Turbulent open channel flow with heat transfer subjected to the control of a spanwise travelling wave

Turbulent open channel flows with heat transfer subjected to the control of a spanwise travelling wave have been investigated by means of direct numerical simulation (DNS). The three-dimensional Navier–Stokes and energy equations are numerically solved using a fractional-step method. The spanwise travelling wave is induced by a body force that is confined within the viscous layer with its maximum at the bottom wall and decaying exponentially away from it. The objective of this study is to reveal the near-wall turbulence behaviours, the turbulent heat transfer, and thermal structures under the control of the spanwise travelling wave. Three typical frequencies of the spanwise travelling wave, i.e., high-, middle- and low-frequency, corresponding to the exciting periods at T+ = 25, 50 and 100, are investigated to reveal the dynamics of turbulent motions and heat transfer. The Prandtl number (Pr) varies from 1 up to 100. To elucidate the behaviours of turbulence statistics and heat transfer, some typical quantities, including the mean velocity, velocity and vorticity fluctuations, temperature and its fluctuation, turbulent heat fluxes, and the structures of the temperature fluctuation, are exhibited and analyzed.