Wind-Wave-Current System in Coastal Ocean

Wind-wave-current system in coastal ocean

T. Yamashita, S. Kato & Y. Baba Disaster Prevention Research Institute, Kyoto University, Japan

Abstract

Observational discoveries of coastal current structure in Ogata Coast, Japan, were summarized with respect to characteristics of wind and waves in the wave-shoaling region. The observations of flow structure under the storm condition (strong wind & high wave) showed that (1) the coastal longshore current that has a vertically uniform flow profile, was developed in the wide area of coastal zone including the surf zone, and (2) strong shear flow with undertow (offshore-going near-bottom current) was developed in the surf zone. As a generation mechanism of such flow structures, it was designated that sea surface stress was emphasized under storm condition with the energy transfer from wind to waves through whitecap dissipation of shoalkg waves.

A mathematical model of whitecaps dissipation stress,z,, ,was proposed as an energy transfer interface between atmosphere and coastal ocean. Using this interface model, numerical Wind-Wave-Current System (WWC System) was established, in which the relation between wind stresses (wind field), whitecap breaker stresses (wave field) and bottom stresses (current field) were integrated. Enhancing effects of whitecap dissipation stress due to wave shoaling was also taken into consideration in the system.

1. Introduction

One of the most important problems in coastal management is the prediction of changes in coastal morphology, which is equivalent to prediction of winds, waves, currents and sediment transport in the coastal zone. So much research has been carried out to make clear the mechanism of beach erosion, to develop its

64 Coastal Engineering V1 control measures, and to create a desirable coastal environment. In these researches, very few mathematical models consider the effect of wind-induced currents under the storm condition, such as hurricane and typhoon. Too much attention has been given to the wave action in the surf zone as a major external force for morphological and dynamical changes in coastal environment. We should give attention to the material movement and sediment transport, which are driven by both wind-induced and wave-induced currents in wide areas of the coastal sea. The point of the beach management in the Japan Sea is that wind and wave-induced coastal current systems (coastal current in the coastal zone under the strong wind condition) are the driving forces of sediment transport in the wide coastal zone (from the shore to 20-30m deep sea-area). Recent observations of currents and waves in the Central Japan sea coasts show that winter monsoon winds develop high waves, together with strong wind-induced currents in the wide area of the nearshore zone (Yamashita et al., 1998)[1]. The wind-induced currents combine with nearshore currents generated by depth-limited breaking waves to generate surf zone currents. A new wind-wave-current system in the shoaling region was proposed in this study. The current enhancing effect due to whitecap dissipation of wind waves is considered in the system in terms of the whitecap shearing stress,.tb, , which is an additional sea-surface shear stress for fluid motions caused by wave breaking. The idea is that the rate of work of the surface roller of whitecap breaker (=shearing stress times wave celerity) balances against the energy dissipation rate of wind waves. These effects are enhanced in the shoaling water by increasing wave steepness. Comprehensive consideration of theses effects was taken in the storm surge prediction system.

2. Coastal current system: observational discoveries

Investigation of coastal current induced by both wind and wave in the Japan Sea is important to predict beach changes. The Disaster Prevention Research

Institute (DPRI), Kyoto University has condueted Eeld observations of coastal currents, waves and wind under the winter monsoon condition, every winter since 1997 in the Ogata Coast (see Fig. I). From the observational results, we obtained (Yamashita et al., 1998[1]; Kato and Yamashita 2000[2]) that: (1) strong offshore-going currents are generated by strong wind and high waves inside the surf zone; (2) outside the surf zone, the longshore component of coastal currents is mostly generated by strong wind; (3) longshore currents in the offshore region are strong enough to transport sediment alongshore. Besides, we found that these wind effects for the coastal currents are remarkable outside the surf zone, over a region of 10 to 15 m depth. Therefore, in planning large-scale coastal structures, such as harbor breakwaters and offshore reclamations, the estimation of wind and wave-induced currents in the coastal region is of great importance. In this study, a simple formulation of the cross-shore profile of wind and wave-induced longshore currents is derived based on the results from observations and numerical simulation.

Coastal Engineering V1 65

Field observation in Ogata Coast velocity profile

wave property EM: electromagnetic current meter ADCP: Acoustic Doppler Current Profiler

Naoetsu o 1.0 Ogata" Kakizaki lkbor U Fishing Port Fishing Port

0 Wave Hunter EM H ADCP

Fig. 1 Observation stations (St.1- St.13)

Figure 2 shows the results of the joint observation, in which the significant wave height at 15m depth, the wind speed on TOP, the cross-shore and longshore currents at the points of 20m, 15m, 8m and 5m-depth are shown. Observation stations at 8m and 5m-depth are inside the surf zone in the storm condition, in which strong offshore-going currents are observed intermittently and the occurrence of these currents coincides with high wave conditions. The intensity of offshore-going currents is extremely strong at tke depth of 5m. The offshore-going current intensities outside the surf zone (stations of 15m and 20m-depth) are less than 10 crnts, however, onshore-going currents are predominant. It is important that the occurrence of strong offshore-going currents is limited near the surf zone and this current may cause offshore-going sediment transport in the nearshore zone. On the other hand, the variational tendency of longshore current is similar to that of wind speed as shown by thick line in Fig. 2. The overlaid thick line is the smoothed observational data of wind speed. The relation between longshore current near the bottom and wind speed is quite clear outside the surf zone. Therefore, longshore currents induced by winds are widely generated in the coastal region. Moreover, the intensity of longshore currents is enough to transport sediment. Strong longshore currents are much bigger than cross-shore currents outside the surf zone.

66 Coastal Engineering VI

0 0. f 0. G 0. e -0. B

q -0.

0 0. 0.

4 -0.

Time (day) Time (day) Fig. 2 Coastal currents observed in Ogata Coast in winter.

2.1 Wind and wave-induced longshore currents The cross-shore profiles of the near bottom component of longshore coastal currents induced by wind are simulated by a quasi-31) model (Kato and Yamashita. 2000[2]). An idealized computational domain, with a uniform bottom slope, 1/100, in the cross-shore direction and constant in the longshore direction, is used for the simulation(Fig. 3). The maximum depth in this domain is 100 m. These profiles were approxhated by fhe log-normal distribution function with water depth h as proposed by Kato et d. (1999)[3]

where, a, b, c are fitting parameters. Using this formulation, an equation for the depth-dependent bottom friction coefficient, based on observations and numerical simulations, is obtained as (ln h - b)' f(h) = 27WaC~a2 pc2 where a, b and c are parameters that can be determined by adjusting cross-shore profile of coastal currents. In this study, wave-effects on coastal currents are considered with the surface shear stress enhanced by whitecap dissipation and the wave breaking in the surf zone. Wind generates currents directly by the wind

Coastal Engineering V1 67 shear stress at the sea surface, and indirectly through whitecap in the wide area of coastal regions. In the shoaling region, waves are deformed by sea bottom topography and waves become steeper in the shallow region. Then whitecaps occur. Wave energy dissipates via whitecaps (whitecap dissipation) and the surface shear stress is enhanced by whitecap dissipation. Therefore, wind shear stress and shear stress enhanced by whitecap dissipation are separated to explicitly consider the wave shoaling effect. The surface shear stress is assumed as follows

q = Pa~D~2+ pABgH sin cx (3)

1 A = -C,,H,~~Ks -KS,MIN, 8g tanh kh where, B is the ratio of wave steepness (H,/L,), H is the local wave height, a is the local wave direction, k is the local wave number, Ksand are the

shoreline

Fig. 3 Schematized computational domain for wind-induced current simulation

using quasi-3D model shoaling coefficient and its minimum value, CO is the angular frequency of waves, Cdisis a constant, and subscript ""0" stands for "offsfiore".

For calculation of the longshore component of nearshore currents by wave breaking in the surf zone, the following typical formulation by Longuet-Higgins (1970)[4] is employed. Ubr(y/yb)is the cross-shore profile of longshore currents, y is the cross-shore distance from the shoreline, yb is the breaking point

(distance) from the shoreline, uo is the Iongshore currents at the breaking point, y is a constant, f, is the bottom friction coefficient due to wave motion, hb is the breaking water depth, s is the bottom slope, aband cb are the wave direction and wave velocity at the breaking point respectively. Consequently, the cross-shore profile of wind and wave-induced coastal currents is given by Eq.(5).

68 Coastal Engineering V1

Figure 4 shows a comparison with observed data and computed results for the wind velocity W=10.0 m/s and the wave conditions Ho=5 m, T=8 S and a =g0. The dash line indicates the result in which neashore currents are not considered. In the computation, using Eq.(5), the Longuet-Higgins theory results in remarkable nearshore currents. In the observed data, however, the nearshore currents are negligible. This difference explains why a predominant direction of wind-induced currents, which were eastward in the observed data, exists outside the surf zone (right figure of Fig.2); whereas wave-induced currents inside the surf zone frequently change direction (left figure of Fig. 2) This means that waves have a predominant direction in this coast even in winter storm conditions.

5 - - - Knd-induced Current -Wind and Wave-induced Current 0 Observed datafbottom) A ADCP data(depth-averaged)

0 10 20 30 40 50

Fig. 4: Comparison with observed data computed results.

2.2 Wind and wave-induced cross-shore currents The characteristics of observed cross-shore currents are summarized and a simple formulation of cross-shore current near the bottom is derived. It is possible to compute a coastal current field for sediment transport with combination of simple formula of cross-shore and longshore currents.

Cross-shore currents treated in this section are limited to the near-bottom currents because we focuse on the sediment transport rate. From observational results, it is found that strong offshore-going currents occur in the surf zone under high wave condition, and that the offshore-going currents are never observed at the stations of 15m deep or more (offshore region). These velocity data are obtained near bottom (50cm above sea bed) under storm conditions. There is a tendency for offshore-going velocity to increase with non-dimensional wave height. Figure 5 shows the relations between normalized offshore-going velocity and the non-dimensional wave height. Here, the offshore-going velocity

Coastal Engineering V1 69 is normalized by Jgh, , where h, is the representative depth which is set up as 10m in this study. Because generation of the offshore-going currents is limited only inside the surf zone, the boundary between surf zone and offshore region can be determined as the area around 10m deep. It is also found that the normalized velocity is formulated with the exponential function with respect to

Hlh.

Sts.4,5,7, and 8

-22

St.7

-8 - -

I I I 0.2 0.3 0.4 0.5

H'h t Line[II] t t St .S Y min min Y mm Ymm Y

Fig. 5 Relationship between normalized offshore-going velocity and the non- dimensional wave height

Deducing from the results mentioned above, a cross-shore distribution of offshore-going near-bottom velocity, f/ ,can be formulated as:

where Y ,in :the minimum of non-dimensional wave height H l h , V *,in : the minimum of offshore-going velocity normalized with . Three distribution functions being included in Eq.(6) are formulated by observational reasons.

= 2 tanh($ l)} c(~) - -

A(x) (x=O is the cross-shore line just on a base trough) reproduces the

70 Coastal Engineering V1 alongshore periodic variation with its trough spacingL,, which is decided by alongshore variation of sea depth topography at the Ogata Coast. Fitting parameters are decided as a = 5.3 and b = 1.7 with observation results. Cross-shore distribution of offshore-going velocity is reproduced with the function of B(y) ( y = 0 is the shore line position, and ybis the distance from the shoreline where undertow fades), where the fitting parameter is decided as c = 1.8with best fitting of normalized wave height and normalized velocity. This function is key in Eq.(7). As mentioned above, the normalized velocity is formulated by the exponential function with respect to the normalized wave height H /h . Notice that a gradient of normalized velocity is different at each measuring point (see Fig. 5). So, the function B(y) should be adjusted to represent an approximate velocity gradient in each depth with tuning the parameters c and y,. However, in this study, as boundary condition at the shoreline is not considered, the function B(y) is determined by assuming the range of depth from 3m to 10m. C(y) is also a distribution adjusting function to extract the far field condition (offshore-going velocity tends to zero in far-offshore. Where, d is assumed to be constant in this study. Figure 6 is the map of estimated current vectors under storm condition. In this calculation, we assume that wind blows parallel to the shore with a speed of

10m/s, and wave height, period 8s, wave angle 2deg in the Ogata Coast.

Fig. 6 Vector map of computed near-bottom coastal currents [H=5(m),T=8(s)]

Coastal Engineering V1 7 1

3. A numerical model of wind-wave-current system

As a wave-current(surge) coupled numerical model, we employed the hydrodynamic model, POM, and the third-generation ocean wave prediction model, WAM Cycle4 together with their interface in which whitecaps breaker stresses acting on the sea water surface were considered. A proposed WWC System is shown in Fig. 7, in which the relation between wind stresses (wind field), whitecap breaker stresses (wave field) and bottom stresses (current field) is summarized. A whitecaps dissipation term, S, , is defined by the following equation in the wave model, WAM C4. As an interface of wave-surge coupled storm surge model, we introduced the whitecaps breaker stresses defined as;

Wind Field Wind speed on the sea surface W (&S)

(prediction: meso-scale meteorological model, GPV data, ECMWF data etc.)

C, is determined by wind turbulence obsewatrion C, may have small dependence on wind-wave height

Sea surface stresses evaluated by wind turbulence Ts = p$ WAAAAAAAAAAA bind- riven Cur (Wave action conservation) z = azs wind-induced

shear stress (hydrodynamic code: POM) breaking wave induced shear stresses

bottom ~rictiod Energy dissipation of shoaling Total shear stresses= waves Wave effects will Wind-induced shear

E, : wave energy be introduced stresses (Ep), : equilibrium spectrum in by + shallow water Grant-Madsen Whitecap breaker shear (wave code: WAM C4) formulation stresses

Fig. 7 A proposed WWC system in which wind-wave-current interaction is taken into consideration

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4. Conclusions

A mathematical and numerical model of Wind-Wave-Current System in the coastal ocean was developed based on the field observations of sea surface wind, waves and currents, to be applied to the researches on environmental and disaster prevention problems in the coastal regions. First, observational discoveries of nearshore current structure were summarized with respect to characteristics of wind and waves in the wave-shoaling region. The observations of flow mechanism under the storm condition (strong wind & high wave) showed that vertically uniform longshore current was developed in the wide area of coastal zone including the surf zone and strong shear flow with offshore-going near-bottom current was developed only in the surf zone. From these experimental and observational results, it was found that sea surface stress was emphasized under storm condition with energy transfer from wind to waves through whitecap dissipation of shoaling waves.

Then, the mathematical model of whitecaps dissipation of wind waves and sea surface stresses was proposed as an interface between atmosphere and coastal ocean. Using this interface, numerical Wind-Wave-Current System (WWC

System) was proposed. In the system, the relation between wind stresses (wind field), whitecap breaker stresses (wave field) and bottom stresses (current field) were integrated, in which current enhancing effect due to whitecap dissipation of wind waves was considered in terms of the whitecap shearing stress, an additional sea-surface shear stress for mean fluid motion caused by wind wave breaking.

References [l] Yamashita, T., H. Yoshioka, S. Kato, M. Lu, and T. Shimoda : ADCP observation of nearshore current structure in the surf zone, Proc. 26th Int. Conf:

on Coastal Eng., ASCE, pp.787-800, 1998. [2] Kato, S and T. Yamashita : Three-dimensional model for wind, wave-induced coastal currents and its verification by ADCP observations in the nearshore zone, Proc. 27th Znt. Conf: on Coastal Eng., ASCE, ~p.3~777-3,790,2000.

[3] Kato, S., T. Yamashita, M. Ito and T. Mishima,: Evolution and cross-shore distribution of wind-induced coastal currents, Proc. of Coastal Eng., JSCE, Vol. 48, pp.431-435,1999. (in Japanese) [4]Longuet-Higgins, M. S. : Longshore currents generated by obliquely incident

sea waves, 1 & 2, Jour. Geophys. Res., Vo1.75, No.33, ~p.6~778-6,780, pp.6,790-6,801,1970.