Estuarine water circulation is controlled by the inflow of

river A river is a natural flowing watercourse, usually freshwater, flowing towards an ocean, sea, lake or another river. In some cases, a river flows into the ground and becomes dry at the end of its course without reaching another body of wate ...

s, the

tides Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables can ...

rainfall Rain is water droplets that have condensed from atmospheric water vapor and then fall under gravity. Rain is a major component of the water cycle and is responsible for depositing most of the fresh water on the Earth. It provides water f ...

and

evaporation Evaporation is a type of vaporization that occurs on the surface of a liquid as it changes into the gas phase. High concentration of the evaporating substance in the surrounding gas significantly slows down evaporation, such as when humidi ...

, the

wind Wind is the natural movement of air or other gases relative to a planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating of land surfaces and lasting a few hou ...

, and other oceanic events such as an

upwelling Upwelling is an oceanographic phenomenon that involves wind-driven motion of dense, cooler, and usually nutrient-rich water from deep water towards the ocean surface. It replaces the warmer and usually nutrient-depleted surface water. The nutr ...

, an eddy, and storms. Estuarine water circulation patterns are influenced by vertical mixing and stratification, and can affect residence time and exposure time.

Residence time

The ''

residence time The residence time of a fluid parcel is the total time that the parcel has spent inside a control volume (e.g.: a chemical reactor, a lake, a human body). The residence time of a set of parcels is quantified in terms of the frequency distribution ...

'' of

water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...

is a key variable determining the health of an

estuary An estuary is a partially enclosed coastal body of brackish water with one or more rivers or streams flowing into it, and with a free connection to the open sea. Estuaries form a transition zone between river environments and maritime environment ...

, particularly from human-induced stresses. Rapid flushing ensures that there is insufficient time for

sediment Sediment is a naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of wind, water, or ice or by the force of gravity acting on the particles. For example, sand an ...

accumulation or dissolved oxygen depletion in the estuary; thus a well flushed estuary is intrinsically more robust than a poorly flushed estuary.Wolanski, E. (2007) "Estuarine Ecohydrology." Amsterdam, The Netherlands: Elsevier. Residence time also affects other parameters such as

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, dissolved nutrients,

suspended solids Suspended solids refers to small solid particles which remain in suspension in water as a colloid or due to motion of the water. Suspended solids can be removed by sedimentation if their size or density is comparatively large, or by filtration. It ...

, and

algal Algae (; singular alga ) is an informal term for a large and diverse group of photosynthetic eukaryotic organisms. It is a polyphyletic grouping that includes species from multiple distinct clades. Included organisms range from unicellular mic ...

blooms that may affect the health of estuaries.Balls, B.W. (1994) "Nutrient inputs to estuaries from nine Scottish East Coast Rivers: influence of estuarine processes on inputs to the North Sea." Estuarine, Coastal and Shelf Science, 39, 329-352. A simple way to calculate residence time is using a simple classic estuary model, which can be useful for acquiring a conceptual understanding of an estuary, but is coarse in time and space. A classic estuary has the following components: 1)

freshwater Fresh water or freshwater is any naturally occurring liquid or frozen water containing low concentrations of dissolved salts and other total dissolved solids. Although the term specifically excludes seawater and brackish water, it does include ...

inflow with a discharge and a

salinity Salinity () is the saltiness or amount of salt dissolved in a body of water, called saline water (see also soil salinity). It is usually measured in g/L or g/kg (grams of salt per liter/kilogram of water; the latter is dimensionless and equal ...

(generally ); 2) oceanic inflow with a discharge and salinity ; and 3) outflow to the ocean with a discharge of and a salinity . The inflow and outflow of water is equal because mass is conserved.

Salt Salt is a mineral composed primarily of sodium chloride (NaCl), a chemical compound belonging to the larger class of salts; salt in the form of a natural crystalline mineral is known as rock salt or halite. Salt is present in vast quantitie ...

is also a conserved, therefore, the inflow and outflow fluxes of salinity are also equal. If

groundwater Groundwater is the water present beneath Earth's surface in rock and soil pore spaces and in the fractures of rock formations. About 30 percent of all readily available freshwater in the world is groundwater. A unit of rock or an unconsolidate ...

inputs and evaporation are ignored, the continuity equation is: : The residence time is the volume of water within the estuary (Vol) divided by the flow rate of the river: :

Exposure time

Residence time considers the time it takes for the water particles to leave the estuary, however, some water particles that leave the estuary during an ebb tide may re-enter the system during a flood tide. The amount of time a water particle spends in the estuary until it never returns is called ''exposure time''. The exposure time can be much larger than the residence time if the water particles are leaving with the ebb tides and returning with the rising tide. The ratio between the number of water particles returning to the estuary and the number of water particles leaving is known as the ''return coefficient'', . In order to quantify exposure time, the water circulation outside of the estuary must be determined. However, the circulation near the mouth of the estuary is complex due to the tidal mixing processes that occur between the estuarine and ocean waters. If the coast is rugged with headlands, a mosaic of complex flow fields consisting of

eddies In fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime. The moving fluid creates a space devoid of downstream-flowing fluid on the downstream side of the object. Fluid beh ...

, jets, and stagnation zones will occur, further complicating the circulation patterns outside of the estuary. In cases involving

delta Delta commonly refers to: * Delta (letter) (Δ or δ), a letter of the Greek alphabet * River delta, at a river mouth * D (NATO phonetic alphabet: "Delta") * Delta Air Lines, US * Delta variant of SARS-CoV-2 that causes COVID-19 Delta may also re ...

s or wetlands that drain into multiple tidal creeks, such as Missionary Bay,

Australia Australia, officially the Commonwealth of Australia, is a Sovereign state, sovereign country comprising the mainland of the Australia (continent), Australian continent, the island of Tasmania, and numerous List of islands of Australia, sma ...

, water leaving one creek at the ebb tide may enter another estuary during the flood tide. When there is a series of estuaries involved, a large exposure time (larger than that of the individual estuaries), will occur if the tidal outflow from one estuary re-enters a different estuary during the flood tide. Along a rugged

coastline The coast, also known as the coastline or seashore, is defined as the area where land meets the ocean, or as a line that forms the boundary between the land and the coastline. The Earth has around of coastline. Coasts are important zones in n ...

with headlands, however, mixing of estuary and oceanic waters can be intense. When estuarine water leaves the estuary, it gets flushed out to coastal waters, so exposure time and residence time are close equal. In some cases it is possible to measure the fluxes of volume, salt, and temperature across the mouth of an estuary through a

tidal cycle Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables can ...

. Using this data, can be calculated ( is the return coefficient): it is equal to the fraction of the volume of water (mean tidal prism volume) leaving the estuary during the ebb tide that is replaced with coastal waters prior to re-entering the system. When , the same water is re-entering the estuary, and if , the estuarine water that has left the estuary during the ebb tide has been replaced with coastal waters entering the estuary during the rising tide. The exposure time is estimated by: : is defined as the mean estuarine volume and is the tidal period. The total fluxes of brackish water through the river mouth during tidal events is often much higher (often by a factor of 10 to 100) than the volume flux from riverine inflow. Therefore, if measurements are not precise, the estimate of the net flux will be unreliable. Direct measurements of the return coefficient are often complicated by unsteady oceanic events such an upwelling, the passage of an eddy, or storms, so the success of a correct direct measurement of the return coefficient is rare.

Vertical mixing and stratification

The residence time of water in an estuary is dependent on the circulation within the estuary that is driven by density differences due to changes in salinity and temperature. Less dense freshwater floats over saline water and warmer water floats above colder water (temperatures greater than 4 °C). As a result, near-surface and near-bottom waters can have different trajectories, resulting in different residence times. ''Vertical mixing'' determines how much the

and

temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...

will change from the top to the bottom, profoundly affecting water circulation. Vertical mixing occurs at three levels: from the surface downward by wind forces, the bottom upward by boundary generated turbulence (estuarine and oceanic boundary mixing), and internally by turbulent mixing caused by the water currents which are driven by the tides, wind, and river inflow. Different types of estuarine circulation result from vertical mixing:

Salt wedge estuary

These estuaries are characterized by a sharp density interface between the upper layer of

and the bottom layer of

saline water Saline water (more commonly known as salt water) is water that contains a high concentration of dissolved salts (mainly sodium chloride). On the United States Geological Survey (USGS) salinity scale, saline water is saltier than brackish water, ...

. River water dominates in this system, and tidal effects have a small role in the circulation patterns. The freshwater floats on top of the seawater and gradually thins as it moves seaward. The denser seawater moves along the bottom up the estuary forming a wedge shaped layer and becoming thinner as it moves landward. As a

velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...

difference develops between the two layers, shear forces generate

internal waves Internal waves are gravity waves that oscillate within a fluid medium, rather than on its surface. To exist, the fluid must be stratified: the density must change (continuously or discontinuously) with depth/height due to changes, for example, in ...

at the interface, mixing the seawater upward with the freshwater.Kennish, M.J. (1986) "Ecology of Estuaries. Volume I: Physical and Chemical Aspects." Boca Raton, FL: CRC Press, Inc. An example is the

Mississippi Mississippi () is a state in the Southeastern region of the United States, bordered to the north by Tennessee; to the east by Alabama; to the south by the Gulf of Mexico; to the southwest by Louisiana; and to the northwest by Arkansas. Miss ...

estuary.

Partially stratified estuary

As tidal forcing increases, the control of river flow on the pattern of circulation in the estuary becomes less dominating.

Turbulent In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between t ...

mixing induced by the current creates a moderately stratified condition. Turbulent eddies mix the water column, creating a mass transfer of freshwater and

seawater Seawater, or salt water, is water from a sea or ocean. On average, seawater in the world's oceans has a salinity of about 3.5% (35 g/L, 35 ppt, 600 mM). This means that every kilogram (roughly one liter by volume) of seawater has appro ...

in both directions across the density boundary. Therefore, the interface separating the upper and lower water masses is replaced with a water column with a gradual increase in salinity from surface to bottom. A two layered flow still exists however, with the maximum salinity gradient at mid depth. Partially stratified estuaries are typically shallow and wide, with a greater width to depth ratio than salt wedge estuaries. An example is the

Thames The River Thames ( ), known alternatively in parts as the River Isis, is a river that flows through southern England including London. At , it is the longest river entirely in England and the second-longest in the United Kingdom, after the R ...

Vertically homogeneous estuary

In these estuaries,

tidal flow Tidal is the adjectival form of tide. Tidal may also refer to: * ''Tidal'' (album), a 1996 album by Fiona Apple * Tidal (king), a king involved in the Battle of the Vale of Siddim * TidalCycles, a live coding environment for music * Tidal (servic ...

is greater relative to river discharge, resulting in a well mixed water column and the disappearance of the vertical salinity gradient. The freshwater-seawater boundary is eliminated due to the intense turbulent mixing and eddy effects. The width to depth ratio of vertically homogeneous estuaries is large, with the limited depth creating enough vertical shearing on the seafloor to mix the water column completely. If tidal currents at the mouth of an estuary are strong enough to create turbulent mixing, vertically homogeneous conditions often develop.

Fjords

Fjord In physical geography, a fjord or fiord () is a long, narrow inlet with steep sides or cliffs, created by a glacier. Fjords exist on the coasts of Alaska, Antarctica, British Columbia, Chile, Denmark, Germany, Greenland, the Faroe Islands, Ice ...

s are examples of highly stratified estuaries; they are basins with sills and have freshwater inflow that greatly exceeds evaporation. Oceanic water is imported in an intermediate layer and mixes with the freshwater. The resulting brackish water is then exported into the surface layer. A slow import of seawater may flow over the sill and sink to the bottom of the fjord (deep layer), where the water remains stagnant until flushed by an occasional storm.

Inverse estuary

Inverse estuaries occur in dry climates where evaporation greatly exceeds the inflow of freshwater. A salinity maximum zone is formed, and both riverine and oceanic water flow close to the surface towards this zone. This water is pushed downward and spreads along the bottom in both the seaward and landward direction. The maximum salinity can reach extremely high values and the residence time can be several months. In these systems, the salinity maximum zone acts like a plug, inhibiting the mixing of estuarine and oceanic waters so that freshwater does not reach the ocean. The high salinity water sinks seaward and exits the estuary.

References

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