Estuarine Hydrodynamics Arnoldo Valle-Levinson University of Florida Civil and Coastal Engineering Department Gainesville, Florida arnoldo@ufl.edu
What is an estuary? Estuaries Coastal lagoons Semi-enclosed coastal body of water free communication with ocean ocean salinity is measurably diluted by runoff
Types of Estuaries According to Their Origin (Pinet, 2003) Types of Estuaries According to Their Origin
(Pinet, 2003)
(Pinet, 2003)
San Francisco Bay (Pinet, 2003)
Typical Estuarine Circulation
Types of Estuaries According to Their Stratification (Pinet, 2003) Competition between tidal forcing and buoyancy forcing
Typical circulation in a fjord Typical profile of net velocity mouth head Typical profile of salinity (density) depth
(Pinet, 2003)
Rio de la Plata Estuary Argentina
(Pinet, 2003)
Axial Salinity Distributions mouth Axial Salinity Distributions Chesapeake Bay Spring of 1999
(Pinet, 2003)
Example of Well-Mixed Estuary
Types of Estuaries According to their water balance Net Mass Loss No Mass Loss
Inverse Estuary Normal Estuary Looking into lagoon Red = Water going out Blue = Water going in Inverse Estuary Normal Estuary
Salt-plug estuary E ≥ R M. Tomczak’s Web Site
Review of conservation equations Mass and Momentum
Flux of mass out (kg/s) = , w , v Mass per area per time (kg/(m2 s)) Flux of mass in (kg/s) = Flux of mass out (kg/s) = Net Flux of mass in ‘x’ = Net Flux of mass in ‘y’ = Net Flux of mass in ‘z’ =
The change of mass per unit time going through the volume element is: And the change of mass per unit time per unit volume is: which is the same as: or
Boussinesq approximation This is the Continuity Equation or Equation of Conservation of Mass
z x Continuity Equation in Bulk Form:
Advective flux of salt/unit area , w , v Conservation of Salt Advective flux of salt/unit area Diffusive flux of salt/unit area Flux of salt into dydz = Flux of salt out of dydz = Net Flux of Salt in ‘x’ =
Salt Conservation Net Flux of Salt in ‘y’ = Net Flux of Salt in ‘z’ = Net Salt Flux per unit volume = Salt Conservation
Advection-Diffusion Equation Conservation of Salt: At steady state and assuming constant diffusivities: Advection-Diffusion Equation Further assuming motion in one direction and integrated over the volume considered, the statement of CONSERVATION OF SALT may be given as: Vin Sin = Vout Sout
z Sb S0 x Continuity Equation in Bulk Form: Salt Conservation Equation in Bulk Form: VbSb = V0S0
Conservation of Salt: Conservation of Heat: Equation of State:
TEOS-10 Manual “Thermodynamic properties of seawater are more accurately represented as functions of SA than of SP.” Reference Composition Salinity SR does have units! SR = 35.16504/35 Sp (g/kg)
Still much work to be done on SA Absolute Salinity SA : “ratio of the mass of dissolved material in sea water to the mass of sea water.” ----- cannot be measured in practice. Reference Salinity SR gives our best estimate of SA SA = SR + SA SR = 35.16504/35 Sp (g/kg) (From TEOS-10 Manual) Still much work to be done on SA
TEOS-10
TEOS-10
90 % of Ocean Water Greater influence of salinity on density Mean T & S for World Ocean Greater influence of salinity on density
Effects of Temperature and Salinity on Density Thermal Expansion Saline Contraction x 10-4 oC-1 x 10-4 S-1 Density changes by 0.2 kg/m3 for a T change of 1oC, and by 0.8 kg/m3 for a S change of 1.
Conservation of Momentum (Equations of Motion)
Pressure gradient: Barotropic and Baroclinic + friction + tides + gravity + Coriolis Pressure gradient: Barotropic and Baroclinic Friction: Surface, bottom, internal Tides: Boundary condition Gravity: Only in the vertical Coriolis: Only in the horizontal REMEMBER, these are FORCES PER UNIT MASS
Pressure gradient: Barotropic and Baroclinic + friction + tides + gravity + Coriolis Pressure gradient: Barotropic and Baroclinic Friction: Surface, bottom, internal Tides: Boundary condition Gravity: Only in the vertical Coriolis: Only in the horizontal REMEMBER, these are FORCES PER UNIT MASS
Pressure gradient force per unit mass Hydrostatic Pressure Total Pressure Pressure gradient force per unit mass Barometric Barotropic Baroclinic Note that even if the density is constant with depth, the horizontal pressure gradient increases with depth if there is a horizontal density gradient
Pressure gradient: Barotropic and Baroclinic + friction + tides + gravity + Coriolis Pressure gradient: Barotropic and Baroclinic Friction: Surface, bottom, internal Tides: Boundary condition Gravity: Only in the vertical Coriolis: Only in the horizontal REMEMBER, these are FORCES PER UNIT MASS
Gravity [0, 0, g] = [0, 0, 9.81] Coriolis [-fv, fu, 0]