1. Estuarine circulation
Announcements
Research groups
Cruise dates
Added another project – WC respiration
Thursday: Thompson paper discussion

2. Equations of motion, momentum (Navier-Stokes equations)
Momentum equations:
Force/vol Pressure Coriolis Gravity Friction
Dρu/Dt = ∂p/∂x + ρ2Ωvsin(φ) Kx(∂2ρu/∂x2+∂2ρu/∂y2+∂2ρu/∂z2 )
Dρv/Dt = ∂p/∂y - ρ2Ωusin(φ) Ky(∂2ρv/∂x2+∂2ρv/∂y2+∂2ρv/∂z2 )
Dρw/Ddt = ∂p/∂z ρg Kz(∂2ρw/∂x2+∂2ρw/∂y2+∂2ρw/∂z2 )
where Dρu/Dt = ∂ρu/∂t + u∂ρu/∂x + v∂ρu/∂y + w∂ρu/∂z
Dρv/Dt = ∂ρv/∂t + u∂ρv/∂x + v∂ρv/∂y + w∂ρv/∂z
Dρw/Dt = ∂ρw/∂t + u∂ρw/∂x + v∂ρw/∂y + w∂ρw/∂z (non-linear terms)
Equation of Continuity:
∂u/∂x + ∂v/∂y + ∂w/∂z = 0
Number of unknowns: 7 (u, v, w, p, Kx, Ky, Kz) (velocities, pressure, eddy viscosities)
Number of equations: 4
Turbulence closure: 3 equations to relate Kx, Ky, Kz to u, v, and w
(This problem remains unsolved in a general way, but many approximate solutions exist)

3. Pressure gradient terms
Barotropic fields
Isobars and isopyncnals parallel
Baroclinic fields
Isobars and isopyncnals inclined
Sea surface
Isobar
Isopycnal
Level surface

4. Estuary density gradients

5. Estuary density gradients
Salinity distributions in Puget Sound
South Sound Admiralty Inlet

6. Ebbesmeyer et al.

7. Estuarine circulation with sills
Thompson 1994

8. Residual circulation
Mean circulation after subtracting the oscillating tidal circulation
Important for calculating mean transport in and out of Puget Sound

9. PS mean circulation
Ebbesmeyer et al.

10. Instantaneous circulation
Several numerical models of Puget Sound circulation:
Department of Ecology – South Puget Sound
PNNL Salish Sea Model
UW MoSSea
King County model
USGS model

11. Equations of motion, momentum (Navier-Stokes equations)
Momentum equations:
Force/vol Pressure Coriolis Gravity Friction
Dρu/Dt = ∂p/∂x + ρ2Ωvsin(φ) Kx(∂2ρu/∂x2+∂2ρu/∂y2+∂2ρu/∂z2 )
Dρv/Dt = ∂p/∂y - ρ2Ωusin(φ) Ky(∂2ρv/∂x2+∂2ρv/∂y2+∂2ρv/∂z2 )
Dρw/Ddt = ∂p/∂z ρg Kz(∂2ρw/∂x2+∂2ρw/∂y2+∂2ρw/∂z2 )
where Dρu/Dt = ∂ρu/∂t + u∂ρu/∂x + v∂ρu/∂y + w∂ρu/∂z
Dρv/Dt = ∂ρv/∂t + u∂ρv/∂x + v∂ρv/∂y + w∂ρv/∂z
Dρw/Dt = ∂ρw/∂t + u∂ρw/∂x + v∂ρw/∂y + w∂ρw/∂z (non-linear terms)
Equation of Continuity:
∂u/∂x + ∂v/∂y + ∂w/∂z = 0

12. Modeled currents in southern PS
DOE SPS model

13. Equations of motion Momentum equations:
Force/vol Pressure Coriolis Gravity Friction
ρDu/Dt = ∂p/∂x + ρ2Ωvsin(φ) ρKx(∂2u/∂x2+∂2u/∂y2+∂2u/∂z2 )
ρDv/Dt = ∂p/∂y - ρ2Ωusin(φ) ρKy(∂2v/∂x2+∂2v/∂y2+∂2v/∂z2 )
ρDw/Ddt = - ∂p/∂z ρg ρKz(∂2w/∂x2+∂2w/∂y2+∂2w/∂z2 )
where Du/Dt = ∂u/∂t + u∂u/∂x + v∂u/∂y + w∂u/∂z
Dv/Dt = ∂v/∂t + u∂v/∂x + v∂v/∂y + w∂v/∂z
Dw/Dt = ∂w/∂t + u∂w/∂x + v∂w/∂y + w∂w/∂z (non-linear terms)
Equation of Continuity:
∂u/∂x + ∂v/∂y + ∂w/∂z = 0

14. Scaling momentum equation
Importance of individual terms
Re = Reynolds number = L u / n
Inertial forces / viscous forces
(100m) (0.1 m/s) / 10-6 m2/s) = 107
R0 = Rossby number = u / (f L), f = 2ωsin(φ)
Non-linear terms / coriolis term
(1 m/s) / ((10-4 s-1)(104 m)) = 1
Rossby radius of deformation ~ u/f = 10 km
Ez = Ekman number = Kz/(f H2)
Friction term / coriolis term
(10-4 m2/s) / ((10-4 s-1)(100m)2) = 10-4
Friction only important along the boundaries of Puget Sound
(sea surface, bottom boundary layer)

15. SJF cross section
Northern shore Southern shore
Out In