Modeling of a Rough-Wall Oscillatory Boundary Layer Using Two-Equation Turbulence Models Ahmad Sana 1 ; Abdul-Razzaq Ghumman 2 ; and Hitoshi Tanaka 3 Abstract: The standard k -  turbulence model and two versions of blended k -  / k -  models have been used to study the characteristics of a one-dimensional oscillatory boundary layer on a rough surface. The wall boundary condition for the specific dissipation rate of turbulent kinetic energy at the wall is specified in terms of a function based on wall roughness. A detailed comparison has been made for mean velocity, turbulent kinetic energy, Reynolds stress, and wall shear stress with the available experimental data. The three models predict the above properties reasonably well. In particular, the prediction of turbulent kinetic energy for the rough case by the blended models is much better than that for smooth oscillatory boundary layers as reported in previous studies. As a result of the present study, the use of one of the blended models in calculating the sediment transport in coastal environments may be recommended. DOI: 10.1061/ASCE0733-94292009135:160 CE Database subject headings: Oscillatory flow; Boundary layers; Turbulence; Shear stress; Coastal environment; Velocity. Introduction For the estimation of bed-load movement in coastal environments an accurate knowledge of bottom shear stress is required. More- over, the cross-stream profiles of velocity, turbulent kinetic en- ergy, and Reynolds stress may be helpful in suspended load predictions. A rapid development in computational resources has encouraged the researchers and consultants in hydraulic and coastal engineering to utilize more sophisticated turbulence mod- els to predict velocity, turbulent kinetic energy, and shear stress. In the case of steady flows, a wide range of problems has been solved by turbulence models. Rodi 1984 and Patel et al. 1985 have reviewed some of the models proposed earlier. For oscilla- tory boundary layers on smooth surfaces two-equation turbulence models have proved to be reasonably efficient. A number of stud- ies have been published on this topic Justesen 1988; Justesen and Spalart 1990; Tanaka and Sana 1994; Sana and Tanaka 2000; and Sana and Shuy 2002. In most of these studies, a low Reynolds number k -  model has been utilized which has proved to be successful in the case of smooth oscillatory boundary layers. Menter 1994 proposed blended k -  models based on the fact that the k -  model performs better in the lower layer vis- cous and logarithmic regions than the k -  model, whereas in the upper layer wake region the k -  model is observed to perform better than the k -  model. Therefore, a blended model based on the governing equations of the k -  model in the lower layer and those of the k -  model transformed into k -  type equations would prove to be efficient. Another benefit in using this model would be the simplicity in the implementation of surface rough- ness in the model. Sana and Shuy 2002 have applied these blended k -  / k -  models to wave boundary layers on a smooth wall and found good agreement with the corresponding direct numerical simulation data. In order to study a rough boundary layer, generally a wall- function approach is employed, i.e., the high Reynolds number version of the k -  model is used with the wall boundary condi- tions specified at y 0 which is the cross-stream distance from the- oretical bed level to the zero-velocity location, taken as k s / 30, where k s is Nikuradse’s equivalent sand roughness. This approach has been successfully used for steady flow but in the case of oscillatory boundary layers, the flow is subjected to adverse pres- sure gradient during deceleration and an important assumption of isotropic eddy viscosity breaks down close to the wall during a part of the wave cycle. A brief list of numerical modeling studies on rough-wall wave boundary layers is shown in Table 1. Puleo et al. 2004 and Foti and Scandura 2004 utilized the k -  model and compared it with the experimental data of Test No. 13 by Jensen et al. 1989 for a rough-wall case. In the present study, the standard k -  model by Wilcox 1988 and two versions of blended k -  / k -  models proposed by Menter 1994 are applied to a rough oscillatory boundary layer. The experimental data of Test 12 by Jensen 1989 is used for comparison. The present study provides complementary infor- mation to that provided by Puleo et al. 2004 and Foti and Scandura 2004 by virtue of the choice of numerical models and the experimental data. The cross-stream profiles of mean velocity, turbulent kinetic energy, and Reynolds stress are presented. More- over, the time variation of wall shear stress is also plotted to elucidate the performance of different k -  model versions for rough-bed wave boundary layers. Governing Equations For a one-dimensional 1D oscillatory boundary layer, the equa- tion of motion may be expressed as 1 Assistant Professor, Dept. of Civil and Architectural Engineering, Sultan Qaboos Univ., P.O. Box 33, Al-Khod, Muscat 123, Sultanate of Oman corresponding author. E-mail: sana@squ.edu.om 2 Professor, Dept. of Civil Engineering, Univ. of Engineering and Technology, Taxila, Pakistan. 3 Professor, Dept. of Civil Engineering, Tohoku Univ., Sendai, Japan. Note. Discussion open until June 1, 2009. Separate discussions must be submitted for individual papers. The manuscript for this technical note was submitted for review and possible publication on June 22, 2007; approved on May 5, 2008. This technical note is part of the Journal of Hydraulic Engineering, Vol. 135, No. 1, January 1, 2009. ©ASCE, ISSN 0733-9429/2009/1-60–65/$25.00. 60 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JANUARY 2009 Downloaded 14 Jan 2009 to 130.34.82.160. Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright