Long Waves (Shallow Water Waves)...

"Wind Rose"...

Short waves (deep water waves) show normal dispersion, i.e. wave speed depends on the period, with the longer period waves moving faster than the shorter period waves (and the longer period waves have the longer wave lengths). In contrast, long waves (shallow water waves) are non- dispersive. Their wave speed is independent of their period. It depends only on the water depth. The velocity structure in a long wave is described by the surface elevation (wave amplitude) and the horizontal particle velocity ;



It follows that u is independent of depth and the vertical particle velocity varies linearly with depth. Particles move on very flat elliptic paths in nearly horizontal motion.

Tsunamis...

Tsunamis are long waves generated by submarine earthquakes. Tsunami is Japanese for "tidal wave"; it is therefore a misnomer, since tsunamis have nothing to do with tides. The strongest tsunami in known history was produced by the eruption of the Krakatau of the Sunda Island group in 1883. It reached a wave height of 35 m and claimed 36,830 lives. Four tsunamis with heights in excess of 30 m have been documented in the Pacific Ocean since 684 A.D. A strong tsunami in the Atlantic Ocean was observed in 1755 after an earthquake near Lisbon (Portugal). In the vicinity of the epicentre of an earthquake, tsunamis can result in extreme wave heights. Once they reach the deep ocean tsunamis have extremely small amplitudes but travel fast, in 4,000 m water depth at about 700 km / h. On approaching a coast they build up wave height again through shoaling. The period of tsunamis is in the range 10-60 minutes. shows a record of a tsunami from an Alaskan earthquake recorded in Hawaii. Tsunamis were used to estimate the depth of the ocean in 1856, when direct depth measurements were virtually impossible, by observing their phase speed. The result for the North Pacific was 4,200 - 4,500 m, which was a considerable improvement on the previous estimate of 18,000 m.

Because of the destructive force of tsunamis, a tsunami warning system has been set up. It uses seismographic observations of earthquakes and calculates arrival times around the coastlines of the oceanic basin. Another possibility is the monitoring of compression waves linked with volcanic eruptions; they travel at the speed of sound (1,500 m / s) in the SOFAR channel. No warning system is available for areas in the vicinity of the epicentre. gives an example of a sea level record showing the passage of a tsunami in Hawaii. You can also view some photos showing the impact of a major tsunami .

Seiches...

Seiches are standing waves in closed basins. Consider a basin of length L and depth h with long wave speed. The time it takes a wave to travel through distance L is ;



Reflection occurs at the wall and the same time is needed to return to the starting point. Thus the basic period of a standing wave in the basin is ;



This is the period for the free oscillation of lowest (first) order. Higher order waves are possible with periods T1/n for order n. The order is given by the number of nodes in the surface oscillation. shows the first order seiche (of period T1), the second order seiche (of period T2 = 1/2 T1). shows a first order seiche in the Baltic Sea, where such oscillations of water level are usually produced by storms systems travelling across. The storm triggers a free oscillation (seiche) which then continues for several days before it is damped by bottom friction.

If the basin is open, the connecting line to the open sea has to be a node. The corresponding period for the lowest order wave is therefore twice that of the lowest order seiche that would exist if the basin were closed (The effective wave length is twice the length of the basin). It is determined in analogy to the frequency determination of organ pipes and is ;



Higher order seiches, with period T1/n, are again possible.

Internal Waves...

It was said before that waves are periodic movements of interfaces. If the water column consists of an upper layer and a denser lower layer, the interface between the layers can undergo wave motion. This motion, which does not affect the surface and mostly is not observable at the surface, is an example of an internal wave. The restoring force for waves is proportional to the product of gravity and the density difference between the two layers (the relative buoyancy). At internal interfaces this difference is much smaller than the density difference between air and water (by several orders of magnitude). As a consequence, internal waves can attain much larger amplitudes than surface waves. It also takes longer for the restoring force to return particles to their average position, and internal waves have periods much longer than surface gravity waves (from 10 - 20 minutes to several hours, compared to several seconds or minutes for surface gravity waves). In contrast to surface waves in which horizontal particle velocities are largest at the surface and either decay quickly with depth (in deep water waves) or are independent of depth (in shallow water waves), horizontal water movement in internal waves is largest near the surface and bottom and minimal at mid-depth. Internal waves can often be observed in the atmosphere, where they travel on the interface between warm and cold air. and show two examples.

shows an example of an internal wave travelling on the seasonal thermocline in coastal waters. Such waves typically have wave lengths of several tens of metres and periods of about 30 minutes. Convergence of surface particle movement above the wave troughs near the surface often collects floating matter and makes the waves visible as slick marks ( ). If the interface on which the wave travels is very shallow, ships may find themselves in a situation that most of the energy put into the propeller goes into driving the circular particle motion of the internal wave at the interface, with the ship making little or no progress through the water. This phenomenon is known as "dead water" and is common in fjords, where the interface is produced by a shallow layer of freshwater from glacier runoff overlying oceanic water underneath. The most common internal waves are of tidal period and manifest themselves in a periodic lifting and sinking of the seasonal and permanent thermocline at tidal rythm. In some ocean regions their surface expressions, produced by convergence over the wave troughs, is visible in satellite images ( ).

Tides...

Tides are long waves, either progressing or standing. The dominant period usually is 12 hours 25 minutes, which is 1/2 of a lunar day. Tides are generated by the gravitational potential of the moon and the sun. Their propagation and amplitude are influenced by reflection, refraction, Coriolis force and friction. The most obvious expression of tides is the rise and fall in sea level. Equally important is a regular change in current speed and direction; tidal currents are among the strongest in the world ocean.

Description of Tides...

High water : A water level maximum ("high tide"), Low water : A water level minimum ("low tide"), Mean Tide Level : The mean between high and low tide, Tidal range : The difference between high and low tide, Daily inequality : The difference between two successive low or high tides, Spring tide : The tide following full and new moon, Neap tide : The tide following the first and last quarter of the moon phases. The result of alternate spring and neap tides is a half monthly inequality in tidal heights and currents. Its period is 14.77 days, which is half the synodic month (synodic: the positions of the sun and the moon coincide). There are other inequalities with similar and longer periods.

The Tide-Generating Forces...

As the earth rotates around the gravitational centre of the earth/moon system, the orientation of the earth´s axis in space remains the same. This is called revolution without rotation. The tide generating force is the sum of gravitational and centrifugal forces. In revolution without rotation the centrifugal force is the same for every point on the earth´s surface, but the gravitational force varies ( ). It follows that the tide generating force varies in intensity and direction over the earth's surface. Its vertical component is negligibly small against gravity; its effect on the ocean can be disregarded. Its horizontal component produces the tidal currents, which result in sea level variations ( ). The tide-generating force is proportional to the mass of the celestial body but inversely proportional to the square of the distance. The larger distance between the sun and earth, compared to the distance between the moon and earth, means that the tide-generating force from the sun is only about 46% of that from the moon. Other celestial bodies do not exert a measurable tidal force.

Main Tidal Periods...

(1) Tides produced by the moon : M2 (semidiurnal lunar) 1/2 lunar day = 12h 25min and O1 (diurnal lunar) 1 lunar day = 24h 50min.
(2) Tides produced by the sun : S2 (semidiurnal solar) 1/2 solar day = 12h and K1 (diurnal solar) 1 solar day = 24h.
The tides can be represented as the sum of harmonic oscillations with these periods, plus harmonic oscillations of all the other combination periods (such as inequalities). Each oscillation, known as a tidal constituent, has its amplitude, period and phase, which can be extracted from observations by harmonic analysis. 396 such oscillations have been identified, but in most situations and for predictions over a year or so it is sufficient to include only M2, S2, K1 and O1. Practical predictions produced on computers for official tide tables use between 10 and 70 terms.

Tidal Classification...

The form factor F is used to classify tides. It is defined as ;

F = ( K₁ + O₁ ) / ( M₂ + S₂ )

where the symbols of the constituents indicate their respective amplitudes. Four categories are distinguished :

Value of F	Category
0 - 0.25	Semidiurnal
0.25 - 1.5	Mixed, mainly semidiurnal
1.5 - 3	mixed, mainly diurnal
> 3	Diurnal

shows examples.

Shape of the Tidal Wave...

The scales of variations in the forcing field are of global dimensions. Only the largest water bodies can accommodate directly forced tides, and the tides are always standing waves. On a non-rotating earth they would attain the shape of seiches, ie a back and forth movement of water across lines of no vertical movement (nodes). On a rotating earth the tidal wave is transformed into movement around points of no vertical movement known as amphidromic points. (1) At amphidromic points the tidal range is zero, (2) Co-range lines (lines of constant tidal range) run around amphidromic points in quasi-circular fashion, (3) Co-phase lines (lines of constant phase, or lines which connect all places where high water occurs at the same time) emanate from amphidromic points like spokes of a wheel. The animation compares seiche movement with tidal movement around an amphidromic point.

Details of the shape of the tidal wave depend on the configuration of ocean basins and are difficult to evaluate. Computer models can give a description of the wave on an oceanic scale ( shows examples. ). Their results have to be verified against observations of tidal range and times of occurrence of high and low water. Distortions of the wave on the continental shelf caused by shallow water make it difficult to assess results for the open ocean. In deep water the tidal range rarely exceeds 0.5 m.

Co-oscillation Tides...

Tides in marginal seas and bays cannot be directly forced; they are co-oscillation tides generated by tidal movement at the connection with the ocean basins. Depending on the size of the sea or bay they take the shape of a seiche or rotate around one or more amphidromic points. If the tidal forcing is in resonance with a seiche period for the sea or bay, the tidal range is amplified and can be enormous. This produces the largest tidal ranges in the world ocean (14 m in the Bay of Fundy the Canadian east coast; 10 m at St. Malo in France, 8 m on the North West Shelf of Australia; all are mainly semidiurnal tides). Tidal range is then largest at the inner end of the bay, in accordance with the dynamics of seiches in open basins. Modest amplification is exerienced in Spencer and St. Vincent Gulfs of South Australia where the tidal range at spring tide is 3 m at the inner end. shows examples. shows an example of a co-oscillation tide in a large bay. The tide is forced from the open end by the oceanic tide, which has an maximum tidal range (at spring tide) of about 1 m. Because of the width of the basin the Coriolis force is able to shape the wave, producing amphidromic points around which the wave propagates. Amplification is particularly large along the British coast and in the English Channel.

Estuaries...

Estuaries are regions of the coastal ocean where salinity variations in space are so large that they determine the mean circulation. They are related to mediterranean seas in the sense that the major driving forces for their circulation are thermohaline processes. They differ from mediterranean seas mainly in size and configuration. Most estuaries are found at river mouths; they are thus long and narrow, resembling a channel. Compared to the flow in the direction of the estuary axis, cross-channel motion is very restricted, and the estuarine circulation is well described by a two-dimensional current structure. This is not true for mediterranean seas, which are wide enough to accommodate flow in three directions and allow the Coriolis force to exert its influence (e.g. in inertial motion). Modification of the circulation by winds is also stronger in mediterranean seas than in estuaries, where the circulation is restricted to the direction of the estuary axis regardless of winds.

A semi-enclosed coastal body of water having free connection to the open sea and within which sea water is measurably diluted with fresh water deriving from land drainage.

This definition works well for estuaries in the temperate zone where estuaries are linked with river mouths but does not include bodies of anomalously high salinity such as lagoons, or coastal inlets which are connected to the ocean only occasionally. For Australian (and indeed world-wide) application it is advisable to amend the definition to :

An estuary is a semi-enclosed coastal body of water having free connection to the open sea at least intermittently, and within which the salinity is measurably different from the salinity in the adjacent open sea.

Estuaries can be grouped into classes, according to their circulation properties and the associated steady state salinity distribution. The most important estuary types are ; (1) salt wedge estuary, (2) highly stratified estuary, (3) slightly stratified estuary, (4) vertically mixed estuary, (5) inverse estuary and (6) intermittent estuary. The balance of forces that establishes a steady state in types 1-4 involves advection of freshwater from a river and introduction of sea water through turbulent mixing. Mixing is achieved by tidal currents. (This is another aspect where estuaries differ from mediterranean seas; mixing in mediterranean seas is usually associated with eddies but not with tidal currents, which in most mediterranean seas are quite small.) The ratio of freshwater input to sea water mixed in by the tides determines the estuary type. One way of quantifying this is by comparing the volume R of freshwater that enters from the river during one tidal period, with the volume V of water brought into the estuary by the tide and removed over each tidal cycle. R is sometimes called the river volume, while V is known as the tidal volume. It is important to note that it is only the ration R : V that determines the estuary type, not the absolute values of R or V. In other words, estuaries can be of widely different size and still belong to the same type. Salt wedge estuaries for example can be produced by a small creek in a nearly tide-free bay, or they can be of the scale of the Mississippi and Amazon rivers, which carry so much water that even strong tidal mixing is insignificant in comparison.

Salt Wedge Estuary...

River volume R is very much larger than the tidal volume V, or there are no tides at all. The fresh water flows out over the sea water in a thin layer. All mixing is restricted to the thin transition layer between the fresh water at the top and the "wedge" of salt water underneath. Vertical salinity profiles therefore show zero salinity at the surface and oceanic salinity near the bottom all along the estuary. The depth of the interface decreases slowly as the outer end of the estuary is approached ( shows examples. ). Examples of large salt wedge estuaries are the Mississippi and the Congo Rivers. Other examples may be as small as only a few kilometres long. Note the vertical exaggeration in this and the following figures.

Highly Stratified Estuary...

River volume R is comparable to but still larger than tidal volume V. Strong velocity shear at the interface produces internal wave motion at the transition between the two layers. The waves break and "topple over" in the upper layer, causing entrainment of salt water upward. Entrainment is a one-way process, so no fresh water is mixed downward. This results in a salinity increase for the upper layer, while the salinity in the lower layer remains unchanged, provided the lower layer volume is significantly larger than the river volume R and can sustain an unlimited supply of salt water ( shows examples. ). Examples of this type of estuary are fjords, which are usually very deep and have a large salt water reservoir below the upper layer. Moderately deep river beds often exhibit this type of stratification during periods of weak river flow. The upward mass flux of salt water leads to an increase of flow speed in the upper layer. This increase of mass transport in the upper layer can be quite significant, to the extent that the river output appears insignificant compared with the overall circulation ( shows examples. ). A 20-fold amplification of the mass transport into the sea is quite realistic. The surface velocity increases likewise, although not as dramatically, as the downstream increase in width of the estuary compensates for some of the increase in mass transport.

Slightly Stratified Estuary...

River volume R is small compared to tidal volume V. The tidal flow is turbulent through the entire water column (the turbulence induced mainly at the bottom). As a result, salt water is stirred into the upper layer and fresh water into the lower layer. Salinity therefore changes along the estuary axis not only in the upper layer (as was the case in the highly stratified estuary) but in both layers ( shows examples. ). There is some increase in surface velocity and upper layer transport towards the sea but not nearly as dramatic as in the highly stratified case. This type of estuary is widespread in temperate and subtropical climates; many examples are found around the world.

Vertically Mixed Estuary...

River volume R is insignificant compared with tidal volume V. Tidal mixing dominates the entire estuary. Locally it achieves complete mixing of the water column between surface and bottom, erasing all vertical stratification. As a result, vertical salinity profiles show uniform salinity but a salinity increase from station to station as the outer end of the estuary is approached ( shows examples. ). This type of estuary is found in regions of particularly strong tides; an example is the River Severn in England.

As said above, the estuary type is determined by the ratio R : V. Varying this ratio produces a range of salinity distributions, which can be classified by the ratio of surface salinity Ss against bottom salinity Sb. The ratio Ss : Sb can therefore be used as a substitute for the ratio R : V. Salinities are easier to measure than tidal and river volume, and a ratio based on salinities is therefore of practical value. shows examples. shows the unified classification scheme based on salinity. The salt wedge estuary has freshwater at the surface, oceanic water at the bottom and is thus identified by a salinity ratio of zero. It occupies the bottom line of the diagram. Salinity in the vertically mixed estuary varies along the estuary but is the same at the surface and at the bottom everywhere, so the vertically mixed estuary has a salinity ratio of one and occupies the top line of the diagram. The highly stratified estuary is found in the lower left triangle, the slightly stratified estuary in the upper right triangle. Estuaries can change type as a result of variations in rainfall and associated river flow. They may show different characteristics in different parts as a result of topographic restrictions on the propagation of the tide along the estuary which affect the tidal volume. The classification diagram can be used to establish changes of estuary type in space and time.

Inverse Estuaries...

These estuaries have no fresh water input from rivers and are in a region of high evaporation. Surface salinity does not decrease from the ocean to the inner estuary, but water loss from evaporation leads to a salinity increase as the inner end of the estuary is approached ( shows examples. ). This results in a density increase and sinking of high salinity water at the inner end. As a result, movement of water is directed inward at the surface and towards the sea at the bottom, with sinking at the inward end. Compared to the estuaries discussed above their circulation is reversed, which explains the name inverse estuary. Some tropical Australian estuaries show a combination of 'normal' and 'inverse' circulation. shows examples. shows the example of the Alligator River. The estuary receives some fresh water from river inflow but evaporation is so strong that at some intermediate position all river water has evaporated and salinity becomes higher than in the open sea. Upstream from this position the circulation is "normal"; downstream it is "inverse". Other examples are the Escape River and the Wenlock and Duncie Rivers.

Intermittent Estuaries...

Many estuaries change their classification type because of highly variable rainfall over the catchment area of their river input. River input may be small, but as long as some fresh water enters the estuary, the estuarine character is maintained (in the form of a salt wedge estuary). If the river input dries up completely during the dry season, estuaries loose their identity and turn into oceanic embayments. An example is the South West Arm of Port Hacking south of Sydney which turns into a highly stratified estuary for a few weeks after heavy rains. During their estuarine periods intermittent estuaries can be classified on the basis of the classification diagram of , but the effect of their high environmental variability on marine life is so overwhelming that a separate classification appears justified. Marine life in intermittent estuaries undergoes a complete change of communities between the estuarine and oceanic phases - very few plants or animals can cope with the salinity changes that occur between the two phases.