1. ocean surface waves - nearshore littoral currents (e.g., rip current)‏ - upper ocean mixing (e.g., Langmuir cells)‏ Wave-Current Interaction in ROMS: A Vortex-Force Formalism Yusuke Uchiyama (UCLA)‏ collaborators: J. C. McWilliams, M. Buijsman & A. Shchepetkin - SBL alteration due to breaking/white capping - Stokes advection for material dispersal - BBL process & sediment transport etc...

2. outline: 1. introduction 2. governing equations and implementation 3. shoreface test (vs. Rutgers/USGS-ROMS/CSTMS)‏ 4. Duck 94 surfzone case (vs. Data & NearCom/POM)‏ 5. Martha's Vineyard inner-shelf case 6. effects of WCI on upwelling/downwelling circulation 7. summary

3. Three-dimensional Wave-Current Interaction Models 1. Rutgers-USGS ROMS (Warner et al., 2008; Haas & Warner 2009)‏ - generalized Lagrangian-mean (GLM) radiation stress formalism (Mellor 2005, 2007, 2009)‏ - prognostic variables are in Lagrangian frame (e.g., B.C.s, mixinig, friction...)‏ - interchangeable via Stokes drift: u E =u L -u St - treats conservative/non-conservative wave effects as a single RSG term 2. NearCom/POM (Newberger and Allen, 2007a & b)‏ - Eulerian-averaged vortex-force formalism - WCI are modeled as depth-averaged - conservative/non-conservative wave effects are separable --> details are found in Lane et al. (2007); see also Smith (2006)‏ generally, interchangeable via wave action balance equation The present model: an Eulerian-averaged VF-based model for ROMS with fully 3D WCI forces

4. Wave-Averaged Current & Tracer Equations (McWilliams et al. 2004)‏ U = U c + U w non-conservative forces (wave breaking etc..)‏ vortex force (CL-VF + Stokes-Coriolis)‏Bernoulli head

5. in ROMS Stokes drift quasi-static setup Stokes-Coriolisvortex forcenon-conservative terms mass: x momentum y momentum wave breaking Tracer equation H z c = h +  +  ex. U = -U St ~anti-Stokes flow

6. Primary Wave Equations: Current Effects on Waves‏...or external wave driver (e.g., SWAN; Booij et al., 1999)‏ wave breakingwave friction Depth-induced wave breaking dissipation,  b, (Church & Thornton, 1993)‏ Wave bed frictional dissipation,  f, (Madsen et al., 1988)‏ non-conservative body force term in the momentum equations correction to bottom stress for vertical viscous terms

7. “Surface Roller Model” for Nearshore Broken Waves (Svendsen, 1984; Reiners et al, 2004)‏ Nairn et al. (1991)‏ Nadaoka et al. (1989)‏ roller mass (Stokes) transport B term including primary breaking & rollers roller action balance eq. bb bb  b roller current & turbulence rr breaking  b  b   r primary waves

8. Vertical Distribution Function in B (Breaking Acceleration) Term Warner et al. (2008)‏ Relaxed Analogous to wave solution (present study)‏ k B -1 =  H s...or as surface stress (c.f., Newberger & Allen, 2007)‏ if compared with wind stress:  w ~  DB ~  b / sqrt(gh)‏ given  b /  =0.05 m 3 /s 3, h = 5 m, then  DB ~ 3.5 (Pa)‏  < ~ 0.5 (above trough level)‏  = 1

9. Enhanced Vertical Eddy Viscosity/Diffusivity (KPP)‏ surface KPP (Large at al., 1994) s : resolved vertical shear (bulk Richardson + Ekman depth)‏ w : internal wave breaking d : double diffusion b : surface wave breaking (new)‏ Bottom KPP (Durski et al., 2004; Blaas et al., 2007)‏ no buoyancy flux at bottom no breaking wave effect take max(SKPP, BKPP) for  when Hbl overwraps new s-coordinate (bottom refinement)‏ Hbbl smoothing (as UCLA-SKPP has)‏

10. “Shoreface Test”: Comparison with Rutgers-USGS ROMS compared with SHORECIRC (Haas & Warner 2009)‏ V.F. vs. R.S. (Mellor 2005...)‏ KPP vs. GLS closure same wave field by SWAN (H s = 2m, T p = 10s,  o =10o)‏ no stratification, no roller no other forcing 2DH analytical solution (Uchiyama et al. 2009)‏ significant wave height surface elevation ~wave setup/down depth-averaged onshore velocity (ubar)‏ alongshore vbar 1:80 F B /D profile at 5-m depth with H s =2 m courtesy of John Warner

11. Shoreface Test: Cross-Shore Vertical Slices onshore velocity, u alongshore velocity, v vertical eddy viscosity, K v surface body force depth-scale body force depth-scale Brk Frc + same Kv as HW09 HW09/M05

12. “DUCK '94” Surf-zone Field Experiment

13. surface body force DUCK '94: Model vs. Observation (1)‏ u (m/s)‏ K v (m 2 /s)‏ v (m/s)‏ u (m/s)‏ v (m/s)‏ breaking ~ PGF brk ~ drag, VF ~ adv H rms = 1.6 m, T p = 6 s,  o =-13 deg.

14. depth-scale body force DUCK '94: Model vs. Observation (2)‏ u (m/s)‏ K v (m 2 /s)‏ v (m/s)‏ u (m/s)‏ v (m/s)‏ brk ~ drag, VF ~ adv breaking ~ PGF

15. GOTM (Umlauf & Burchard, 2003) example for Grizzly Bay, Calif., USA Jones and Monismith (2007)‏ BBL only BBL + SBL BBL + SBL + wave breaking POM-MY2.5 example for Duck case with Craig & Banner (1990)-type modification Newberger & Allen (2007)‏ Vertical Eddy Viscosity in Other Turbulent Closure Models

16. Inner-Shelf (Outer-Surfzone) Wave-Driven Current at Martha's Vineyard Coastal Observatory (MVCO), MS, USA MVCO: south of Cape Cod ~3 km offshore ~12 m deep

17. Innershelf Wave-driven Current (Lentz et al., 2008)‏ Stokes transport, T St Low-passed barotropic velocity, correlation between T St and depth (m)‏ offshore velocityalong-shelf velocity

18. Steady Wave-Driven Current Model in Lentz et al. (2008)‏ Stokes-Coriolis Force (c.f., Hasselemann,1970; McWilliams & Restrepo, 1999)‏ along-shelf momentum: cross-shelf momentum: continuity: surface and bottom wave-streaming (Longuet-Higgins, 1953; Xu and Bowen, 1994)‏ already in the model replaced with breaking and friction terms in the present model A (= K v ): vertical eddy viscosity (m 2 /s)‏

19. Lentz et al. (2008)‏ROMS-UCLA h = 12 m (const.), H sig = 2 m, T p = 7s, normal incident monochromatic wave no stratification, no other forcing constant vertical eddy viscosity K v = 10 -6 ~ 10 -1 (m 2 /s)‏ offshore velocity ualong-shelf velocity voffshore velocity ualong-shelf velocity v

20. Steady-State Momentum Budget without Streaming K v = 10 -3 (m 2 /s)‏ K v = 10 -5 (m 2 /s)‏ velocity (m/s)‏u momentum (m/s 2 )‏v momentum (m/s 2 )‏ x 10 -6 PGF = COR VMIX = COR COR - ST-COR Ekman balance 12 m H s = 2 m, T p = 7s 10 km 7 km

21. Steady Upwelling Solutions on the MVCO Topography with and without Wave-Current Interaction variable wave field given by the WKB wave driver (includes surfzone) KPP (surface & bottom)‏ upwelling-favorable (westerly) moderate wind stress at 0.05 Pa with WCI w/o WCI offshore velocityalong-shelf velocityeddy viscosity

22. left: with WCI, right: no WCI wave condition: H rms = 3.2 m, T p = 7 s,  o = 0 o Cross-Shelf Thermal Response to Varying Wind w/ & w/o WCI downwelling upwelling along-shelf wind stress day  y s (Pa)‏ - nearshore cell - mix-layer depth - timing and intensity of up/downwelling

23. Summary: 1. WCI based on a VF formalism implemented in ROMS 2. tested against Duck '94 (surf-zone) and MVCO (inner-shelf) cases 3. importance of breaking acceleration in the surfzone - must be surface-intensified - balance with PGF in the cross-shore direction (wave set-up)‏ - balance with bottom drag in the alongshore (alongshore current) 4. Ekman balance + Stokes-Coriolis force in the offshore - momentum balance altered by vertical eddy viscosity 5. surfzone circulation and anti-Stokes advection affects inner-shelf dynamics - isolation of nearshore water (“sticky water”)‏ - influence on mix-layer depth, timing and intensity of upwelling and downwelling