TY - JOUR

T1 - A modified defect function for wave boundary layers

AU - Teng, Yunfei

AU - Lu, Lin

AU - Cheng, Liang

AU - Tong, Feifei

AU - Tang, Guoqiang

PY - 2022/1

Y1 - 2022/1

N2 - In the present paper, a new defect function is proposed to predict the first harmonic motion in turbulent wave boundary layer (WBL) flows, based on the existing and newly acquired experimental evidences over a universal range of the governing flow parameters (A/ks & Re), taking the advantage of the existing defect function models. The defect function, denoted as D(z), having a complex form, describes the spatio-temporal velocity deficit in the WBL as the only function of z. For the new defect function, two sets of model parameters (p1 & λ1, p2 & λ2) are introduced to formulate the amplitude and phase defects, namely −ln|D|=(z/λ1)p1 and arg(D)=(z/λ2)p2. Correlation relationships between model parameters (p1 & λ1, p2 & λ2) and governing flow parameters (A/ks & Re) were established. Through (i) matching the logarithmic and the defect laws of velocity distribution and (ii) the ‘one particle analysis’ of turbulent diffusion process, we demonstrated that the model parameters λ1 and λ2 represent the characteristic length scales, and the model parameters p1 and p2 reflect the nonlinearities of amplitude defect and phase defect respectively. The new defect function not only leads to better predictions of the flow in the phase space than the existing models but also extends the applicable parameter ranges of the existing models.

AB - In the present paper, a new defect function is proposed to predict the first harmonic motion in turbulent wave boundary layer (WBL) flows, based on the existing and newly acquired experimental evidences over a universal range of the governing flow parameters (A/ks & Re), taking the advantage of the existing defect function models. The defect function, denoted as D(z), having a complex form, describes the spatio-temporal velocity deficit in the WBL as the only function of z. For the new defect function, two sets of model parameters (p1 & λ1, p2 & λ2) are introduced to formulate the amplitude and phase defects, namely −ln|D|=(z/λ1)p1 and arg(D)=(z/λ2)p2. Correlation relationships between model parameters (p1 & λ1, p2 & λ2) and governing flow parameters (A/ks & Re) were established. Through (i) matching the logarithmic and the defect laws of velocity distribution and (ii) the ‘one particle analysis’ of turbulent diffusion process, we demonstrated that the model parameters λ1 and λ2 represent the characteristic length scales, and the model parameters p1 and p2 reflect the nonlinearities of amplitude defect and phase defect respectively. The new defect function not only leads to better predictions of the flow in the phase space than the existing models but also extends the applicable parameter ranges of the existing models.

KW - Defect function

KW - Turbulence

KW - Wave boundary layer

UR - http://www.scopus.com/inward/record.url?scp=85119176428&partnerID=8YFLogxK

U2 - 10.1016/j.coastaleng.2021.104050

DO - 10.1016/j.coastaleng.2021.104050

M3 - Article

AN - SCOPUS:85119176428

VL - 171

JO - Coastal Engineering

JF - Coastal Engineering

SN - 0378-3839

M1 - 104050

ER -