Temporal Variability in an Estuary:Keeping it Linear

Jim Lerczak

Woods Hole Oceanographic Institution

PhD 1995-2000

Myrl with studentCirca 1998

Rick Salmon

Geophysical Fluid Dynamics teacher extraordinaire

Shares Myrl’s gift for clarity and eloquence

Dave Chapman

First met at OS 2000

Post-doctoral mentor

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.

6

22

33

43

55

75

0

Field Work Here

Wine/DineHere

Hudson RiverEstuary 2004

River Discharge(m3s-1)

Tidal Amplitude(m/s)

EstuaryLength (km)

Decimal Days (2004)

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

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)

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

Equilibrium Estuary Lengthfor Mean Tidal Conditions

Equ

ilibr

ium

Len

gth

(km

)

Mean Freshwater Discharge (m3s-1)

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

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