymetry. They are most common in estuaries and very shallow water. Their symbols have subscripts like 4 or 6, meaning there are approximately 4 or 6 cycles per day.
- Semidiurnal: these have periods close to 12 hours, and their symbols have the subscript 2, for 2 cycles per day.
- Diurnal: these have periods close to 24 hours, and their symbols have the subscript 1.
- Low frequency: these have periods of days to years. There is no special pattern to their symbols.

The character of the tidal sea level varations at any given location is determined by the relative amplitudes (sizes) and phases (timing) of these different constituents. This is illustrated in the figure below and at the following web site: http://www.ams.org/featurecolumn/archive/tidesIII3.html

From NOS Tidal Datums Pub.

Use the tide-predicting machine at the website above to determine which of the following three locations has a primarily diurnal tide and which has a primarily semidiurnal tide:

- Recife, Brazil
- Kurile Islands
- Matarani, Peru

Enter your answers in the space provided below and click the submit button.

Because water levels vary over the course of hours and days, sometimes by many feet, water depths must be referred to a known level, or **datum**.
A number of different datums are in use, many of which are illustrated in the figure below.

The principal tidal datums related to a beach profile. The intersection of the tidal datum with land determines the landward edge of a marine boundary. From NOS Tidal Datums Pub.

There are many different tabular and graphical ways to present tidal information. Just a few of them are described and illustrated here. One common method to show how the tidal sea level amplitude and phase of a given constituent vary over a geographic area of the ocean is to use charts with lines connecting areas of the same phase (cotidal lines) and lines or colors showing areas with the same amplitude (corange lines). Places along the same cotidal line will experience high tide for that constituent at the same time. The following two pictures represent the M2 tide in the northern Indian Ocean and the K1 tide in the Yellow and East China sea and were derived from a data-assimilating model developed by Laksmi Kantha of University of Colorado in conjunction with Mississippi State University and the Naval Oceanographic Office. They are taken from the web site: http://www.ssc.erc.msstate.edu/Tides2D/tides_synopsis.html, and have been made available courtesy of Dr. Kantha.

Gary Egbert of Oregon State University has generated tidal charts using sea surface height data measured by satellite altimetry. An example for the M2 constituent in the Mediterranean follows. It was taken from the regional model section of the web site http://www.coas.oregonstate.edu/research/po/research/tide/index.html. All three figures include amphidromes, which are locations where the amplitude is zero and the phase lines come together in a point. At those points, sea level does not go up and down at the period of that constituent, and the tide can be pictured as a wave that rotates around that point.

This might be a good place to point out that the term “tidal wave” has nothing to do with tides, but rather is a wave generated by instantaneous forcing such as an earthquake or a landslide. Tsunami is a better term to describe those waves so as not to confuse them with waves of true tidal origin.

A common way to illustrate how tidal currents vary in space, either horizontally or with depth, is to use tidal ellipses.

Over the course of one period, for example 12.4 hours for the M_{2} constituent,
the tip of the current vector will trace out a path along the ellipse.

The figure above shows the M_{2} surface current tidal ellipses for Monterey Bay.
The red lines indicate
the direction at which the current is pointing at a given time.
The blue ellipses indicate a counterclockwise rotation; the green ellipses indicate a clockwise rotation.

There are numerous words used to describe tides, only a few of which have been introduced here. The following web site is a good resource to look for definitions of tidal terms you are unfamiliar with: http://co-ops.nos.noaa.gov/publications/glossary2.pdf (pdf)

The following web site will let you review and test your knowledge of tides, as well as introduce some material about tides which we didn't cover here.

http://www.es.flinders.edu.au/~mattom/IntExerc/basic5/index.html

A seiche is a stationary wave that oscillates (changes aspect) without progressing. Also called a "standing wave", seiches are caused by strong winds and/or changes in barometric pressure. Found in enclosed / semi-enclosed areas. Seiche period is determined by the length and depth of the water. Currents associated with seiches are at maximum speed near the axis (node) and minimum speed (or not at all) at either end (loops). From JMTAC course (cd).

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Continue on to the next section on Approximations
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