Transcript Development and Implementation of Depth Dependent Wave

Development and Implementation
of Depth Dependent Wave Forcing
and Stokes Drift into Coupled 3D
PADCIRC/PUNSWAN
Joshua Todd
Coastal Engineering
Department of Marine and Environmental Systems
Florida Institute of Technology
Advisor: Dr. Robert Weaver
April 29,2013
Objective
• To modify the three dimensional version of
ADCIRC to use wave forcing and mass flux in
the calculation of sea surface elevation and
current velocities
Background
• Stokes 1847
– Study of Water Waves
• Longuet-Higgins and Stewart 1962
– Studied shoreward directed momentum flux by water waves
• Mellor 2003,2008
– Included wave effects on three dimensional equations of
motion in addition to the LHS radiation stress
Modifications
• Add three dimensional depth dependent
radiation stress to the momentum equations
• Add depth dependent Stoke’s drift to the
velocity solution
Mellor 2008
𝑆𝑥𝑥 = 𝑘𝐸
𝑘𝑥 𝑘𝑥 cosh 𝑘 𝑧 + ℎ
cosh 𝑘 𝑧 + ℎ
sinh 𝑘 𝑧 + ℎ
sinh 𝑘 𝑧 + ℎ
(
)(
)
−
(
)(
) + 𝐸𝐷
𝑘2
sinh 𝑘𝐷
cosh 𝑘𝑑
cosh 𝑘𝐷
sinh 𝑘𝐷
𝑆𝑦𝑦 = 𝑘𝐸
𝑘𝑦 𝑘𝑦 cosh 𝑘 𝑧 + ℎ
cosh 𝑘 𝑧 + ℎ
sinh 𝑘 𝑧 + ℎ
sinh 𝑘 𝑧 + ℎ
(
)(
)
−
(
)(
) + 𝐸𝐷
𝑘2
sinh 𝑘𝐷
cosh 𝑘𝑑
cosh 𝑘𝐷
sinh 𝑘𝐷
𝑆𝑥𝑦 = 𝑘𝐸
𝑘𝑥 𝑘𝑦 cosh 𝑘 𝑧 + ℎ
cosh 𝑘 𝑧 + ℎ
(
)(
)
𝑘2
sinh 𝑘𝐷
cosh 𝑘𝑑
𝐸𝐷 =
𝐸
2
when at the Sea Surface and 0 everywhere else
Stokes Drift
• Incorporates mass transport from waves into the 3D model
𝑢𝑖𝑠 (𝑧)
=
𝑎2 𝜎𝑘
cosh 2𝑘(ℎ + 𝑧)
𝑖
2 𝑠𝑖𝑛ℎ2 𝑘ℎ
SWAN Coupling
• Uses SWAN to provide:
– Wave Number
– Direction
– Frequency
– Energy (from the Action Density)
Couple2Swan
• Added 3D Radiation Stress equation to the
ComputeRadiationStress and
ComputeWaveDrivenForces Subroutines
• Created Compute3DStokesDrift Subroutine
• Set up equations to be able to turn them on and off
with Input File Flags
VSMY
• Added Stoke’s Drift Velocity to the velocity at
each node
• Added the 3D Radiation Stress to the RHS
forcing vector in the VSSOL subroutine
IM Types
• 3 Different Models
– IM 7 - Depth Dependent Radiation Stress
– IM 8- Depth Dependent Radiation Stress and Stokes Drift
– IM 9- Stokes Drift
Stability Testing
• Hurricane Gustav
– EC95 Grid
– Quick Run
– No Tides
– 5 day run
• Results Pending
Questions?