**Near Shore Wave Processes**

Edward B. Thornton

Oceanography Department

Naval Postgraduate School

Monterey, CA 93943‑5000

phone:
(831) 656‑2847 fax: (831)
656‑2712 email:
thornton@nps.navy.mil

Timothy P. Stanton

phone: (831) 656‑3144 email:stanton@oc.nps.navy.mil

Award #’s: N0001401WR20023;
N0001401WR20021

http://www.oc.nps.navy.mil/~thornton/

http://www.oc.nps.navy.mil/~stanton/

http://www.frf.usace.army.mil/SandyDuck/SandyDuck.stm

** **

Long‑term
goals are to predict the wave‑induced three‑dimensional velocity
field and induced sediment transport over arbitrary bathymetry in the near
shore given the offshore wave conditions.

The
interrelationship of wave-induced hydrodynamic and sediment processes over the
vertical and morphologic processes at the bed are measured and modeled. The
primary mechanism for changes in moment flux that drive near shore
hydrodynamics is due to the dissipation by breaking waves, the processes of
which are poorly understood. To improve
our understanding of breaking waves, the dissipation associated with bubble
injection is measured along with the velocity fields over the vertical. Bottom boundary layer measurements are
obtained to determine bottom stress and dissipation. Sediment transport is measured in response to the measured mean
longshore and cross-shore currents, wave velocities and induced stresses. The
small-scale morphology, which acts as hydraulic roughness for the mean flows
and perturbs the velocity-sediment fields, is measured as a function of time
and over large areas to examine cross-shore and alongshore variation.

A
comprehensive six-week experiment was conducted during April/May 2001 at Sand City, California, to measure processes
on a steep beach.** **It is hypothesized
that the plunging and collapsing/surging breaking wave processes occurring on a
steep beach are significantly different than plunging/spilling breaking wave
processes previously measured at Duck over a moderately sloping bar. Wave
reflection can be significant on steep beaches. It is further hypothesized that
the radiation stresses are modified by reflected waves owing to modulation of
the water depth and the kinematics of the breaking waves steepened by the
superimposed reflected wave energy. The effects of reflected wave energy on
sediment transport is being studied with high resolution BCDVSP profiles of
sediment flux and velocity over 50cm range above the bed. The modulation of the
breaker location can then modify the dynamics of the nearshore, such as wave
set-up and undertow.

The
comprehensive Delft3D morphodynamic model developed by Delft Hydraulics is
being assessed by comparing with field data. In addition, process models for
breaking waves, momentum mixing due to the interaction of longshore and cross-shore
vertical mean profiles, and bottom shear stress enhanced by the form drag of
bedforms and by turbulence of wave breaking are compared with
observations. Both linear and nonlinear
(Boussinesq) wave models are considered.

** **

**SteepBeach Experiment**. An unexpectedly large variation in
incident waves occurred during the experiment owing to a series of storms,
resulting in waves up to 4 m at breaking.** **The Steep Beach Experiment was
designed to test instrumentation and techniques to be used in NCEX, and to
examine processes on a steep beach (high Iribarren number) where reflection is
important. The large-scale morphology is a barred shoreline cut by rip channels
spaced 100-200 m apart. Offshore of the bar the slope is 1:20, and the beach slope
is steep at 1:5. Comprehensive wave and
current data have not been obtained previously on a steep beach, and these data
greatly expand the range of measured beach processes. Objectives of the Steep
Beach experiment were to measure wave transformation, reflection and
set-up/down, breaking wave and current‑induced turbulent bottom and
surface boundary layers, and sediment flux in the surf zone. Data selected for
analysis are from a cross-shore array of wave and current sensors that bisected
the shoal between rip channels. **Measurements
include **vertical profiles of horizontal velocity with 8 em
sensors, and void fraction (bubble content) with 12 conductivity cells, and
surface elevation with surface piercing wave staff and co-located pressure
sensors. Bottom boundary layer observations included small-scale morphology
measured by an x‑y scanning altimeter, and turbulence and sediment
concentration profiles measured with a Bistatic Coherent Doppler Velocity and
Sediment Profiler (BCDVSP) (Stanton 1996, 2001). Directional wave spectra were
measured by an offshore buoy in 18 m water depth. The 2 m spring tidal range
caused the surf zone to sweep past the fixed tower measurement location over a
tidal cycle, so that the vertical profile of the entire surf zone was measured
over tidal cycles. Bathymetry of the measurement area was surveyed during the
experiment using an instrumented jetski (Jamie MacMahan, University of
Florida). The beach was surveyed using DPGS mounted on a wader for the shoal
areas and on a motorized vehicle (Gator) at low tide to overlap the jetski
survey region. Surface elevation measurement techniques of breaking waves are
being intercompared at the central array using, a surface piercing wave-wire,
and a LIDAR at a fixed point. The cross-shore array was configured to form
reflection measurement arrays for the waves reflecting off the beach and off
the bar. Wave reflection varied with
the tide. At low tide the incident
waves were dissipative. At
approximately mean tide and higher, waves reflected off the steep beach face
resulted in obvious nodes in spectra, even at the sea-swell wave band,
indicating strong reflection.
Reflection coefficients are being determined as a function of the tide
stage.** **Preliminary results of the experiment can
be found at http://www.oc.nps.navy.mil/ripex/.

The Delft3D
nearshore hydrodynamic model was assessed by comparing model output with data
from comprehensive nearshore NSTS and Duck field experiments, which include
observations from barred and planar beaches and a wide range of conditions with
maximum mean currents of 1.5 m/s.

** **

The
Delft3D model has two free parameters, a depth dependent breaking term, _{}, and the bed roughness length, _{}, in the White-Colebrook formulation for bottom shear stress.
The calibration formula developed by Battjes and Stive (1985) to determine the
breaking wave dissipation parameter _{} as a function of the
deep water wave steepness, _{}, in the Battjes and Janssen (1978) wave transformation model
was verified. Good comparisons of the predicted and measured _{} values were obtained
on both barred and planar beaches using _{} from Battjes and
Stive (1985) for _{}>0.002. For* *_{}<0.002, _{} was found independent
of _{}, and a new parameterization for _{} was introduced based
on the Iribarren number, which includes the beach slope. Improved _{} predictions were
obtained using the _{} formulation based on
the Iribarren number for _{}<0.002, with overall model rms error < 8%.

A bed shear
stress formulation in which _{} represented a
measurable quantity was sought. Values for _{} that provided a
computed best fit to mean current observations for the entire data sets were _{} m for the barred
beach and _{} m for the planar
beach. However, these values do not correspond to either the measured bed
roughness height, O(0.04), or the sediment grain size, O(0.0002 m). Tests
indicate that model predictions are not sensitive to order of magnitude
variations in _{}. Using the best fit _{}suggests that the cross-shore variation of _{} is not overly
sensitive to changes in _{}, and is mostly controlled by depth changes associated with
tidal variation.

The inclusion of
the roller was needed to properly model the magnitude of the cross-shore
distribution of the alongshore current. Including
rollers in the wave forcing results in significantly improved predictions of
the observed alongshore current structure by shifting the predicted velocity
maxima shoreward and increasing the velocity in the trough of the bar compared
with model predictions without rollers. On near-planar beaches and high-energy
events on barred beaches, a 1-D (alongshore uniform bathymetry) model performs
as well as 2-D. On barred beaches under moderate conditions when alongshore
non-uniform bathymetry prevails, the 2-D model performs better than the 1-D
model, particularly in the bar-trough region. Wave forcing balances the bottom
stress with a second balance between alongshore variation in the mean surface
elevation (pressure gradients) and the inertia of the alongshore current. An
example of the mean currents over an alongshore inhomogeneous, barred beach is
shown in Figure 1. Using the classic 1-D alongshore current model for this data
results in two maxima over the bar and at the beach (see for example Church and
Thornton, 1995). Applying the 2-D model, the mean alongshore currents at the
measurement array compare well as the result of including alongshore pressure
gradients (middle panel, Fig. 1). Paradoxically, the currents to the south show
2 maxima, which are the result of the local pressure gradients.

On the basis of
Delft3D hydrodynamic model comparisons with comprehensive nearshore field data
acquired over two decades funded in all or part by ONR, it is recommended the
U.S, Navy adopt Delft3D as an operational surf model.

** **

** **

** **

** **

** **

*Figure 1. Delft3D
model comparisons with observations during Delilah experiment at Duck, N.C. on
Oct. 15, low tide. Top panel: Bathymetry overlaid with H _{rms }predicted
contours (magnitude in meters). Middle panel: model computed pressure gradients
at low tide (shaded background in N/m). The red shades represent positive
pressure gradients that act in the direction of wave forcing (right to left).
Darker blue shades are negative pressure gradients that act left to right.
Bottom panel: Mean (1 hour) velocities. The shaded background represents
velocity magnitude in m/s. The red circles are measurement locations*

* *

It is
recommended on the basis of comparisons with comprehensive nearshore field data
that the Delft3D hydrodynamics model be modified to include roller dynamics and
then be adopted by the U.S, Navy as an operational surf model.

1. Results of
process modeling obtained on this project are being applied to nearshore
modeling efforts under the following programs: Surf Model (ONR), Modeling Wave
Dissipation within the Wave Boundary Layer (ONR), and Development and
Verification of a Comprehensive Community Model for Physical Processes in the
Nearshore (NOPP).

2. Collaborative
modeling and data comparisons of breaking waves using Boussinesq equations is
being performed by PhD students at the U of Quebec under co-direction with
Barbara Boczar‑Karakiewicz.

3. Collaborative
2D modeling of BBL turbulence and sediment suspension using the DUNE2D
model with Dianne Foster at Ohio State
University.

4. Collaborative
modeling of BBL flow and near-bed stresses using a 3 D hybrid LES model with
Emily Zedler and Bob Street at Stanford University.

Battjes, J. A. and J.P.F.M. Janssen, 1978, Energy loss and
set-up due to breaking of random waves, Proc. 16^{th} Int. Conf. on
Coastal Eng., ASCE, 569-587.

Battjes, J.A.
and M.J.F. Stive, 1985, Calibration and verification of a dissipation model for
random breaking waves, J. Geophys. Res., 90 (C5), 9159-9167.

Church,
J.C. and E.B. Thornton, 1993, "Effects of Breaking Wave Induced Turbulence
within

a
Longshore Current Model", *J. Coastal
Engineering*, 20, 1‑28.

** **

**PUBLICATIONS**

Garcez Faria,
A.F.G., E.B. Thornton, T.C. Lippmann and T.P. Stanton, 2000, Undertow over a
barred beach, J. Geophysical Research, 105 (C7), 16,999-17,010.

** **

**REFEREED PAPERS SUBMITTED:**

Reniers,
A.J.H.M., A. van Dongeren, J. Battjes, and E.B. Thornton, 2001, Linear
modelling of infragravity waves during Delilah, submitted to J. Geophysical
Research.

Saulter,
A.N., P.E. Russell, J.R. Miles, and E.L. Gallagher, 2001, Observations of Bed
Level Change in a Satruated Surf Zone, submitted to J. Geophysical Research.

Feddersen,
F. E.L. Gallagher, R.T.Guza, and S. Elgar, 2001, The Drag Coefficient in the
Nearshore, submitted to J.
Geophysical Research.

Gallagher,
E. L., E.B. Thornton, R.L. Kendall, T.P. Stanton, 2001, Sand Bed Roughness in
the Nearshore of Two Beaches, submitted to J. Geophysical Research.

Chen, Q., J.T.
Kirby, R.A. Dalrymple, F. Shi, and E.B. Thornton, 2001, Boussinesq Modeling of
Longshore Currents, submitted to J. Geophysical Research.

Reniers, A.J.H.M., E.B.
Thornton and T.C. Lippmann, 2000, Effects of Alongshore Non-uniformities on
longshore currents measured in the field, submitted to the J. Geophysical
Research.

** **

**NON-REFEREED
PUBLICATIONS**

**CONFERENCE PROCEEDINGS**

Blondeaux, P., T. Stanton,
E. Thornton, G. Vittori, 2000, An Approach to Measure Turbulent Stress in the
Nearshore Region, Proc. 27^{th} Int’l. Conf. Coastal Eng., ASCE, 48-58.

Stanton, T.P. and E.B.
Thornton, 2000, Profiles of Void Fraction and Turbulent Dissipation Under
Breaking Waves in the Surf Zone, Proc. 27^{th} Int’l. Conf. Coastal
Eng., ASCE, 70-79.

Grasmeijer, B.T., L.C. Van
Rijn, S. Elgar and E. Gallagher, 2000, Verification of a cross-shore profile
model using field data, Proc. 27^{th} Int’l. Conf. Coastal Eng., ASCE,
2522-2535.

Van Dongeren, A., A.
Reniers, 2001, Nonlinear modeling of infragravity wave response under field
conditions, Proc. Coastal Dynamics ’01, ASCE, 283-292.

** **

Reniers, A., G. Symonds and
E. Thornton, 2001, Modelling of rip currents during RDEX, Proc. Coastal
Dynamics ’01, ASCE, 493-499.

Lippmann, T.C., T.H.C.
Herber, and E.B. Thornton, 2001, Observations of infragravity waves in the
nearshore, Proc. Coastal Dynamics ’01, ASCE, 55-61.

Morichon, D., B.
Boczar-Karakiewicz, and E.B. Thornton, 2001, Boussinesq wave model compared
with field data, 2001, Proc. Coastal Dynamics ’01, ASCE, 365-372.

Morris, B., E.B. Thornton
and A. Reniers, 2001, Nearshore wave and current predictions compared with
field observations, Proc. Coastal Dynamics ’01, ASCE, 788-797.

Foster, D.L., T. Stanton,
K. Andersen, J. Fredsoe, and E. Thornton, 2001, Model-data comparisons of
velocity and suspended sediment in a wave dominated environment, Proc. Coastal
Dynamics ’01, ASCE, 751-758.

**CONFERENCE PRESENTATIONS:**

Stanton, T.P. and E.B.
Thornton, Vertical Profiles of Dissipation and Eddy Viscosity in the Surf Zone
During SandyDuck, American Geophysical Union Fall Mtg., San Francisco, Dec.
2000.

Foster, D.L., Stanton, T.P.,
K.H. Anderson, E.B. Thornton and J. Fredsoe, Model-Data Comparisons of
Turbulence and Suspended Sediment, American Geophysical Union Fall Mtg., San
Francisco, Dec. 2000.

Reniers, A., G. Symonds, and
E.B. Thornton, Morphodynamic Modeling of Rip-Currents, American Geophysical
Union Fall Mtg., San Francisco, Dec. 2000.

Thornton, E.B., T.P. Stanton
and D. Dixon, Geometry and Migration of Wave Ripples on the Inner Shelf,
American Geophysical Union Fall Mtg., San Francisco, Dec. 2000.

Newberger, P.A., J.S. Allen,
and E.B. Thornton, Model Studies of Tidal Elevation Changes on Nearshore
Circulation, American Geophysical Union Fall Mtg., San Francisco, Dec. 2000.

Morris, B. and E.B.
Thornton, Comparison of NSTS and Duck Field Data with the Numerical Model
Delft3D, American Geophysical Union Fall Mtg., San Francisco, Dec. 2000.

Gallagher, E.L., E.B.
Thornton, and T.P. Stanton, Observation of Bedform Length Scales and
Orientation, American Geophysical Union Fall Mtg., San Francisco, Dec. 2000.

Morichon,
D., B. Boczar-Karakiewicz, and E.B. Thornton, Boussinesq model for breaking
wave height distributions and velocity moments compared with lab and field
data, American Geophysical Union Fall
Mtg., San Francisco, Dec. 2000.

Martin, S.D.,
E.B. Thornton and T.P. Stanton, DUNE2D Modeling of Vortex Ripple Migration,
American Geophysical Union Fall Mtg., San Francisco, Dec. 2000.

Morichon,
D., B. Boczar-Karakiewicz, and E.B. Thornton, Boussinesq model for breaking
wave height distributions, mean currents and morphology compared with field
data, Waves’01 Conference, San
Francisco, August 2000.

**THESIS DIRECTED:**

Dixon, D.B., Evolution of
Bedforms on the Inner-Shelf, M.S. Thesis, Naval Postgraduate School, September
2000.

Kendall, R., Seafloor
Roughness in the Nearshore, Coast 3D Experiment, Egmond ann Zee, The
Netherlands, M.S. Thesis, Naval Postgraduate School, June 2000.

Plager, W.L., Mine Burial in
the Surf Zone, M.S. Thesis,** **Naval
Postgraduate School, Sep. 2000.

Martin,
Steve, Vortex Ripple Morphology Using Dune2D Model,** **M.S. Thesis,** **Naval
Postgraduate School, March 2001.

Morris, Bruce, Nearshore Wave and Current Dynamics,** **Ph.D. Thesis,** **Naval Postgraduate School, September 2001