Turbulence characteristics in open-­‐channel flows with highly rough beds.

Abstract

River motion is one of the most attractive and fascinating phenomena in nature. Since ancient times many scientists have been drawn into a vortex of confusion observing river motion. Flow observation is often simplified, running tests in a laboratory under controlled conditions, in order to test a specific phenomenon of a much more complex issue. A great number of these phenomena has been collected by researchers throughout the history of science, and other researchers have tried to merge the available knowledge to clarify the tangled phenomena. This work is focused on the turbulent characteristics of Open-Channel Flows (OCFs) over a highly rough bed. The use of coarse sediments is an attractive technique to solve many problems in rivers as well as to safeguard aquatic life. Issues like sediment transport phenomena or erosion and local scour, e.g. at bridge piers and abutments, can be counteracted by introducing coarse sediments. In this work the bed roughness effect on the turbulence characteristics of the flow is investigated through the relative submergence parameter Δ, which is the ratio between the roughness characteristic dimension and the water depth. Most of the theories and literature works has been developed for smooth-wall flows and rough-bed flows at very high relative submergence, whereas its applicability in OCFs with low relative submergence remains questionable; the simplest example is the velocity distribution (i.e., the universal logarithmic law). This thesis aims at improving the knowledge of turbulence structure developed over a highly rough bed in OCFs by varying the relative submergence. According to the relative submergence definition given before, it can be changed by modifying the water depth for a fixed roughness or varying the roughness keeping the water depth constant. The choice settled on the second strategy, because of the measurement instrument configuration. It will be described in detail in the chapter “Experimental equipment and procedures”. The relative submergence varied in the range from 3.13 to 10.07. Three long-duration experiments (each one with a given coarse sediment size) were performed in uniform flow conditions by using a 100 Hz ADV down-looking probe, in order to record the 3D velocity vector in each point of a given grid of measurements. The contribution of the Reynolds stress, the viscous and the form-induced shear stress was analysed, as well as the averaged velocity profiles, second- and third-order moments . A statistical tool will be proposed to verify the frozen-in Taylor hypothesis by comparing two typical time-scales, namely the large scale advection time and the characteristic nonlinear time. The proposed method based on the characteristic eddies timescales is more restrictive with respect to the classic frozen-in Taylor hypothesis, in which a simple comparison of the flow velocity and the fluctuation magnitude is made. Furthermore, one-point temporal correlations analysis will be performed in order to give a first indication of the integral scales lengths along the channel varying the relative submergence. Spectral analysis is introduced both in the frequency and in wavenumber domain. In experimental practice it is quite hard to obtain direct measures, which can allow computing directly a wavenumber spectrum. Temporal velocity signals are commonly recorded in a single point, and they are used to compute the frequency spectrum and then converted to wavenumber spectrum through the Taylor frozen-in hypothesis. Hence, the k−5/3 slope is investigated in the longitudinal velocity spectra. k is the wavenumber. Spectral analysis will be introduced in order to test the observed k−5/3 slope, in order to confirm that the inertial subrange is well visible at the investigated Re numbers. Furthermore, the validity of the −5/3 scaling region will be also tested by using the third-order longitudinal velocity structure function, which is expressed as a function of the turbulent kinetic energy (TKE) dissipation rate. The third-order longitudinal velocity structure function will be also used to provide an estimate of the magnitude of the TKE dissipation rate. In addition, in order to quantify the energy contribution of different eddyscales, premultiplied spectra will be employed. Thanks to this analysis, the Large Scales (LSs) and the Very Large Scale (VLSs) will be investigated. These scales will be associated with a characteristic wavenumber and intensity. ADV velocity measurement also allows exploring the longitudinal-vertical velocity co-spectra. In order to locate the normalized wavenumber associated with the peak in the premultiplied spectra, a systematic procedure to find the correct position of the peaks based on the center of mass concept will be proposed. Moreover, the peak distribution over the water depth will be plotted in inner and outer coordinates.