How Estuaries Work: A Charlotte Harbor Exampleby

R.H. Weisberg and L. ZhengCollege of Marine Science, University of South Florida, St. Petersburg, FL.

AbstractWe consider the time-averaged, estuarine circulation through an analysis of its mechanical energy balance; hence the title of our poster: “How estuaries work.” The venue is the Charlotte Harbor on Florida’s west coast, and the analysis medium is the primitive equation ECOM3D-si model. We are motivated by an estuary classification dilemma. Being that estuarine circulation is buoyancy driven by the horizontal salinity gradient, and that the gradient increases with increasing vertical mixing as the salinity isolines rotate from horizontal to vertical, it follows that an increase in mixing should lead to an increase in circulation. Yet, at some point, intermediate between partial and well mixed, the estuarine circulation decreases. Weexplore this conundrum by considering the sources and sinks of mechanical energy, derived from river, tide, and wind forcing, through analyses of pressure work, work by stresses operating on the surface and the bottom, work against buoyancy through mixing and advection, and turbulence energy production by velocity component shears. How the energy partitions between work against buoyancy (that sets the driving force) and turbulence production (that serves as a brake) provides an answer. Depending on tides and winds, if the incremental rate of turbulence production exceeds that of buoyancy work the estuarine circulation slows. A useful measure is the ratio of buoyancy work to turbulence production. As this ratio increases so does the circulation, and conversely. For the Charlotte Harbor, tides alone may cause peak circulation. Weak, oscillatory winds may add to this, but with increasing wind stress the tide and wind averaged estuarinecirculation decreases. Further exploration of these effects across Rayleigh number space with varying estuarine geometries and forcing functions may lead to improved understandings of estuary workings in general.

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Mechanical energy control volume analysis

Where te is the total mechanical energy (kinetic plus potential energy); and(I) is the local change of te integrated over the control volume;(II) and (III) are the fluxes of te into the control volume by the horizontal velocity components;(IV) is the pressure work on the bounding surface;(V) is the work performed by the wind stress on the free surface; (VI) is the work performed by friction along the bottom;(VII) is the energy dissipation by turbulent shear production via the velocity component’s vertical shears;(VIII) is the buoyancy flux by vertical advection and diffusion;(IX) is the energy dissipation by turbulent shear production viathe velocity component’s horizontal shears;and (X) and (XI) are the horizontal diffusive fluxes of te into the control volume.

Fig. 1: The geometry of the Charlotte Harbor Estuary and the adjacent West Florida Shelf

Fig. 2: The model grid consisting of 250 (along-shelf) × 148 (across-shelf) × 11 (vertical) grid points. Denoted in bold are the control volume and the along-axis (I) and across-axis (II) sections sampled.

Fig. 3: Comparisons between the computed and observed tidal elevation over a period of one month at the Naples and Ft. Myers tide gauge stations. Comparisons are based on summations of the M2, S2, K1, and O1 constituents.

Fig. 4: Comparisons between the computed and observed M2, S2, K1, and O1 tidal constituent velocity hodographs at the ECM6 location.

ConclusionEstuarine circulation is driven by the

horizontal buoyancy gradient caused by vertical mixing. Increasing mixing should therefore lead to increasing circulation as the salinity isolines rotate from horizontal under salt wedge conditions to vertical under well mixed conditions. Yet, at some point, the opposite occurs. How may we explain this?

We approach the problem through a control volume analysis of the mechanical energy equation for the Charlotte Harbor estuary using the ECOM3D-si model. By forcing the model with rivers, tides, and winds we establish the increase and subsequent decrease in the circulation and account for this behavior through a term-by-term analysis of the mechanical energy equation. While the rate of work against buoyancy increases with increasing tide and wind forcing, there is a point where the rate of turbulent energy production exceeds that of the buoyancy flux. When the ratio of these two terms switches from increasing to decreasing, the estuarine circulation decreases. This explains why the circulation of a well mixed estuary may be sluggish despite large buoyancy torque.

ReferenceBlumberg, A. F., 1993: A primer of ECOM3S-si. Technical Report, HydroQual, Inc., Mahwah, New Jersey, 73 pp.

Fig. 5: Along-axis (I) non-tidal current (left) and salinity (right) distributions. From top to bottom, the model is forced by rivers only; rivers, plus half tides; rivers, plus full tides; rivers, plus full tides, plus either 2.5 ms-1, 5 ms-1, or 10 ms-1 oscillatory (with a period of 8 M2 tidal cycles) winds.

Fig. 6: As in Fig. 5 for the across-axis section II.

Fig. 7: Net outflow averaged over 80 M2tidal cycles and integrated over section II as a function of tidal amplitude, α, and wind speed.

Fig. 8: Turbulent kinetic energy square root (q) distributions at sections I (left) and II (right) under conditions of rivers, plus full tides (upper) and rivers, plus full tides, plus 5 ms-1 oscillatory winds (lower), averaged over 80 M2 tidal cycles (10 wind cycles).

Fig. 9: Time series (36 hr. low-pass filtered) of salinity (left) and turbulent kinetic energy square root (right) under conditions of rivers, plus full tides (upper) and rivers, plus full tides, plus 5 ms-1

oscillatory winds (lower) at the deepest location in section II.

Fig. 10: Time series (36 hr. low-pass filtered) of the control volume integrated terms in equation (1) for the cases of rivers, plus full tides (upper); rivers, plus full tides, plus 2.5 ms-1 wind (middle); and rivers, plus full tides, plus 5 ms-1

wind (lower).

Fig. 11: Averaged (over 80 M2 tidal cycles), control volume integrated rate of work against buoyancy (upper), rate of dissipation by vertical shear production (middle), and their ratio (lower) as functions of oscillatory wind speed.

AcknowledgmentsThis work was supported by the Office of Naval Research, grants # N00014-98-1-0158 and N00014-02-1-0972.