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 FormalismYusuke 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...

outline:

1. introduction2. governing equations and implementation3. shoreface test (vs. Rutgers/USGS-ROMS/CSTMS)4. Duck 94 surfzone case (vs. Data & NearCom/POM)5. Martha's Vineyard inner-shelf case6. effects of WCI on upwelling/downwelling circulation7. summary

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: uE=uL-uSt

- 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

Wave-Averaged Current & Tracer Equations (McWilliams et al. 2004)

U = Uc + Uw

non-conservative forces(wave breaking etc..)

vortex force (CL-VF + Stokes-Coriolis)Bernoulli head

in ROMS Stokes drift

quasi-static setup

Stokes-Coriolis vortex force non-conservative terms

mass:

x momentum

y momentum wave breaking

Tracer equationHzc = h + +

ex. U = -USt

~anti-Stokes flow

Primary Wave Equations: Current Effects on Waves

...or external wave driver (e.g., SWAN; Booij et al., 1999)

wave breaking wave 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

“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

roller current &turbulence

r

breaking

b

b

r

primary waves

Vertical Distribution Function in B (Breaking Acceleration) Term

Warner et al. (2008)

Relaxed

Analogous to wave solution (present study)

kB -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 m3/s3, h = 5 m,

then DB ~ 3.5 (Pa)

< ~ 0.5 (above trough level)

= 1

Enhanced Vertical Eddy Viscosity/Diffusivity (KPP)

surface KPP (Large at al., 1994)

s: resolved vertical shear (bulk Richardson + Ekman depth)w: internal wave breakingd: double diffusionb: surface wave breaking (new)

Bottom KPP (Durski et al., 2004; Blaas et al., 2007)

no buoyancy flux at bottomno breaking wave effecttake max(SKPP, BKPP) for when Hbl overwrapsnew s-coordinate (bottom refinement)Hbbl smoothing (as UCLA-SKPP has)

“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

FB/D profile at 5-m

depth with Hs=2 m

courtesy of John Warner

Shoreface Test: Cross-Shore Vertical Slices

onshore velocity, u

alongshore velocity, v

vertical eddy viscosity, K

v

surfacebody force

depth-scale body force

depth-scale Brk Frc+ same Kv as HW09 HW09/M05

“DUCK '94” Surf-zone Field Experiment

surface body force

DUCK '94: Model vs. Observation (1)

u (m/s) Kv (m2/s)v (m/s)

u (m/s)

v (m/s)

breaking ~ PGF

brk ~ drag, VF ~ adv

Hrms

= 1.6 m, Tp= 6 s,

o=-13 deg.

depth-scale body force

DUCK '94: Model vs. Observation (2)

u (m/s) Kv (m2/s)v (m/s)

u (m/s)

v (m/s)brk ~ drag, VF ~ adv

breaking ~ PGF

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 casewith Craig & Banner (1990)-type modification

Newberger & Allen (2007)

Vertical Eddy Viscosity in Other Turbulent Closure Models

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

Innershelf Wave-driven Current (Lentz et al., 2008)

Stokes transport, TSt

Low-passed barotropic velocity, <u>

correlation between TSt and <u>

depth (m)

offshore velocity along-shelf velocity

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 breakingand friction terms in the present model

A (= Kv): vertical eddy viscosity (m2/s)

Lentz et al. (2008) ROMS-UCLA

h = 12 m (const.), Hsig

= 2 m, Tp = 7s, normal incident monochromatic wave

no stratification, no other forcing constant vertical eddy viscosity K

v = 10-6 ~ 10-1 (m2/s)

offshore velocity u along-shelf velocity v offshore velocity u along-shelf velocity v

Steady-State Momentum Budget without Streaming

Kv = 10-3 (m2/s)

Kv = 10-5 (m2/s)

velocity (m/s) u momentum (m/s2) v momentum (m/s2)

x 10-6 x 10-6

x 10-6 x 10-6

PGF = COR

VMIX = COR

COR - ST-COR

Ekman balance

12 m

Hs = 2 m, T

p = 7s

10 km

7 km

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 velocity along-shelf velocity eddy viscosity

left: with WCI, right: no WCI

wave condition:H

rms = 3.2 m, T

p = 7 s,

o = 0o

Cross-Shelf Thermal Responseto Varying Wind w/ & w/o WCI

dow

nwel

ling

dow

nwel

ling

upw

ellin

g

along-shelf wind stress

day

ys

(Pa)

- nearshore cell- mix-layer depth- timing and intensity of up/downwelling

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