The objectives of research project are to study the turbulent structures and passive scalar transport (in the form of heat flux) in oscillatory plane Couette flow at Reynolds number equal to 5,000 by solving the unsteady incompressible Navier-Stokes equations with direct numerical simulation.

Plane Couette flow is the basic underlying flow of many mechanical systems such as hydrodynamic lubrication. It involves the flow of a fluid sandwiched between two plane rigid walls, where the flow is forced by one of the walls moving in its own plane.  When the flow is steady (i.e., the wall moves at a constant speed), the velocity profile is always monotonous and the shear stress distribution is constant across the channel, irrespective of the flow being laminar or turbulent.  In the steady case, turbulent plane Couette flow can be conveniently solved by assuming the classical log-laws to hold locally near the walls.  In sharp contrast, no simple analyses will come by when the flow becomes unsteady, as in the case when one of the walls oscillates periodically with time in its own plane.  Difficulties arise owing to the time-dependent accelerating terms in the Navier-Stokes equations. The oscillatory boundary may lead to periodic flow reversal and therefore detachment of the boundary layer from the wall. The classical theory of wall turbulence no longer applies here, and the problem can be solved only through some well-devised numerical computation. To this end, a contemporary numerical technique, known as the direct numerical simulation (DNS) will be adopted in this work.  DNS is computationally intensive and resources demanding, but it is free from empirical closure hypotheses. Results generated by a good quality DNS are usually highly regarded by the research community.

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