Turbulence in Open-Channel Flows

The turbulence in a fluid flow is characterized by irregular and chaotic motion of fluid particles. It is a complex phenomenon. In this chapter, the turbulence characteristics are discussed with reference to the flow over a sediment bed. An application of Reynolds decomposition[aut]Reynolds decomposition and time-averaging to theStokes, G. G., Navier–Stokes equations yields the Reynolds-averaged Navier–Stokes (RANS) equations[aut]Reynolds averaged Navier-Stokes (RANS) equationsRANS equations, containing the terms of Reynolds stresses. The RANS equations along with the time-averaged continuity equation are the main equations to analyze the turbulent flow[aut]Turbulent flow. The classical turbulence theories were proposed by PrandtlPrandtl, L., and von KármánVon Kármán, T.,. PrandtlPrandtl, L., simulated the momentum exchange on a macro-scale to explain the mixing phenomenon in a turbulent flow[aut]Turbulent flow establishing the mixing length[aut]Mixing length theory, while von Kármán’sVon Kármán, T., relationship for the mixing length[aut]Mixing length is based on the similarity hypothesis. The velocity distribution in an open-channel flow follows the linear law[aut]Velocity distributionlinear law in viscous sublayer in viscous sublayer[aut]Flow layersviscous sublayer, the logarithmic law in turbulent wall-shear layer[aut]Flow layersturbulent wall-shear layer, and the wake law in the outer layer. The determination of bed shear stress is always a challenging task. Different methods for the determination of bed shear stress are discussed. Flow in a narrow channel[aut]Dip phenomenonnarrow channel exhibits strong turbulence-induced secondary currents, and as a result, the maximum velocity appears below the free surface, known as the dip phenomenon. Isotropic turbulence theory deals with the turbulent kinetic energy (TKE) transfer from the large-scale motions to smaller scale until attaining an adequately small length scale so that the fluid molecular viscosity can dissipate the TKE into heat. Anisotropy in turbulence is analyzed by mainly the anisotropic invariant mapping (AIM)[aut]Anisotropyanisotropic invariant map (AIM) and by some other methods to quantify the degree of the departure from an isotropic turbulence. Higher-order correlations are given by skewness[aut]Higher-order correlationsskewness and kurtosis of velocity fluctuations, TKE flux[aut]Turbulent kinetic energyTKE flux, and budget. This chapter also includes most of the modern development of turbulent phenomena, such as coherent structures and burst phenomena, and double-averaging of heterogeneous flow over gravel beds.