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?