Ocean surface waves - nearshore littoral currents (e.g., rip current) - upper ocean mixing (e.g.,...
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Transcript of Ocean surface waves - nearshore littoral currents (e.g., rip current) - upper ocean mixing (e.g.,...
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