Estuarine Variability Tidal Subtidal Wind and Atmospheric Pressure Fortnightly
description
Transcript of Estuarine Variability Tidal Subtidal Wind and Atmospheric Pressure Fortnightly
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