New Method for Calculating Bottom Shear Stress under Skew Waves

Abstract

The bottom shear stress under skew waves can be used in a sediment transport modeling under rapid acceleration occurring in the surf zone. The bottom shear stress in a rough turbulent bottom boundary layer under sawtooth waves has been examined through two methods by Suntoyo and Tanaka°. One is to fit logarithmic velocity profile to the measured velocity in an oscillating wind tunnel, another is a calculation method incorporating acceleration effect. However, an investigation of a more reliable calculation method to estimate the time-variation of bottom shear stress has not been fully dealt with.In the present study, the bottom shear stress of experimental result will be examined with a new calculation method of bottom shear stress based on incorporating velocity and acceleration terms all at once. A new coefficient is proposed to express a wave skewness effect on bottom shear stress under skew waves.

Characteristics of Turbulent Boundary Layer Over a Rough Bed Under Cnoidal Waves Motion

“…Both velocity and acceleration terms are adopted from a calculation method proposed in Eq. (8) by Niel sen 11) , but that method could not give a good agreement with experimental data as shown by Suntoyo et al 4) , so in the new calculation method is proposed a new acceleration coefficient, a c expressing the non-linearity effect on the bottom shear stress under cnoidal waves that is determined empirically from both experimental and baseline turbulent model results. The instantaneous bottom shear stress can be calculated proportional to the square of the proposed instantaneous friction velocity, as shown in Eq.…”

“…Hereafter, friction velocity factor, f w proposed by Tanaka and Thu 13) is used to examine the bottom shear stress for all methods, while the phase difference, ϕ used it is an approximation obtained from the relation proposed by Suntoyo et al 4) .…”

“…Therefore, the accuracy of bottom shear stress estimation used to evaluate the amount of sediment transport obtained from the sinusoidal wave is necessary to be clarified with the sediment transport estimation incorporating the acceleration effect term in its calculations. Recently, Suntoyo et al 4) have proposed a new estimation method of the instantaneous bottom shear stress under saw-tooth waves based on incorporating both velocity and acceleration terms all at once and a good agreement between the new calculation method and experimental results of bottom shear stress under skew waves has been obtained. More recently, Suntoyo and Tanaka 5) have applied the new calculation method of bottom shear stress into sheet flow sediment transport rate calculation induced by skew waves and a good agreement with the sediment transport rate data from Kouchi et al 6) has been obtained.…”