MODEL RESPONSE SENSITIVITY TO WAVES, NONLINEAR ADVECTION, AND BOTTOM FRICTION Patrick C. Kerr 17 th ADCIRC WORKSHOP April 29-30, 2013 1 Patrick Corbitt.

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