Estuarine Variability

Tidal

SubtidalWind and Atmospheric Pressure

FortnightlyM2 and S2

MonthlyM2 and N2

Seasonal (River Discharge)

Estuarine Variability

Tidal

SubtidalWind and Atmospheric Pressure

FortnightlyM2 and S2

MonthlyM2 and N2

Seasonal (River Discharge)

Tidal Straining

River Ocean1 2 3 4 5 6

Slack Before Ebb

6321

Ocean

Ebb

6321

Tidal Flow

1 2 3 4 5 6

End of Ebb

6321

1 2 3 4 5 6

Flood

6321

Tidal Flow

1 2 3 4 5 6

xu

t

xzu

zt

zK

zxzu

zt z

2

2

Animation of Shear Instability

Example of Tidal interaction with density gradient

Chilean Inland Sea

Pitipalena Estuary

1

2

CTDTimeSeries

1

2

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

Mixing increases the potential energy of the water column

z

z2

z1

Potential energy per unit volume: HgV ,

Vol

Potential energy of the water column: HgmV

But )(z

dzzH

g

H

0

The potential energy per unit volume of a mixed water column is:

dzzH

g

Hm

0

dzH H

01

322

321

m

J

sm

kgm

m

kg

s

m

m

Ψ has units of energy per unit volume

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

dzz)(H

g

Hm

0

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

z

z2

z1

It is a proxy for stratification

The greater the φ the more stratified the water column

If 0

no energy is required to mix the water column

3

0

m

Jdzz)(

H

g

H

dzzttH

g

t H

0

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

Simpson et al. (1990, Estuaries, 13, 125)

t,z,y,xQz

Kzy

Kyx

Kxz

wy

vx

ut zhh

Q

zK

zK

yH''v

xH''u

yHv

xHu

tH

Hzz

zz

0

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

1st and 2nd terms on RHS are shear dispersion3rd term is density flux at the surface4th term is density flux at the bottom5th term is depth-integrated source/sink term vv'v

uu'u

'

are deviations from

depth-mean values

Plugging t into

tt

dzz

zK

HyK

yzK

z

zK

HxK

xzw

Hg

dzz

yH''v

Hy'

'vy'

vy

'v

xH''u

Hx'

'ux'

ux

'u

Hg

t

H

F

Hzz

H

h

E

z

F

zz

H

h

D

H

'CCAB

'CCAB

by

sx

yyyy

xxxx

00

0

1

1

1

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

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

0

1

1

H

D

'CCAB

'CCAB

dzzz

w

y

H''v

Hy

''v

y

'v

y'v

x

H''u

Hx

''u

x

'u

x'u

H

g

t

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

Sketch of changes in stratificationby the main mechanisms

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

1-D idealized numerical simulation of tidal straining

0

HE

z

B

dzzz

Kzx

'uHg

t

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

0 1

Hz dzz

x

H''u

Hx

''u

zw

x

'u

zK

zx'u

H

g

t

stratified entire period

destratified @ end of flood

Another dynamical implication of tidal flows is the generation of a mean non-linear term:

xu

uxu

u

21

21 0

0 because AA 2cos121

cos2

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

e.g.

xuu

xgz

xg

xP 00

2

xgz

xu

gu

xg

00

21

Tidal stresses tend to operate with the barotropic pressure gradient.

dttuux

tuudtxu

u

coscos

21

21

0

2

00

2

0

The mean over a tidal cycle ofxu

u is:

0

Estuarine Variability

Tidal

SubtidalWind and Atmospheric Pressure

FortnightlyM2 and S2

MonthlyM2 and N2

Seasonal (River Discharge)

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 mixinginduce circulationgenerate surface slopes

zS

Kzx

Szu

zS

t v2

2

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:3

1010 WCW ba

But at the air-water interface it is: 1010

210

** and WWCWC

WW baba

00116.0; 31010* WCWW ba

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

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 conditionsweak 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

WeakDepth-Averaged

Transport

s

LargeDepth-Mean

Transport

Mean Momentum Balance?

In a Fjord?

Wind-Induced Surface Slope

Can be assessed from the vertical integration of the linearized u momentum equation,with no rotation @ steady state:

bxsxHgx

1

Note that a westward sx (negative) produces a negative slope.

sx

x1

x2y

x

x1 x2

x

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

bxsxHgx

1

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:

1214

nCL

TN

Forcing from Atmospheric Pressure Gradients

head

dep

th

Low

High

mouth

x

z

mouth

Low

High

head

Indirectly through sea level slope

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

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

xP

gxa

1

aPg

1

m 01.010000/100Pa 100mb 1

Δη = -ΔP/(ρg)

ΔP of 1 mb (100 Pa) = Δη of 0.01 m

Hurricane Felix

Wind Response toFelix

Estuarine Variability

Tidal

SubtidalWind and Atmospheric Pressure

FortnightlyM2 and S2

MonthlyM2 and N2

Seasonal (River Discharge)

Tides in Panama City

Tides in PONCE DE LEON INLET

220

zv

zu

zg

Rio

Fortnightly variability in the Richardson Number

Maximum difference at neaps

Dep

thD

epth

Mean orResidualFlow

Mean orResidualSalinity(Density)

Increasing salinity

Spring

Neap

Ocean

Can you see this modulation from the analytical solution?

3

3

2

23

181948

)(Hz

Hz

AgGH

zuz

Estuarine Variability

Tidal

SubtidalWind and Atmospheric Pressure

FortnightlyM2 and S2

MonthlyM2 and N2

Seasonal (River Discharge)

2

2

2

2

3

3

2

23

131441

123

181948

)(

Hz

Hz

AH

Hz

HR

Hz

Hz

AgGH

zu

z

z

N

C

N C

N C

(Journal of Physical Oceanography, 2007, 2133)

Salt Intrusion vs. River Discharge

tidalnalgravitatioriver

''1

Ax

SKASuASu

xAt

Sx

Model

Response to Floyd (Sep 1999)

Strong outflow from both River Discharge and NW winds

1

2

3

4

5

6

2 / 3 of volume outflow associated with river input1 / 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

Dis

char

ge (

m3 /

s)

Hei

ght (

m)

Wilcox; 50 km upstream

Flood Stage

W

seaward

Influence of Hurricane Bonnie

Axial Distributionsof Salinity

Spring 1999

Fall 1999

H

M

H M

H M

Effects of Freshwater Input

Surface Salinity

Bottom Salinity

Sea level

Wind-driven circulation tends to dominate in coastal embaymentsWind-driven circulation tends to dominate in coastal embayments

Gulf of Arauco