model response sensitivity to waves, nonlinear advection, and bottom friction patrick c. kerr 17 th...

MODEL RESPONSE SENSITIVITY TO WAVES, NONLINEAR ADVECTION, AND BOTTOM FRICTION

Patrick C. Kerr17th ADCIRC WORKSHOP

April 29-30, 20131

Patrick Corbitt Kerr, P.E.University of Notre Dame

Part IWave Bottom Friction

Patrick C. Kerr17th ADCIRC WORKSHOP

April 29-30, 20132

If circulation models are sensitive to bottom friction on the Louisiana-Texas shelf, what is the sensitivity of wave

models to bottom friction formulation in that region?

Wave Bottom FrictionFriction Formulations

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Patrick C. Kerr17th ADCIRC WORKSHOP

April 29-30, 20133

Variable Bottom Material

JONSWAP Formulation

Bottom Friction in SWAN

Recommend by Literature

Muddy Bottom?

Madsen Formulation

Based on Manning’s n

A

CB

D

GE

H

JI

Wave Bottom FrictionSummary of Findings

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Patrick C. Kerr17th ADCIRC WORKSHOP

April 29-30, 20137

• Model Response Sensitivity to Wave Bottom Friction Formulation– Madsen and JONSWAP formulations are both adequate– The JONSWAP friction coefficient is sensitive to bottom type,

therefore a Cjfon=0.019m2s-3 should be used for the muddy LATEX shelf.

Part IIComponent Contributions

Patrick C. Kerr17th ADCIRC WORKSHOP

April 29-30, 20138

What is the spatial and temporal contributions of wave radiation stress and non-linear advection terms in a

hurricane storm surge model and how do these processes compare with the other components of the

shallow water equations?

Contribution of Non-Linear Advection

OVERALL

TEMPORAL

Contribution of Wave Radiation Stress

OVERALL

TEMPORAL

Component ContributionsScaling Ike at 5 Locations

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Patrick C. Kerr17th ADCIRC WORKSHOP

April 29-30, 201311

• Local• Non-Linear Advection• Coriolis• Surface Gradient• Atmospheric Pressure• Tidal Potential Gradient• Wind Stress• Wave Radiation Stress Gradient• Bottom Friction• Diffusion (Momentum) Terms

DBR

s

W

s

TP

s

ZCAL

HHHHg

pgf

t

Mτττuuu

u bwaves,winds,

0000

0

LOCATION 1

Significant Terms:PressureSurface

LocalCoriolis

LOCATION 2

Major Terms:Local

CoriolisPressureSurface

Moderate Terms:Advection

Wind

LOCATION 3

Significant Terms:SurfaceWind

BottomCoriolis

LocalAdvection

LOCATION 4

Significant Terms:SurfaceWind

AdvectionWave

BottomCoriolis

LOCATION 5

Significant Terms:BottomSurfaceWind

Component ContributionsSummary of Findings

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Patrick C. Kerr17th ADCIRC WORKSHOP

April 29-30, 201317

Galveston, TX• Component Contributions for Hurricane Ike (2008)– Non-linear advection captures 10-

20cm of geostrophic setup and increases resonant waves by 30-40cm.

– Wave radiation stress adds 20-40cm to maximum water levels and is responsible for an earlier rise in water levels.

– Bottom Friction and Coriolis were significant components in the development of Ike’s Forerunner.

QUESTIONS

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Patrick C. Kerr17th ADCIRC WORKSHOP

April 29-30, 201318