QUASI-THREE DIMENSIONAL NUMERICAL MODEL OF WAVE-DRIVEN COASTAL CURRENTS

1. QUASI-THREE DIMENSIONAL NUMERICAL MODEL OF WAVE-DRIVEN COASTAL CURRENTS Jinhai ZHENG 27 June, 2011

2. IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 1 INTRODUCTION Coastal current is generated when waves approch and break obliquely to the shoreline. It plays a significant role in the erison and deposition of sediment, the evolution of shoreline and the dipersion of pollutants.

3. IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 1 INTRODUCTION A three dimensional structure: spiral profile of wave-driven coastal current.

4. IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 1 INTRODUCTION Spatial lag phenomenon: the maximum wave induced coastal currents appear at the landward location compared with that of the most intensive wave breaking.

5. IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 1 INTRODUCTION Previous efforts to explain: • the turbulent kinetic energy transport • the wave-induced turbulence of bottom shear stress • the alongshore pressure gradients were found to be responsible for shifting the velocity maximum away from the bar crest into the shoreward trough area, but only a slight improvement for location movement and velocity increase at the trough area. • surface rollers has been implemented in one-dimensional or two-dimensional numerical models for the mean wave set-up and cross-shore currents and demonstrated its role in shifting the location of the maximum currents toward the shore. • radiation stresses has been considered in both depth-average and depth-dependent ways to study wave set-up and set-down, longshore currents, undertow in the surf zone, nearshore circulation. However, the knowledge and the modelling of the complicated three-dimensional coastal currents are still limited.

6. IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 1 INTRODUCTION Emphasis of present study • to develop a quasi three-dimensional numerical model of wave-driven currents by taking a time average over a wave period on the basis of Navier-Stokes equations • to include the terms of the depth-dependent radiation stresses in the momentum equations so as to illustrate the various situation of wave-current interactions and the vertical structure of currents velocity • to improve modeling the spatial lag between the maximum current velocity and the most intensive wave breaking locations through incorporating surface rollers

7. IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 2 WAVE MODEL WABED wave model a 2-D phase-averaged model a practice-oriented random wave model for coastal engineering studies at estuaries and inlets inclusion in the Coastal Modeling System of Coastal Inlets Research Program examination with wave shoaling and breaking around an idealized inlet, waves breaking on plane beach, wave diffraction at breakwater and breakwater gap, wave generation in fetch-limited condition, wave transformation over complicated bathymetry with strong nearshore currents, wave generation at Rich Passage in the southern Chesapeake Bay, and large wave events at the Mouth of Columbia River field applications for Matagorda Bay, Grays Harbor Entrance and Southeast Oahu Coast An important aspect of the wave models used as drivers is that they should be fast enough to avoid slowing down the computation performance of the entire wave and current models.

8. IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 3 CURRENT MODEL Governing equations Boundary conditions (Fresoe & Deigaard, 1998)

9. IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 3 CURRENT MODEL , Depth-dependent radiation stresses (zheng, 2007) Onshore component of the onshore radiation stress Longshore component of the longshore radiation stress Onshore component of the longshore radiation stress where

10. IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 3 CURRENT MODEL The equation for the creation and evolution of the roller area (Dally & Brown, 1995) As waves begin to break, a zone of white foams is created in the wave front and the water in this zone is actively rotated. At the point of incipient wave breaking, the surface roller is just born and its area increases as the breaking-to-broken wave propagates. As the height of broken wave gradually decreases through dissipation of wave energy, the surface roller also becomes small and finally disappears.

11. IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 3 CURRENT MODEL Numerical schemes(Koutitas & O’Connor, 1980; Kuroiwa, 2002) a hybrid methodcombing the fractional step finite difference method in the horizontal plane with a Galerkin finite element one in the vertical direction

12. IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 4 MODEL TESTS Experimental study by Scott et al. (2004) International Conference on Coastal Engineering Experiments:The experiment was conducted in the large wave fume at Oregon State University. Regular waves with a wave height of 0.64 m and a frequency of 0.25 Hz were generated and normally incident on a barred beach which was designed to approximate the bar geometry observed in DUCK94 field experiment.

13. IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 4 MODEL TESTS Comparisons:Good agreements of wave height and setup at 28 cross-shore locations are found with and without considering depth dependent radiation stresses. The depth-averaged velocity achieves its peak near the breaking point and decreases both shoreward and seaward. It is noted that the velocity profiles calculated with and without considering depth dependent radiation stresses show little difference in the inner surf zone. However, outside the surf zone and especially near the breaking point in the outer surf zone, remarkable discrepancies appear. At these locations a seaward leaning tendency of velocity profiles close to the surface is found from observations, implying that there may exist a negative shear stress at wave trough level but not zero. This phenomenon is captured by considering depth dependent radiation stresses, as the increasing wave energy due to the shoaling results in a seaward forcing which is larger than the shoreward forcing due to wave set down.

14. Laboratory measurements of uniform longshore current by Visser (1991) Coastal Engineering IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 4 MODEL TESTS Experiments: The beach had 1:10 slope for the first seaward 1-m distance, 1:20 slope for the next 5m distance, and a flat bottom for the next 5.9 m to the wave generator. Laboratory data set of wave, current and water level were collected for eight incident wave conditions, two beach slopes and two values of bottom roughness.

15. IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 4 MODEL TESTS plunging breaker case transitional breaker case from plunging to spilling Comparisons: the present models can produce satistactory results, including the increase in the wave-driven nearshore current velocity inside the surf zone and the shifting the location of the maximum longshore current velocity landward. If the contribution of surface rollers is neglected, the calculated result yields the longshore current profile much offshore.

16. IAHR WORLD CONGRESS 2011, BRISBANE, AUSTRALIA 5 SUMMARY • A three-dimensional numerical model of wave-driven currents is developed by taking a time average over a wave period on the basis of Navier-Stokes equations. • The present model includes the terms of the depth-dependent radiation stresses in the momentum equations, therefore it can reproduce the observed phenomenon of a seaward leaning tendency of the surface current velocity profiles in the outer surf zone. • The present model incorporates the roller effects in the surface shear stress term so that it can simulate reasonably the spatial lag between the maximum current velocity and the most intensive wave breaking locations. • It is necessary to evaluate the present wave and current models with additional data sets of laboratory tests and field measurements.

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