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Turbulence laws in natural bed flows

Published online by Cambridge University Press:  06 June 2016

Domenico Ferraro ,
Sergio Servidio ,
Vincenzo Carbone ,
Subhasish Dey  and
Roberto Gaudio
Domenico Ferraro*
Affiliation:
Dipartimento di Ingegneria Civile, Università della Calabria, 87036 Rende (CS), Italy
Sergio Servidio
Affiliation:
Dipartimento di Fisica, Università della Calabria, 87036 Rende (CS), Italy
Vincenzo Carbone
Affiliation:
Dipartimento di Fisica, Università della Calabria, 87036 Rende (CS), Italy
Subhasish Dey
Affiliation:
Department of Civil Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India
Roberto Gaudio
Affiliation:
Dipartimento di Ingegneria Civile, Università della Calabria, 87036 Rende (CS), Italy
*
†Email address for correspondence: domenico.ferraro@unical.it
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Abstract

Characterization of turbulence in natural bed streams is one of the most fascinating problems of fluid dynamics. In this study, a statistical description of turbulence in a natural pebble bed flow is presented applying the laws of turbulence. A laboratory experiment was conducted to measure the three-dimensional instantaneous velocity components in a flow over heterogeneous coarse sediments that simulated a natural bed. The analysis reveals that the spectra (in Fourier space) show a power-law scaling, $E(k)\sim k^{{\it\alpha}}$, suggesting the presence of inertial range turbulence. The exponent ${\it\alpha}$ is slightly shallower than the Kolmogorov $5/3$ scaling law, with this deviation possibly due to the bed roughness heterogeneity and to fluctuation anisotropy. The Taylor frozen-in approximation is broken at smaller scales towards the roughness crest level; therefore, a new statistical tool for the validation of this approximation is proposed. The Kolmogorov $4/5$-law for the longitudinal increments and simultaneously the Monin–Yaglom $4/3$-law for the nonlinear normal fluxes (both in physical space) are preserved, providing an accurate estimation of the turbulent kinetic energy dissipation rate. The heterogeneity of the bed acts to induce the transport of finite kinetic helicity to the outer layer through persistently prolonged vortices. An associated $2/15$-law for the cascade of helicity has been locally found. These findings open a new direction in turbulence research for flows over highly rough beds.

JFM classification

Turbulent Flows: Shear layer turbulence Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
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Journal of Fluid Mechanics , Volume 798 , 10 July 2016 , pp. 540 - 571
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© 2016 Cambridge University Press 

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