George Voulgaris - Rip Current Studies

Surfzone Hydrodynamic Measurements
and Modeling: Towards a Rip-Current
Potential Hazard Prediction Tool
George Voulgaris & Nirnimesh Kumar
Department of Geological Sciences
(Department of Earth & Ocean Sciences)
University of South Carolina, Columbia, SC
Outline
• Introduction / Motivation
• Methodology
• Data Collection for Model Set-Up
– Recovering data for a 2-beam Aquadop
• Modeling Approach
• Discussion
Rip Current Forecasting
From Engle et al., 2002
http://www.ripcurrents.noaa.gov/
From Komar et al., Prentice Hall, 1976
Engle et al., 2002- Modified ECFL LURCS used
lifeguard rescue logs from Daytona
Beach, Florida to correlate rip current rescues to
concurrent wind and wave measurements 3
Nearshore Coastal Observing Systems
Voulgaris et al, MTS, 2008
http://www.geol.sc.edu/gvoulgar/ww.html
Directional wave characteristics and currents at 56m MWL some 2000 ft off the coast.
These data provide wave climatology, but need for
added value products.
Motivation
• Create a nearshore condition model that adds
value to the nearshore wave monitoring
stations operated by Regional Associations.
• Build a nowcast rip-current hazard system
based on physics.
• Make it transportable to other areas.
• Use it for forecasting nearshore hazard
prediction.
The Bathymetry Problem
• Flow and Bathymetry feedback that facilitates the
development of rip currents.
• No 3-D bathymetric evolution models available to date.
Ratio of rip channel width to rip
channel spacing: (Lt/L)= 1/5
(Haller et al., 2002)
Ratio of rip channel spacing to bar
distance: (L/Xc) = 4
(Haller et al., 2002-(2.7-4); Huntley
et al., 1992-(1.5-8))
Lc= L - Lt
Folly Beach, SC
Maximum bar height-1.7 m
Location: 130 m from the high tide mark
Myrtle Beach, SC
Maximum Bar Height: 0.45 m
Location: 100 m from high tide mark
Modeling
Two-way coupling of waves (SWAN) and currents (ROMS)
Offshore Boundary
Domain
Shoreline
Boundary Conditions
7
Field Experiments to Evaluate Models
• SC Coastal Erosion Study (USGS)
• 2 Nearshore Experiments at 3 locations
– 1st Experiment December 2003 (1 location)
– 2nd Experiment December 11-18, 2005 (2
locations)
Extracting Data from a 2-beam Aquadop
Stations A & B = Nortek Aquadopp
• Operating Frequency = 2 MHz
• Sampling Frequency = 1 Hz
• Number of Samples = 1024
•(~17 minutes)
Stations C & D = ADV
Beam 2 of this
Aquadop was
inactive
Beam 3
V1
V2
Beam 2
z-axis
V3
Original Aquadop
Beam Geometry
Beam 1
Aquadop Operating
Beam Geometry
Artificial Aquadop
Beam Geometry
z-axis
Beam 3
Beam 2
Beam 3
Beam 1
Beam 1
Extracting Data from a 2-beam Aquadop
Generalized Transformation Matrix
V = T ⋅U
U = T −1 ⋅ V
V3
V = (V1 ,V2 ,V3 )
V2
U = ( u , v , w)
V1   sin(φ1 ) ⋅ cos(θ1 )
V  = sin(φ ) ⋅ cos(θ + θ )
2
1
2
 2 
V3   sin(φ3 ) ⋅ cos(θ1 + θ 3 )
sin(φ1 ) ⋅ sin(θ1 )
sin(φ2 ) ⋅ sin (θ1 + θ 2 )
sin(φ3 ) ⋅ sin (θ1 + θ 3 )
V1
w v
w
cos(φ1 )  u 
cos(φ2 ) ⋅  v 
  
cos(φ3 )  w
φi = Angle of beam i from vertical z-axis
θi = Angle of beam i projection to x-y plane from x-axis, measured
counterclockwise
Transformation Matrices
T −1normal
1.5775 − 0.7887 − 0.7887
= 0
− 1.3661 1.3661 


0.3678 
0.3678 0.3678
Original 3-Beam Configuration
T −1modified
0 
2.3662 − 2.1445
= 1.3661 − 3.7144 2.7323


1
0 
 0
Modified 3-Beam Configuration
Calculating Vertical Velocity (artificial
Aquadop beam) from Pressure Data
H cosh k ( h + z1 )
p=
cos(kx − σt )
2
cosh(kh )
dp Hσ cosh k ( h + z1 )
=
sin(kx − σt )
dt
2
cosh(kh )
Hσ sinh k ( h + z 2 )
w=
sin(kx − σt )
2
sinh(kh )

1
 dp  sinh k ( h + z 2 ) 

w =  

 dt  cosh k ( h + z1 )  tanh(kh ) 
MWL
z2
w
z1
h
p
Mean Velocity Error Analysis for
Modified Beam Aquadopp
−1
U = T ⋅V
u  b11 b12
v  = b
   21 b22
 w b31 b32
b13  v1 + v1n 



b23  v2 + v2 n 
b33  v3 + v3n 
u = b11v1 + b12 v2 + b13v3 + b11v1n + b12v2 n + b13v3n
u = b11v1 + b12 v2 + b13v3 + b11v1n + b12v2 n + b13v3n
v1n = v2 n = v3n = vn
<u>n=0
<v>n=0
u = b11v1 + b12v2 + b13v3 + (b11 + b12 + b13 ) ⋅ vn
<u>n=0.22·vn
Error in u= (b11 + b12 + b13 ) ⋅ v n
<v>n=0.33·vn
Covariance Error Analysis for
Modified Beam Aquadopp
u  b11 b12
v  = b
   21 b22
 w b31 b32
b13  v1 + v1n 
b23  v2 + v2 n 
b33  v3 + v3n 
uv = b11v1 + b12 v2 + b13v3 ⋅ b21v1 + b22 v2 + b23v3
+ (b11 + b12 + b13 ) ⋅ (b21 + b22 + b23 ) ⋅ v 2n
Noise Contribution
uv
uv
normal
modified
= (1.5774 − 0.7891 − 0.7891) ⋅ (0 − 1.3662 + 1.3662) ⋅ vn2 = 0
= (2.3662 − 2.1445 + 0) ⋅ (1.3661 − 3.7144 + 2.7323) ⋅ v n2 = 0.0851 ⋅ v n2
Comparison between data obtained by the three beam
solution (red) and data obtained using the wave orbital
velocity as beam 2.
Mean alongshore and cross-shore velocities at Station A0 are consistent and comparable to
velocities at other stations
Radiation Stresses (m2 s-2)
Incorrect values obtained as Radiation Stress is a
function of the product of the instantaneous
horizontal velocities
December 2005 Experiment
ADV
ADCP
Aquadopp
Evaluation of SWAN for surf-zone
(a)
(b)
(c)
(d)
ROMS-SWAN, 2 way-coupling
C
(a) h (m)
(b) Hsig (m)
(c) θw(deg)
(d) v (m/s)
(e) u(m/s)
B
A
Rip Current Generation
(Setup as in Haller et al., JGR 2002)
Rip Channel Width
Grid Resolution: 2 meters
(74 X 131)
262 m
18.2 m
91 m
Wave Forcing:
Wave height:
0.5 meters
Wave Direction: 0°
Wave Period:
3.16 seconds
Rip Current Spacing
30 m
174 m
Surf Zone Width
Depth and Time Averaged Current
In channel
Over bar
Vertical Distribution of Cross-shore Velocities
In channel
Over bar
Vertical Distribution of Alongshore Velocities
Vorticity
50cm/s
Vorticity
50cm/s
Vorticity
50cm/s
Vorticity
50cm/s
Vorticity
50cm/s
Nearshore Circulation
and Wave Angle of
Approach
Acknowledgments
• John C. Warner. US Geological Survey
• Funding: NOAA, USGS