Development and Implementation of Depth Dependent Wave Forcing
and Stokes Drift into Coupled 3D
PADCIRC/PUNSWANJoshua Todd
Coastal EngineeringDepartment of Marine and Environmental Systems
Florida Institute of TechnologyAdvisor: 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(𝑘𝑥𝑘𝑥
𝑘2(cosh (𝑘 (𝑧+h ) )sinh (𝑘𝐷 )
)(cosh (𝑘 (𝑧+h ) )cosh (𝑘𝑑 )
)−(s∈h (𝑘 (𝑧+h ) )cosh (𝑘𝐷 )
)(sin h (𝑘 (𝑧+h ) )sinh (𝑘𝐷 )
))+𝐸𝐷
𝑆𝑥𝑦=𝑘𝐸 (𝑘𝑥𝑘𝑦
𝑘2(cosh (𝑘 (𝑧+h ) )sinh (𝑘𝐷 )
)(cosh (𝑘 (𝑧+h ) )cosh (𝑘𝑑 )
))
𝑆𝑦𝑦=𝑘𝐸 (𝑘𝑦𝑘𝑦
𝑘2(cosh (𝑘 (𝑧+h ) )sinh (𝑘𝐷 )
)(cosh (𝑘 (𝑧+h ) )cosh (𝑘𝑑 )
)−(s∈h (𝑘 (𝑧+h ) )cosh (𝑘𝐷 )
)(sin h (𝑘 (𝑧+h ) )sinh (𝑘𝐷 )
))+𝐸𝐷
Stokes Drift
𝑢𝑖𝑠(𝑧)=𝑎2𝜎 𝑘𝑖
cosh 2𝑘(h+𝑧)2 h𝑠𝑖𝑛 2 h𝑘
• Incorporates mass transport from waves into the 3D model
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?