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Turbulence in open-channel flows
Published in Springer Verlag
2014
Volume: 4
   
Pages: 95 - 187
Abstract
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 flow over a sediment bed. An application of Reynolds decomposition and time-averaging to the Navier–Stokes equations yields the Reynolds-averaged Navier–Stokes (RANS) equations, containing terms of Reynolds stresses. The RANS equations along with the time-averaged continuity equation are the main equations to analyze turbulent flow. The classical turbulence theories were proposed by Prandtl and von Kármán. Prandtl simulated the momentum exchange on a macro-scale to explain the mixing phenomenon in a turbulent flow establishing the mixing length theory, while von Kármán’s relationship for the mixing length is based on the similarity hypothesis. The velocity distribution in open-channel flow follows the linear law in viscous sublayer, the logarithmic law in turbulent 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 exhibits strong turbulence-induced secondary currents, and as a result, the maximum velocity appears below the free surface, known as dip phenomenon. Isotropic turbulence theory deals with the turbulent kinetic energy (TKE) transfer from the large-scale motions to smaller-scale motions 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 the anisotropic invariant mapping (AIM) and the anisotropy invariant function to quantify the degree of the departure from isotropy. Higher-order correlations are given by skewness and kurtosis of velocity fluctuations, TKE 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. © 2014, Springer-Verlag Berlin Heidelberg.
About the journal
JournalGeoPlanet: Earth and Planetary Sciences
PublisherSpringer Verlag
ISSN21905193