Direct numerical simulations of second-order Stokes wave driven smooth-walled oscillatory channel: investigation of net current formation

ABSTRACT

In wall-bounded time-periodic flows, nonlinearity, associated with higher harmonic term(s) in velocity and/or acceleration outside the boundary layer, can significantly change the wall turbulence compared with that in the linear Stokes Boundary Layer. A significant feature of a nonlinear wall-bounded turbulent time-periodic flow is the formation of a net current which has not yet been mechanistically explained. This study investigates the effects of asymmetric velocity outside the boundary layer on wall turbulence and net current formation through Direct Numerical Simulations of a smooth-walled planar channel driven by the Second-order Stokes Wave. Simulation results suggest that net current characteristics depend on whether developed turbulence is present. When turbulence is developed, asymmetric viscous length scale is found to be the primary reason of the net current whereby a vertical offset between negative and positive Reynolds shear stress profiles, associated with forward and reverse flows, respectively, is created in a cycle. After averaging over a cycle, residual Reynolds shear stress, which drives the net current, is observed to be within the offset layer.

KEYWORDS:

• Boundary-layer turbulence
• asymmetric wave
• oscillatory flows

Acknowledgements

The simulations presented in this publication are conducted as a part of the graduate course entitled ‘CE 7701: High-performance Computing Applications of Environmental Flows.’ High-performance computational resources provided by the Louisiana State University (http://www.hpc.lsu.edu) is greatly acknowledged. The first author also acknowledges the support from the Louisiana Board of Regents (No. LESQF-RD-A-11) through research competitiveness subprogram.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Louisiana Board of Regents [grant number LEQSF-RD-A-11].