1. Estuarine Variability  Tidal  Subtidal Wind and Atmospheric Pressure  Fortnightly M 2 and S 2  Monthly M 2 and N 2  Seasonal (River Discharge)

2. Estuarine Variability  TidalTidal  Subtidal Wind and Atmospheric Pressure  Fortnightly M 2 and S 2  Monthly M 2 and N 2  Seasonal (River Discharge)

3. Tidal Straining River Ocean Slack Before Ebb Ocean Ebb Tidal Flow

4. End of EbbFlood Tidal Flow Animation of Shear Instability

5. Example of Tidal interaction with density gradient Chilean Inland Sea Pitipalena Estuary

6. 1 2 CTD Time Series

7. 1 2

8. To mix the water column, kinetic energy has to be converted to potential energy. Mixing increases the potential energy of the water column z z2z2 z1z1

9. Potential energy per unit volume: Potential energy of the water column: But The potential energy per unit volume of a mixed water column is: Ψ has units of energy per unit volume

10. The energy difference between a mixed and a stratified water column is: with units of [ Joules/m 3 ] φ is the energy required to mix the water column completely, i.e., the energy required to bring the profile ρ(z) to ρ hat It is called the POTENTIAL ENERGY ANOMALY z z2z2 z1z1 It is a proxy for stratification The greater the φ the more stratified the water column If no energy is required to mix the water column

11. But the changes of stratification per unit time are given by: Simpson et al. (1990, Estuaries, 13, 125) Integrating with depth, the depth-integrated density equation is: 1 st and 2 nd terms on RHS are shear dispersion 3 rd term is density flux at the surface 4 th term is density flux at the bottom 5 th term is depth-integrated source/sink term are deviations from depth-mean values Plugging

12. B x and B y are the along-estuary and cross-estuary straining terms A x and A y are the advection terms C x and C y interaction of density and flow deviations in the vertical C’ x and C’ y correlation between vertical shear and density variations in the vertical; depth-averaged counterparts of C E is vertical mixing and D is vertical advection H x and H y are horizontal dispersion; F s and F b are surface and bottom density fluxes De Boer et al (2008, Ocean Modeling, 22, 1)

13. Burchard and Hofmeister (2008, ECSS, 77, 679) Sketch of changes in stratification by the main mechanisms

14. Burchard and Hofmeister (2008, ECSS, 77, 679) 1-D idealized numerical simulation of tidal straining

15. Burchard and Hofmeister (2008, ECSS, 77, 679) stratified entire period destratified @ end of flood

16. Another dynamical implication of tidal flows is the generation of a mean non-linear term: because The tidal stress is independent of z as is the barotropic pressure gradient. e.g. Tidal stresses tend to operate with the barotropic pressure gradient. The mean over a tidal cycle of is: 0

17. Estuarine Variability  Tidal  Subtidal Wind and Atmospheric Pressure  Fortnightly M 2 and S 2  Monthly M 2 and N 2  Seasonal (River Discharge)

18. Subtidal Variability Produced by direct forcing on estuary (local forcing) or on the coastal ocean, which in turn influences estuary (remote forcing - coastal waves) Wind forcing may:produce mixing induce circulation generate surface slopes Wind-produced mixing The energy per unit area per unit time or power per unit area generated by the wind to mix the water column is proportional to W 3 At a height of 10 m, the power per unit area generated by the wind stress is: But at the air-water interface it is: The wind power at the air water interface is only 0.1 % of the wind power at a height of 10 m.

19. Wind-induced circulation The wind-induced circulation can compete with estuarine circulation, or act in concert The wind-induced circulation will depend on stratification: depth-dependent under stratified conditions weak depth-dependence under homogeneous conditions Acts from the surface downward May destratify the entire water column when forcing is large and buoyancy is low ss Weak Depth-Averaged Transport ss Large Depth-Mean Transport

21. Mean Momentum Balance? In a Fjord?

22. Wind-Induced Surface Slope Can be assessed from the vertical integration of the linearized u momentum equation, with no rotation @ steady state: Note that a westward  sx (negative) produces a negative slope.  sx x1x1 x2x2 y x x1x1 x2x2  Wind will pile up water in the direction toward which it blows.

24. Slopes produced by different winds in Chesapeake Bay

25. The perturbation produced by the wind propagates into the estuary and may cause seiching if the period of the perturbation is close to the natural period of oscillation:

26. Forcing from Atmospheric Pressure Gradients head depth Low High mouth x z Low High head Indirectly through sea level slope Another mechanism that may cause subtidal variability in estuaries comes from atmospheric or barometric pressure.

28. Δη = -ΔP/(ρg) ΔP of 1 mb (100 Pa) = Δη of 0.01 m Hurricane Felix

29. Wind Response to Felix

30. Estuarine Variability  Tidal  Subtidal Wind and Atmospheric Pressure  Fortnightly M 2 and S 2  Monthly M 2 and N 2  Seasonal (River Discharge)

31. Tides in Panama City

32. Tides in PONCE DE LEON INLET

34. Fortnightly variability in the Richardson Number

35.  

36. Maximum difference at neaps

37. Depth Mean or Residual Flow Mean or Residual Salinity (Density) Increasing salinity Spring Neap Ocean Can you see this modulation from the analytical solution?

38. Estuarine Variability  Tidal  Subtidal Wind and Atmospheric Pressure  Fortnightly M 2 and S 2  Monthly M 2 and N 2  Seasonal (River Discharge)

41. N C NC NC

42. (Journal of Physical Oceanography, 2007, 2133) Salt Intrusion vs. River Discharge Model

43. Response to Floyd (Sep 1999)

44. Strong outflow from both River Discharge and NW winds 1 2 3 4 5 6 2 / 3 of volume outflow associated with river input 1 / 3 to wind forcing

45. Nearly 50 km from the ocean – Wilcox station Mean Discharge in past 20 years: 200 m 3 /s 60 Suwannees = 1 Mississippi

46. Discharge (m 3 /s) Height (m) Wilcox; 50 km upstream Flood Stage

47. W seaward landward

49. Influence of Hurricane Bonnie

50. Axial Distributions of Salinity Spring 1999 Fall 1999 H M HM HM

51. Effects of Freshwater Input

53. Surface Salinity Bottom Salinity Sea level

59. Wind-driven circulation tends to dominate in coastal embayments Gulf of Arauco