Relating River Plume Structure to Vertical Mixing
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SEPTEMBER 2005 H E T LAND 1667 Relating River Plume Structure to Vertical Mixing ROBERT D. HETLAND Department of Oceanography, Texas A&M University, College Station, Texas (Manuscript received 30 March 2004, in final form 24 February 2005) ABSTRACT The structure of a river plume is related to the vertical mixing using an isohaline-based coordinate system. Salinity coordinates offer the advantage of translating with the plume as it moves or expanding as the plume grows. This coordinate system is used to compare the relative importance of different dynamical processes acting within the plume and to describe the effect each process has on the structure of the plume. Vertical mixing due to inertial shear in the outflow of a narrow estuary and wind mixing are examined using a numerical model of a wind-forced river plume. Vertical mixing, and the corresponding entrainment of background waters, is greatest near the estuary mouth where inertial shear mixing is large. This region is defined as the near field, with the more saline, far-field plume beyond. Wind mixing increases the mixing throughout the plume but has the greatest effect on plume structure at salinity ranges just beyond the near field. Wind mixing is weaker at high salinity classes that have already been mixed to a critical thickness, a point where turbulent mixing of the upper layer by the wind is reduced, protecting these portions of the plume from further wind mixing. The work done by mixing on the plume is of similar magnitude in both the near and far fields. 1. Introduction and Geyer 2001; García Berdeal et al. 2002; Hetland and Signell 2005). However, analysis of the plume is River plumes are central to a number of important difficult, particularly interpreting observations, because societal oceanographic problems. For example, a toxic of the changing position of the plume. In the case of dinoflagellate, Alexandrium spp., is associated with the wind forcing, the plume may change position so much the Kennebec–Penobscot River plume in the Gulf of that, at many points, the plume may be only occasion- Maine (Franks and Anderson 1992). Stratification ally present. Also, even when the plume is present, dif- caused by Mississippi–Atchafalaya outflow prevents ferent regimes of the plume may be measured, for ex- ventilation of lower-layer waters, allowing hypoxic con- ample, frontal regions versus the core of the plume. ditions to develop on the continental shelf (Rabalais et Many of these difficulties stem from a Cartesian, or al. 1999). Nearly one-half of all oceanic carbon burial Eulerian, view of the plume. occurs in large river deltas (Hedges and Keil 1995). This paper examines the plume in salinity coordi- Many papers have reported on the various features nates, a natural coordinate system for the plume. Al- of river plumes, particularly a recirculating bulge that though this approach is not Lagrangian, in that the forms in the vicinity of the outflow (e.g., Garvine 1987; plume may be steady in salinity space even while water O’Donnell 1990; Yankovsky and Chapman 1997; Fong flows through it, salinity coordinates offer the advan- 1998; Nof and Pichevin 2001; Garvine 2001; Yankovsky tage of translating with the plume as it moves or ex- et al. 2001) and the on- and offshore motion of the panding as the plume grows. For example, the addition plume in response to upwelling and downwelling wind of wind causes the plume to mix as well as to change stresses (Fong et al. 1997; Pullen and Allen 2000; Fong horizontal position. Salinity coordinates are used to here to examine changes in vertical mixing in isolation by following the plume as it is shifted by currents. The focus in this paper is buoyancy-forced flow from Corresponding author address: Robert D. Hetland, 3146 TAMU, Department of Oceanography, College Station, TX narrow estuaries, where the local internal deformation 77843-3146. radius is larger than the width of estuary mouth. For E-mail: [email protected] the narrow-estuary case, as water leaves the estuary, it © 2005 American Meteorological Society Unauthenticated | Downloaded 09/29/21 02:36 PM UTC JPO2774 1668 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 35 FIG. 1. This conceptual model of river plume anatomy shows the major regions and indicates the dominant mixing mechanisms. spreads and shoals, becoming supercritical. Here, the stress and by relating the size of the plume to different estuary mouth acts as a hydraulic constriction for the vertical mixing processes. upper layer (Armi and Farmer 1986). The accelerating flow soon becomes unstable, and strong shear mixing 2. Salinity coordinates occurs in the near field (Wright and Coleman 1971; Interpreting measurements of a river plume in Car- MacDonald 2003). Beyond this region, mixing is pri- tesian space may be difficult—for instance, the plume marily caused by wind stress through a mechanism de- may be only occasionally present at certain locations. scribed by Fong and Geyer (2001). Ekman transport in The analysis methods presented below are less sensitive the upper layer may become large enough that shear to the motions of the plume, because these methods instability is induced. At this point, the plume will mix consider the water mass structure of the plume as a and thicken until the local Richardson number is again whole using a coordinate system based on salinity. This above the critical value. This model of wind mixing salinity-based coordinate system follows the plume as it considers only the local wind stress and stratification. It moves and allows the freshwater introduced into the is not yet clear how this balance affects, and is affected domain to be followed as it is mixed with the back- by, the horizontal plume structure. A cartoon of the ground waters. The analysis presented below is based various dynamical regions within the plume shown in on the approach of MacCready et al. (2002), who ex- Fig. 1 demonstrates the mixing history of a water parcel amine long-term estuarine salt balances by calculating as it leaves the river/estuary and eventually becomes salt fluxes across isohalines. The derivation below ex- part of the background waters. tends MacCready et al.’s analysis by demonstrating The goal of this paper is to relate vertical mixing in how changes in isohaline surface area can be used to different dynamical regions of the plume to changes in estimate salt flux at particular salinity classes within the plume structure. In particular, this paper will compare plume, rather than across the entire isohaline surface. the relative importance of different dynamical pro- Here, we will consider a volume V bounded by the cesses acting within different parts of the plume, the sea surface and ocean floor, a face within the river structure of the plume, and the role of wind mixing in where s ϭ 0, and on the seaward edge by an isohaline, determining that structure. Garvine (1999) notes that s (the shaded area in Fig. 2). A portion of the bound- the steady-state alongshore scale of a river plume with- A ing area A defined by the isohaline surface s com- out wind forcing depends on, among other things, the A pletely divides fresher plume water (s Ͻ s ) from the value of background mixing, the minimum value for A rest of the ocean. There is a net freshwater flux of Q diffusivity, and viscosity in a turbulence closure scheme. R across the face of the volume within the river. Garvine’s results show that increasing the background The three-dimensional salt balance equation, mixing decreases the alongshore scale of the plume (roughly related to the total area of the plume). This Ѩs f, ͑1͒ · su͒ ϭϪ١͑ · ١ ϩ paper expands Garvine’s basic result by including wind Ѩt Unauthenticated | Downloaded 09/29/21 02:36 PM UTC SEPTEMBER 2005 H E T LAND 1669 FIG. 2. The volume V, bounded on the seaward edge by area A, is shaded gray; the area A ϭ is defined by isohaline s sA. A freshwater flux, QR, is input into the volume on the opposite Ϫ ␦ Ͻ face of V. The second isohaline, sA s sA, is used in an example in the text. The difference Ϫ ␦ ␦ in isohaline area between sA s and sA is A. integrated over volume V is is the freshwater content within V, relative to sA.IfEq. (4) is divided by s , an intuitive freshwater balance is Ѩ A ͵ sdVϪ s ͵ u · dA ϩ s ͵ u · dA formed—the freshwater from the river, QR, must either Ѩt A A A V A A increase VfA in time or be compensated by a freshwater flux, f/sA, across A. ϭϪ͵ ͑ ͒ By knowing Q and the change in freshwater content f · dA, 2 R A over time, the average salt flux, f across A may be es- timated. However, it is expected that within the river where u is the three-dimensional flow vector, uA is the Ϫ plume the flux will change at different points within the normal velocity of the surface A itself (such that u uA is the flow through A), and f is the diffusive salt flux. plume, so that an area average of the salt flux over a The generalized Leibnitz theorem (Kundu 1990, p. 75) large isohaline may be difficult to interpret: are changes is used to take the time derivative outside the integral in average flux due to intense localized mixing or in the first term. The advective and diffusive salt fluxes broad-scale changes? through the faces of V are nonzero only on the isoha- Assuming a thin pycnocline, the salt flux across two isohalines within the pycnocline will be similar.