### 1. Introduction

*u*is the fluid velocity in

_{i}*i*direction and

*p*is pressure (압력) and

*ν*is the kinematic viscosity (동점성계수).

*ν*is the kinetic eddy viscosity,

_{t}*k*is the turbulent kinetic energy (TKE, 교란운동에너지) (

*δ*is the Kronecker delta, and

_{ij}*S*is the mean strain rate tensor (

_{ij}*ν*, which generates the RANS turbulence modeling system (Wilcox, 1998). As one example, the

_{t}*k − ε*RANS model closes the system by solving two additional equations of TKE (

*k*) and dissipation (

*ε*) using

*νt~k*(Lauder and Spalding, 1974).

^{2}/ε### 2. Field Experiment and Data Analysis

*H*), peak wave period (

_{s}*T*) and the peak wave directions (

_{p}*θ*) averaged over each data burst from January 2 to 20.

_{p}*H*are lower than 2 m at most of the dates. However, it sharply increases higher than 2 m at January 14. The high wave condition continues until January 18 during which

_{s}*H*varies between 2.0~2.7 m. After January 18,

_{s}*H*sharply decreases below than 2 m. In case of

_{s}*T*, it increases from about 5 sec at January 2 and, during the period from January 14 to 18, it varies between 8 and 10 sec. In this period,

_{p}*θ*slightly varies around 45o indicating that the waves mainly approached the shore from northeast (90o is the shore normal direction). The high waves with the uniform northeast approaching direction at January 14~18 are likely the storm waves (폭풍파) caused by the extratropical cyclone developed in the northeast of the East Sea as shown in the satellite images of Geostationary Ocean Color Imager (GOCI) in Fig. 3. In the present study, we focus to examine the energy distribution of the waves measured during this storm period. The main reason for the analysis of the data selected at this time is because the characteristics of turbulence energy pattern are more clearly observed under high wave conditions in which the flows are strongly disturbed by the unsteady pulsating wave conditions. In addition, under swell-like high wave conditions, individual waves can be more easily distinguished during each wave period while, under lower wave energy conditions, individual waves are not easily separated because the waves are irregular due to the interference between the waves. For this reason, we selected the data from January 14 to 18 for the investigation of this study as this period is marked with the red vertical lines in Fig. 2.

_{p}*T*) to be 10.2 sec and the standard deviation to be 0.9 sec.

_{m}### 3. Model Description and Numerical Experiment

*k − ε*turbulence closure model. The model is characterized by the Volume of Fluid (VOF) method that tracks and locates the free surface by solving additional advection equation for a fluid volume function (Hirt and Nichols, 1981; Hieu and Tanimoto, 2006). The CADMASSURF model has been successfully on wave run-up (처오름) problems on porous seabeds (투과성 해저면) (Nam et al., 2002; Yoon et al., 2005).

*u*and

*w*are the horizontal and vertical flow velocities,

*ρ*is fluid density,

*p*is pressure,

*g*is gravitational force,

*ν*is eddy viscosity (와동 점성계수),

_{e}*D*and

_{x}*D*are the energy attenuation coefficients (에너지 경감 계수),

_{z}*γ*is porosity (다공성),

_{ν}*γ*and

_{x}*γ*are the area transmittance (투과율) in the

_{z}*x*and

*z*direction respectively.

*λ*,

_{ν}*λ*and

_{x}*λ*are functions of

_{z}*γ*,

_{ν}*γ*respectively as they are expressed as

_{x}and γ_{z}*C*is the inertia coefficient (관성계수).

_{M}*R*and

_{x}*R*are the resistance force (저항력) applying quadratic law as

_{z}_{z}are the grid size in the

*x*and

*z*direction respectively and

*C*is the drag coefficient (항력계수).

_{D}*S*,

_{p}*S*and

_{u}*S*are the source terms to generate the wave conditions.

_{z}*F*, that varies between 0 to 1. The 1 value of

*F*at a grid cell indicates that the cell is filled with fluid while 0 value indicates that fluid is empty in the cell. When

*F*is greater than 0 but smaller than 1, the grid cell is partly occupied by fluid indicating that the cell is located at the boundary between the fluid and air. The advection equation of

*F*is given as

*S*is source term to generate wave conditions. In order to close the equations from (5)~(7),

_{F}*k − ε*model is employed to calculate the eddy viscosity,

*ν*, as

_{e}*C*and

_{1}*C*are empirically determined coefficients (경험계수), and the relations between

_{2}*ν*,

_{k}*ν*,

_{ε}*ν*and

_{t}*ν*are given as

_{e}*C*,

_{μ}*σ*,

_{k}*σ*are empirically determined coefficients.

_{ε}### 4. Results

### 4.1 Reynolds stress distribution

*u*) not to be larger than 0.2 m/s. Moreover, we also consider the wave asymmetry (비대칭도) and skewness (왜곡도) as [(

_{max}*u*)

_{max}*− (*

_{onshore}*u*)

_{max}*]/(*

_{offshore}*u*)

_{max}*of each selected regular wave are monitored to be less than 10% and the times of offshore-to-onshore zero-crossing points of the waves are also to be concentrated within 10% range from the mean values.*

_{onshore}*u*)

_{max}*− (*

_{onshore}*u*)

_{max}*, is also about 0.1 m/s for all three groups. In addition, the times of offshore-to-onshore zerocrossing points occur at t/T~0.55 for all three groups. Another similarity is also found in the oscillating periods as the averaged times for the cross-shore velocity to cycle between the two adjacent zero-crossing points are 10.1, 10.1 and 10.3 sec for Group 1, 2 and 3 respectively. These similarities between the cross-shore velocity patterns between the three groups of the selected waves indicate that the only significant difference is the maximum velocity magnitude, and the similar wave pattern enhances the accuracy of turbulence measurement at this time.*

_{offshore}### 4.2 Model comparison

*F*), water pressure (

*P*) and the cross-shore velocity (

*u*) as they are calculated from Eqn. (6) and (10). The red vertical line in the figure denotes the location of the source where the wave generation condition is imposed. The figures show that the model nicely simulates the propagated wave trains on the flat bed. Near the bottom boundary layer below 1 m, the cross-shore velocities show time lags from the velocities in the upper layers due to the bottom drag.

### 5. Conclusion

*S*). Therefore, the development of these turbulence quantities strongly depends on the mean flow pattern, which may not correctly describe the turbulence pattern at the time of flow reversal when the mean velocity diminishes. To overcome this problem, additional contributions may be necessary in formulating the turbulence quantities under high wave energy conditions, which is suggested for future studies.

_{ij}