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
3
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
7
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
11
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
HHHHgpgf
tMτττ
uuuu 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
17
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
18
Patrick C. Kerr17th ADCIRC WORKSHOP
April 29-30, 201318