Estuarine Variability Tidal Subtidal Wind and Atmospheric Pressure Fortnightly

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Estuarine Variability Tidal Subtidal Wind and Atmospheric Pressure Fortnightly

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Estuarine Variability Tidal Subtidal Wind and Atmospheric Pressure Fortnightly

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Estuarine Variability

Tidal

Subtidal

Wind and Atmospheric Pressure

Fortnightly

M2 and S2

Monthly

M2 and N2

Seasonal (River Discharge)

Estuarine Variability

Tidal

Subtidal

Wind and Atmospheric Pressure

Fortnightly

M2 and S2

Monthly

M2 and N2

Seasonal (River Discharge)

Tidal Straining

Slack Before Ebb

Ocean

River

Tidal Flow

Ocean

Ebb

End of Ebb

Tidal Flow

Flood

Animation of Shear Instability

Example of Tidal interaction

with density gradient

Chilean Inland Sea

Pitipalena Estuary

CTD

Time

Series

1

2

1

2

z1

To mix the water column, kinetic energy has to be converted to potential energy.

Mixing increases the potential energy of the water column

z2

z

Potential energy of the water column:

Potential energy per unit volume:

But

The potential energy per unit volume of a mixed

water column is:

Ψ has units ofenergy per unit volume

z1

z2

If

z

no energy is required to mix the water column

The energy difference between a mixed and a stratified water column is:

with units of [ Joules/m3 ]

φ is the energy required to mix the water column completely, i.e., the energy required to bring the profile ρ(z) to ρhat

It is called the POTENTIAL ENERGY ANOMALY

It is a proxy for stratification

The greater the φ the more stratified the water column

But the changes of stratification per unit time are given by:

Integrating with depth, the depth-integrated density equation is:

are deviations from depth-mean values

Plugging

Simpson et al. (1990, Estuaries,

13, 125)

1st and 2nd terms on RHS are shear dispersion

3rd term is density flux at the surface

4th term is density flux at the bottom

5th term is depth-integrated source/sink term

De Boer et al (2008, Ocean Modeling, 22, 1)

Bx and By are the along-estuary and cross-estuary straining terms

Ax and Ay are the advection terms

Cx and Cy 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

Hx and Hy are horizontal dispersion;

Fs and Fb are surface and bottom density fluxes

Sketch of changes in stratification

by the main mechanisms

Burchard and Hofmeister (2008, ECSS, 77, 679)

1-D idealized numerical simulation of tidal straining

Burchard and Hofmeister (2008, ECSS, 77, 679)

destratified @

end of flood

stratified entire period

Burchard and Hofmeister (2008, ECSS, 77, 679)

is:

The mean over a tidal cycle of

because

The tidal stress is independent of z as is the barotropic pressure gradient.

0

e.g.

Another dynamical implication of tidal flows is the generation of a mean

non-linear term:

Tidal stresses tend to operate with the barotropic pressure gradient.

Estuarine Variability

Tidal

Subtidal

Wind and Atmospheric Pressure

Fortnightly

M2 and S2

Monthly

M2 and N2

Seasonal (River Discharge)

Wind forcing may:

produce mixing

induce circulation

generate surface slopes

But at the air-water interface it is:

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-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 W3

At a height of 10 m, the power per unit area generated by the wind stress is:

The wind power at the air water interface is only 0.1 % of the wind power at a height of 10 m.

s

s

Weak

Depth-Averaged

Transport

Large

Depth-Mean

Transport

Acts from the surface downward

May destratify the entire water column when forcing is large and buoyancy is low

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

Mean Momentum Balance?

In a Fjord?

x1

sx

x2

y

x1

x2

x

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.

Wind will pile up water in the direction toward which it blows.

Slopes produced by different winds in Chesapeake Bay

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:

Forcing from Atmospheric Pressure Gradients

Another mechanism that may cause subtidal variability in estuaries comes from atmospheric or barometric pressure.

Low

High

mouth

Low

head

High

head

mouth

depth

z

Indirectly through sea level slope

x

Another mechanism that may cause subtidal variability in estuaries comes from atmospheric or barometric pressure.

Hurricane Felix

Δη = -ΔP/(ρg)

ΔP of 1 mb (100 Pa) = Δη of 0.01 m

Wind Response to

Felix

Estuarine Variability

Tidal

Subtidal

Wind and Atmospheric Pressure

Fortnightly

M2 and S2

Monthly

M2 and N2

Seasonal (River Discharge)

Tides in Panama City

Tides in PONCE DE LEON INLET

Fortnightly variability in the Richardson Number

Maximum difference at neaps

Depth

Mean or

Residual

Flow

Can you see this modulation from the analytical solution?

Ocean

Neap

Spring

Mean or

Residual

Salinity

(Density)

Depth

Increasing salinity

Estuarine Variability

Tidal

Subtidal

Wind and Atmospheric Pressure

Fortnightly

M2 and S2

Monthly

M2 and N2

Seasonal (River Discharge)

N

C

N

C

C

N

(Journal of Physical Oceanography, 2007, 2133)

Salt Intrusion vs. River Discharge

Model

Response to Floyd (Sep 1999)

6

5

4

3

2

1

Strong outflow from both River Discharge and NW winds

2 / 3 of volume outflow associated with river input

1 / 3 to wind forcing

Nearly 50 km from the ocean – Wilcox station

Mean Discharge in past 20 years: 200 m3/s

60 Suwannees = 1 Mississippi

Wilcox; 50 km upstream

Flood Stage

Height (m)

Discharge (m3/s)

seaward

W

landward

Influence of Hurricane Bonnie

Axial Distributions

of Salinity

H

M

H

Spring 1999

H

M

M

Fall 1999

Effects of Freshwater Input

Surface Salinity

Bottom Salinity

Sea level

Wind-driven circulation tends to dominate in coastal embayments

Gulf of Arauco