temporal variability in an estuary: keeping it linear jim lerczak woods hole oceanographic...
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![Page 1: Temporal Variability in an Estuary: Keeping it Linear Jim Lerczak Woods Hole Oceanographic Institution PhD 1995-2000](https://reader036.vdocument.in/reader036/viewer/2022062714/56649d3f5503460f94a18d9e/html5/thumbnails/1.jpg)
Temporal Variability in an Estuary:Keeping it Linear
Jim Lerczak
Woods Hole Oceanographic Institution
PhD 1995-2000
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Myrl with studentCirca 1998
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Rick Salmon
Geophysical Fluid Dynamics teacher extraordinaire
Shares Myrl’s gift for clarity and eloquence
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Dave Chapman
First met at OS 2000
Post-doctoral mentor
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Two Lessons Learned from Myrl
ILS Institute forLinear Science
2) Choose field sites with easyaccess to fine dining
1) Start with linear analyses,even when the underlyingdynamics are far from linear.
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6
22
33
43
55
75
0
Field Work Here
Wine/DineHere
Hudson RiverEstuary 2004
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River Discharge(m3s-1)
Tidal Amplitude(m/s)
EstuaryLength (km)
Decimal Days (2004)
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Salt Balance in an (Exchange Dominated) Estuary
Ocean(salty)
River(f resh)
TidalTurbulent
Mixing
EstuarineCirculation
FluxSaltDrivenExchangeSQdt
ContentSaltdf o
Qf
Salt Flux due to Baroclinic Exchange Flow:
Fe = ∫ueSedA ~ H Δu ΔS
x
S
x
SHg
2
3
82
eF
• ∂S/∂x ≈ So/L
• κ ~ UT
• Linearize about mean estuary length, mean tidal amplitude and mean discharge
L = Lo + L’
Qf = Qo + Q’
UT = UTo + UT’
oo3
11
T
To
U
U
Q
QLL
dt
Ld
o
o
6Q
AL
3
1
o3
o
82o
o
Q
AHSgL
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Linear Response to Sinusoidal ForcingSpring-Neap Cycle (period = 14.8 days)
τ/Tf
0 1 2 3
Res
pons
e am
plit
ude
|L‘|
/ aL
o
0
0.5
1
Pha
se L
ag, φ
(deg
rees
)
0
45
90
221
1
atan
f = sin(ωt)
L'/
Loa
0
1
-1
Time, t0 1 2
τ/Tf = 0.1
τ/Tf = 1
τ/Tf = 3
a)
b)
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τ = 14.8 days
Large spring-neap response
Weak spring-neap response
Theoretical LinearResponse Time
Res
pons
e T
ime
Fro
m M
odel
Fit
Model Fit of Response Time
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Equilibrium Estuary Lengthfor Mean Tidal Conditions
Equ
ilibr
ium
Len
gth
(km
)
Mean Freshwater Discharge (m3s-1)
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Lo
Time-DependentSpring-Neap Range
22o1
45.01
L
22o1
45.01
L
Steady Neap LengthLo(1 + 0.45)
Steady Spring LengthLo(1 - 0.45)
Summary of Linear Analysis
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Na zdrowie, Myrl
• Thanks for your intellectual enthusiam (for oceanography and beyond).
• Thanks for your friendship.
• Thanks also to Art! for organizing the first meeting of the M.H. Fan Club