Ariver plume is afreshenedwater mass that is formed in thesea as a result of mixing ofriver discharge and salineseawater.^[1] River plumes are formed in coastal sea areas at many regions in the World. River plumes generally occupy wide-but-shallow sea surface layers bounded by sharpdensity gradients. The area of a river plume is 3-5 orders of magnitude greater than its depth; therefore, even smallrivers withdischarge rates ~1–10 m/s form river plumes with horizontal spatial extents ~10–100 m. Areas of river plumes formed by the largest rivers are ~100–1000 km². Despite the relatively small volume of totalfreshwaterrunoff to theWorld Ocean, river plumes occupy up to 21% ofshelf areas of the ocean, i.e., several million square kilometers.^[2]

In some occasions river plumes are spoken of asregions of fresh water influence (ROFIs), although it is preferred to use this term for regions in which multiple sources add to thefresh water input of the zone or for shallow, frictionalshelves.^[1]ROFIs and river plumes differ in the variation at temporal and spatial scales. The river plume can be identified as a buoyantwater mass that emerges due toriver discharge into the coastal ocean and varies overdiurnal tosynoptic timescales.^[3] At the edges of thiswater mass mixing takes place, creating a region adjacent to the river plume which is diluted and fresher compared to the open ocean, but does not have a clear boundary. This extended region is called the region of freshwater influence,ROFI.^[3] Due to the indirect influence offreshwater discharge, ROFIs incorporate the dynamics and spatial extent of the river plumes but are typically assessed on seasonal, annual, and decadal timescales.^[3]

River plumes play an important role in global and regional land-ocean interactions.River discharges provide large fluxes ofbuoyancy,heat,terrigenous sediments,nutrients, and anthropogenicpollutants to theocean. River plumes strongly influence manyphysical,biological, andgeochemical processes in the coastal and shelf sea areas includingstratification ofseawater, coastalcurrents,carbon andbiogeochemical cycles,primary production, andseabed morphology.^[1]

A river plume is a dynamical system influenced by processes with a wide range of temporal and spatial scales, which depend on the size and shape of theestuary as well as on the type and variation of the forcing from theestuary and theocean. Feedback mechanisms betweensediment deposited by the plume at thesubmarine delta and the geometry of thedelta make for a complex system. Due to this complexity there is not (yet) a general, simple theory that offers quantitative predictability for the motion of particles and the structure of river plumes;^[1] however, some theories incorporating simplified assumptions have helped in understanding the important aspects ofbuoyancy-influenced coastal flows.^[4] As is commonly used influid dynamics, the description of these complex flows is aided byscaling analysis to determine the relevant processes. The primary parameters which define the structure and scale of an individual river plume arefreshwater discharge,tidal energy,coastlinebathymetry/geometry, ambientocean currents,wind, andthe rotation of the Earth.^[1]

The balance between the important processes varies over the position in the plume. The following regions can be distinguished: the source region, the liftoff point, the front, and the near field region. Beyond the plume itself but within its area of influence are the mid-field region and the far field region.^[1]

In the source or estuarine region, thebuoyancy andmomentum of the freshwater inflow from the estuary are the dominant properties that determine the initiation of the river plume. The competition between river-inducedstratification and tidal mixing sets the river plume's characteristic properties. This competition can be captured in the (dimensionless) estuarineRichardson number, which is defined as^[5]

${\displaystyle R{i}_E=g_r^{\prime }\frac{Q_r}{W_E{u}_{tidal}^3},}$

where

• the reduced gravity${\displaystyle g_r^{\prime }=g(\mathrm{\Delta }\rho /{\rho }_0)}$ is thegravitational acceleration due to thedensity difference betweenfresh river water andsaline ocean water,
• ${\displaystyle Q_r}$ is theriver discharge,
• ${\displaystyle W_E}$ is theestuary width, and
• ${\displaystyle u_{tidal}}$ is the tidal velocity.

where

• ${\displaystyle g_r^{\prime }=g(\mathrm{\Delta }\rho /{\rho }_0)}$ is thegravitational acceleration due to thedensity difference betweenfresh river water andsaline ocean water,
• ${\displaystyle Q_r}$ is theriver discharge,
• ${\displaystyle W_E}$ is theestuary width, and
• ${\displaystyle u_{tidal}}$ is the tidal velocity.

A large estuarine Richardson number (i.e.${\displaystyle R{i}_E\gg 1}$) indicates thatfreshwater processes are dominant compared to thetidal influence, and one can expect development of a river plume.^[1]

In case of strong riverine forcing, often with a large estuarineRichardson number, the front of the plume separates from thebottom. The position at which thisflow separation occurs is called the liftoff point and sets the landward edge of the near-field. This point is important in surface-advected river plumes.^[6][7]

In the near-field the momentum of the plume is larger than itsbuoyancy. This balance is represented in the (dimensionless)Froude number,${\displaystyle Fr=u/\sqrt{gh},}$ and is larger than one in the near-field, indicatingsupercritical flow. Both the liftoff point and the outer boundary of the near-field, the plume front, are characterized by critical flow conditions (${\displaystyle Fr=1}$) and the flow in the near-field region shows features similar to a jet.^[8] Themomentum balance is dominated bybarotropic andbaroclinicpressure gradients,turbulent shear stresses, and flow acceleration. Flow deceleration is mainly caused by theshear stresses on the interface of the plume with the ambientocean. In some cases a near-field region will not exist. This is for example the case if the width of theriver mouth is large relative to theRossby radius of deformation,${\displaystyle L_R=\sqrt{gh}/f}$, and thefresh water inflow will leave theriver mouth as a far-field plume. Whentides are large, the near-field plume is also known as the tidal plume.^[9]

The area at which the near-field inertial jet transfers into a flow in whichgeostrophic orwind-driven processes are dominant is the midfield-area. Themomentum balance of the mid-field is dominated by the rotation of the Earth (Coriolis effect), cross-stream internalpressure gradients, and sometimescentripetal acceleration. The initialmomentum of theoutflow from the source is lost and thewind forcing (orrotation of the Earth in case of smallwind forcing) gradually takes over as the most important parameter. As a result, the flow changes its speed, direction, and spreading pattern. When the influence ofwind forcing is small,outflows can sometimes form a recirculating bulge;^[1][6] however, evidence of such a feature in field observations is scant.^[10]

Even further away from the source region is the far-field, where the plume has lost all memory of the outflow momentum. The momentum balance of the far-field is dominated by the rotation of the Earth (Coriolis effect),buoyancy,wind forcing, and bottom stress. The far-field can cover large areas, up to hundreds of kilometers from its source.Diurnal and semi-diurnal variability of the far-field region is generally governed bytides, synoptic variability bywind forcing, and seasonal variability by river discharge. In the absence of strongwind forcing and strong currents, the far-field plume can behave as a current of relativelyfresh water in the direction of a propagatingKelvin wave. Examples of this can be observed in the RhineROFI, where the river plume can be traced all along the Dutch coast.^[11] The character of this coastal current is different in the case of shallow seas, when the current occupies the wholewater column and its motion is affected by bottomfriction, and in the case of a surface-advected plume whose vertical size is less than the water depth.^[1][6]

At the most basic and idealized level, river plumes can be classified to be either surface-advected or bottom-advected.^[6][12] A plume is considered to be bottom-advected when it occupies the whole water column from the surface to theseabed. In this case itsstratification is mainly horizontal as a result of strongadvection over the wholewater column, especially near thebed. A surface-advected plume does not interact with thebottom because its vertical size is less than its depth. In this case a plume is mainly verticallystratified. Differentiation between these two (idealized) types of river plumes can be made by evaluating a set of parameters, as set up by Yankovsky and Chapman in their paper from 1997.^[6] The distance up to which thefresh water river plume is transported across-shelf by processes at the surface is given by

${\displaystyle y_s=\frac{2}{f}\sqrt{\frac{3g^{\prime }{h}_0+v_i^2}{2g^{\prime }{h}_0+v_i^2}},}$

where

• ${\displaystyle v_i}$ is the inflow velocity from the source region and the near-field jet,
• ${\displaystyle f}$ is the Coriolis force,
• ${\displaystyle g^{\prime }}$ is the buoyancy, and
• ${\displaystyle h_0}$ is the depth of the water column at the mouth of theriver/estuary.

Up to the liftoff point, the plume still "feels" the bottom and one speaks of bottom-advected plumes, and the relevant processes involving bottom dynamics must be accounted for.^[13] Vertical scales of river plumes formed by the largest rivers across the world are 10-20 m, while the vertical scale of the majority of river plumes is less than several meters. As a result, the majority of river plumes in the world are surface-advected; that is, the bottom-advected part near the estuary before the liftoff point at these plumes is much smaller than the surface-advected part. River plumes with large bottom-advected parts are formed mainly by large rivers that flow into shallow sea areas, such as theVolga plume in the northern part of theCaspian Sea.

Bottom-advected plumes are often characterized by large discharge conditions and are generally less sensitive towind forcing and corresponding advection and mixing.^[6] This type of advection is driven by bottomEkman transport, which drives the fresh or brackish river outflow with density${\displaystyle {\rho }_i}$ and velocity${\displaystyle v_i}$ from an estuary of width${\displaystyle L}$ and depth${\displaystyle h_0}$ to the frontal zone across the shelf. This is indicated in the figure to the right. When the frontal zone is far enough from the shore,thermal wind dynamics can transport the complete volume flux away from the estuary. The across-shore position${\displaystyle y_b}$, which denotes the width of the coastal current, and the equilibrium-depth${\displaystyle h_b}$ at which the plume separates from the bottom can be calculated in equilibrium conditions with a certain bottom slope${\displaystyle s}$ by

${\displaystyle h_b=\sqrt{\frac{2f{v}_i{h}_0}{g^{\prime }}}}$

${\displaystyle y_b=\frac{h_0}{s}(\sqrt{\frac{2fL{v}_i}{g^{\prime }{h}_0}}-1)}$.^[6]

Note that this is only valid when${\displaystyle h_b>h_0}$. Whenthe bottomEkman layer cannot transport the river outflow offshore and another process governs the propagation. In that case, only a surface-advected plume is found.^[6][7]

Surface-advected plumes occur when the previously-defined condition of is met. A surface-advected plume has the typical structure of a river plume as described in the sectionriver plume structure. In the region near the mouth the initial momentum of the river outflow is the dominant mechanism, after which other processes such aswind forcing and theCoriolis effect take over. In a surface-advected plume,. processes regarding interaction with the bottom such as the development of a bottomEkman layer are not relevant. Therefore, the defined parameter${\displaystyle y_b}$can be ignored in this approach as it has no physical basis.^[6][7]

In the case that the inflow depth${\displaystyle h_0}$ is smaller than depth${\displaystyle h_b}$, and the distance up to which the bottomEkman layer transports the river discharge is smaller than the distance up to which the surface processes transport the river outflow, (), one can find an intermediate plume. In an intermediate plume both regimes can be found. Naturally, the bottom-advected section can be found closer to the estuary mouth and the surface-advected section can be found further offshore. The liftoff point separates the regions.^[6][7]

The approach can be further generalized by non-dimensionalizing the parameters. Non-dimensional parameters have the benefit of simplifying the dynamics of the relevant processes by evaluating the magnitude of different terms. In the case of river plumes, it gives further direction to the basic classification and their different dynamics. The two most relevant non-dimensional numbers are theBurger number${\displaystyle S=\sqrt{g^{\prime }{h}_0}/(fL)}$, which expresses the relative importance ofbuoyancy, and theRossby number${\displaystyle Ro=v_i/(fL)}$, which expresses the relative importance of advection. Regrouping leads to the following, non-dimensional cross-shore distances${\displaystyle Y_b}$ and${\displaystyle Y_s}$:

${\displaystyle Y_s=\frac{2(3S^2+R{o}^2)}{\sqrt{2S^2+R{o}^2}}}$

${\displaystyle Y_b=\frac{h_0}{sL}(\frac{\sqrt{2Ro}}{S}-1)}$.

The same regimes as discussed above hold for the non-dimensional parameters. Bottom-advected plumes (${\displaystyle h_b>h_0}$,${\displaystyle Y_b>Y_s}$) in general have smallBurger numbers and thereforebuoyancy is relatively unimportant. Surface-advected plumes () in general have largeBurger numbers and thereforebuoyancy is important. Furthermore, theRossby number indicates whether the plume is classified as a surface-advected plume or an intermediate plume. A relatively largeRossby number compared to theBurger number indicates thatadvection is important compared tobuoyancy and will allow at least partial bottom-advection to occur so that one can expect an intermediate plume.^[6][12]

Note that the scheme described above was developed for idealized cases: that is, for river plumes in absence of external forcing which flow into asea with idealizedbathymetry and shoreline.

River plumes vary over diurnal tosynoptic temporal scales.^[3] In this range of temporal scales, the most important periodic variation lies within the tidal cycle, in which atidal cycle (daily) and a spring-neap cycle (two-weekly) can be distinguished.^[14] Thisbarotropic variation in tidal velocity magnitude and direction gives rise to variability in the strength and stability of the river plume.^[7] This is already clear from the competition between river discharge and tidal mixing, captured in the (dimensionless) estuarineRichardson number${\displaystyle R{i}_E=g_r^{\prime }{Q}_r/W_E{u}_{tidal}^3}$, which is used to assess in a general fashion whether a river plume can develop in a certain system.^[5] The tidal dynamics lead to the following general dynamics of river plumes.

Atidal cycle consists of a flood period or landward flow, and an ebb period or seaward flow.^[15] For constantriver discharge${\displaystyle Q_r}$ one can find a stablestratification during ebb conditions and an unstablestratification during flood conditions.^[11] This is schematically portrayed in the figure to the right. The mixing that occurs during flood conditions due to the unstablestratification weakens thestratification and efficient river plume advection^[11] and occurs in situations with low estuarineRichardson numbers.

During ebb conditions thestratification is enhanced. This leads to stable conditions and strong advection at the surface.^[11] Due to mass conservation, this situation requires enhanced landward flows near the bottom. This process is calledtidal straining. In the case of an open coast, two-dimensional effects start playing a role.BaroclinicEkman transport causesupwelling during ebb flows anddownwelling during flood flows.^[5] Therefore, thesebaroclinicupwelling effects can cause ebb flows to transport nutrients and sediment towards the coast.^[11]

Over a spring-neap cycle thebaroclinic effects over atidal cycle amplify and favor either increased tidal straining or tidal mixing.^[11]Spring tides are characterized by relatively large tidal amplitudes and tidal flow velocities.^[15] This leads to increased tidal mixing over the completetidal cycle and weakenedstratification.^[11] In some areas thestratification vanishes completely, resulting in a well-mixed system, and these systems can only incorporate river plumes some of the time.^[7] In open-coast systems,spring tide conditions generally lead to increaseddownwelling effects from thebuoyant river plume, causing increased seaward transport ofsediment andnutrients.^[11]

Neap tides are characterized by relatively low tidal amplitudes and tidal flow velocities.^[15] This situation favors the tidal straining effect as observed during ebb tides due to decreased tidal mixing and increased differential flow over atidal cycle.^[11] Due to the stronger tidal straining effect,neap tide conditions are generally characterized by increased landward flow near the bottom and associated increased coastalupwelling effects.^[11] In extreme cases this can lead to large depositions on thebeach, such as the mass beaching event ofstarfish at thecoast nearScheveningen January 30, 2019.^[16]

An example of a surface-advected plume is theFraser River plume. TheFraser River plume contains all dynamical regions, clearly visible from space. The initial jet-like structure gradually transfers into a far-field plume further offshore, which is deflected to the right as would be expected on theNorthern Hemisphere due to theCoriolis effect. Other similar river plumes are those of theColumbia River, theNiagara River, and theHudson River.^[1][9]

TheAmazon River plume is an example of a river plume in which theEarth's rotation does not play a role. Due to the highdischarge, the correspondingmomentum of theoutflow, and the equatorial latitude, the dynamics of the plume are mainly characterized by the internalFroude number. Ambient currents transport the plume away from the mouth.^[1][13] Similar plumes can be found elsewhere along theEquator.

The dynamics of theMersey River plume at the mouth ofLiverpool Bay show high resemblance to a bottom-advected plume.^[17] This is due to strong influence of the bottom and bottomfriction on the flow, and this controls the cross-shore spreading and length-scale. This type of plume can often be found atmarginal seas andshelf seas, such as in theNorth Sea at the mouth of theRhine.^[1][18]

• Plume (fluid dynamics)
• Region of freshwater influence

• Steven Lohrenz."River Plume Processes and Dynamics". School for Marine Science and Technology, University of Massachusetts, Dartmouth. Retrieved2021-02-13.

• Coastal geography
• Physical oceanography
• Aquatic ecology
• Estuaries
• Limnology
• Coastal engineering

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