Robert J. Bialik

3D Lagrangian modelling of saltating particles diffusion in turbulent water flow

A 3D Lagrangian model of the saltation of solid spherical particles on the bed of an open channel flow, accounting for turbulence-induced mechanisms, is proposed and employed as the key tool of the study. The differences between conventional 2D models and a proposed 3D saltation model are discussed and the advantages of the 3D model are highlighted. Particularly, the 3D model includes a special procedure allowing generation of 3D flow velocity fields. This procedure is based on the assumption that the spectra of streamwise, vertical and transverse velocity components are known at any distance from the bed. The 3D model was used to identify and quantify effects of turbulence on particle entrainment and saltation. The analysis of particle trajectories focused on their diffusive nature, clarifying: (i) the effect of particle mobility parameter; (ii) the effect of bed topography; and (iii) the effect of turbulence. Specifically, the results of numerical simulations describing the abovementioned effects on the change in time of the variance are presented. In addition, the change in time of the skewness and kurtosis, which are likely to reflect the turbulence influence on the spread of particles, are also shown. Two different diffusion regimes (local and intermediate) for each of the investigated flow conditions are confidently identified.

Particle–particle collision in Lagrangian modelling of saltating grains

The effect of particle–particle collision on the trajectories of saltating grains in open-channel flows is investigated. The vertical distributions of saltating particles are also analysed. A stochastic particle–particle collision model was designed to determine the collision probability along a particle trajectory, based on the assumption that inter-particle collision frequency may be described by the formula of kinetic gas theory. This parameter is the key quantity for the calculation of collision probability. The Monte Carlo simulation method is used to obtain the velocity and concentration of saltating particles. It is the first attempt to apply a probabilistic inter-particle collision approach to Lagrangian modelling of saltating grains. Trajectories of different particles with and without particle–particle collision are compared with available data. The proposed procedure allows verification of the hypothesis regarding the effect of the particle–particle collision on sediment transport. The described mechanism affects the vertical particle concentration and therefore may play an essential role in bed-load sediment transport.

Numerical study of saltation of non-uniform grains

A theoretical model of non-uniform saltating grains in a turbulent open-channel flow based on the Lagrangian approach is developed. In the analysis described herein, a more realistic stochastic model of particle-bed collision is proposed. Based on geometrical considerations, new formulas for the minimum and maximum values of the angle of the collision surface with an irregular bed are derived. A Monte Carlo simulation of the distribution of saltating and colliding particles is introduced. Numerical simulations of possible particles trajectories with different sizes in an open-channel flow are presented. It is demonstrated that the particle-bed collision mechanism exactly depends on different particles sizes and the bed structure. Application for the analysis of the longitudinal saltating particle diffusion is presented, and the problem with the initial conditions in numerical simulations of particle motion is briefly described.

Bedform characteristics in natural and regulated channels: A comparative field study on the Wilga River, Poland

This paper presents results of a field investigation conducted to examine the bed sediment, riverbed morphology and flow structure over dunes in natural and regulated channels. Field measurements using an acoustic Doppler current profiler (ADCP) have been carried out on two parts of lowland Wilga River in Poland. It is shown that the bedforms with a low angle of lee side develop more frequently than asymmetrical dunes with high lee-side angles, which are mostly associated with the occurrence of local scours and river meanders. Wavenumber analysis of bed elevation confirms the existence of scaling region in the longitudinal wavenumber spectrum, with “−3” scaling exponents for the natural and regulated channels as well. Moreover, the results of flow velocity field are presented in the form of a 2-D streamwise-vertical vector field, showing several similarities to previous laboratory and field investigations conducted on much deeper rivers than the Wilga. The experimental campaign and methods used to obtain the results are also presented briefly. In addition, a short database of fluvial dunes statistics is provided.

Recent Deceleration of the Ice Elevation Change of Ecology Glacier (King George Island, Antarctica)

Glacier change studies in the Antarctic Peninsula region, despite their importance for global sea level rise, are commonly restricted to the investigation of frontal position changes. Here we present a long term (37 years; 1979–2016) study of ice elevation changes of the Ecology Glacier, King George Island ( 62 ∘ 11 ′ S, 58 ∘ 29 ′ W). The glacier covers an area of 5.21 km 2 and is located close to the H. Arctowski Polish Antarctic Station, and therefore has been an object of various multidisciplinary studies with subject ranging from glaciology, meteorology to glacial microbiology. Hence, it is of great interest to assess its current state and put it in a broader context of recent glacial change. In order to achieve that goal, we conducted an analysis of archival cartographic material and combined it with field measurements of proglacial lagoon hydrography and state-of-art geodetic surveying of the glacier surface with terrestrial laser scanning and satellite imagery. Overall mass loss was largest in the beginning of 2000s, and the rate of elevation change substantially decreased between 2012–2016, with little ice front retreat and no significant surface lowering. Ice elevation change rate for the common ablation area over all analyzed periods (1979–2001–2012–2016) has decreased from −1.7 ± 0.4 m/year in 1979–2001 and −1.5 ± 0.5 m/year in 2001–2012 to −0.5 ± 0.6 m/year in 2012–2016. This reduction of ice mass loss is likely related to decreasing summer temperatures in this region of the Antarctic Peninsula.

Diffusion of bedload particles in open-channel flows: distribution of travel times and second-order statistics of particle trajectories

The motion of bedload particles is diffusive and occurs within at least three scale ranges: local, intermediate and global, each of which with a distinctly different diffusion regime. However, these regimes, extensions of the scale ranges and boundaries between them remain to be better defined and quantified. These issues are explored using a Lagrangian model of saltating grains over the uniform fixed bed. The model combines deterministic particle motion dynamics with stochastic characteristics such as probability distributions of step lengths and resting times. Specifically, it is proposed that a memoryless exponential distribution is an appropriate model for the distribution of rest periods while the probability that a particle stops after a current jump follows a binomial distribution, which is a distribution with lack of memory as well. These distributions are incorporated in the deterministic Lagrangian model of saltating grains and extensive numerical simulations are conducted for the identification of the diffusive behavior of particles at different time scales. Based on the simulations and physical considerations, the local, intermediate, and global scale ranges are quantified and the transitions from one range to another are studied for a spectrum of motion parameters. The obtained results demonstrate that two different time scales should be considered for parameterization of diffusive behavior within intermediate and global scale ranges and for defining the local–intermediate and intermediate–global boundaries. The simulations highlight the importance of the distributions of the step lengths and resting times for the identification of the boundaries (or transition intervals) between the scale ranges.

Dissolved oxygen and water temperature dynamics in lowland rivers over various timescales

Abstract The impact of floodplain hydrology on the in-stream dissolved oxygen dynamics and the relation between dissolved oxygen and water temperature are investigated. This has been done by examining the time series of dissolved oxygen and water temperature coupled with meteorological and hydrological data obtained from two lowland rivers having contrasting hydrological settings. Spectral analysis of long-term oxygen variations in a vegetated river revealed a distinct scaling regime with slope ‘–1’ indicating a self-similar behaviour. Identical slopes were obtained for water temperature and water level. The same power-law behaviour was observed for an unvegetated river at small timescales revealing the underlying scaling behaviour of dissolved oxygen regime for different types of rivers and over various time scales. The results have shown that the oxygenation of a vegetated river is strongly related to its thermal regime and flow conditions. Moreover, analysis of short-term fluctuations in the unvegetated river demonstrated that physical factors such as rainfall and backwaters play a substantial role in the functioning of this ecosystem. Finally, the results show that the relation between water temperature and dissolved oxygen concentration at the diurnal timescale exhibits a looping behaviour on the variable plot. The findings of this study provide an insight into the sensitivity of rivers to changing hydro-physical conditions and can be useful in the assessment of environmental variability.

Wavelet Characteristics of Hydrological and Dissolved Oxygen Time Series in a Lowland River

In this study, we investigated the temporal variability of dissolved oxygen and water temperature in conjunction with water level fluctuations and river discharge in the Narew lowland river reach. For this purpose, high resolution hydrologic and water quality time series have been used. Spectral analyses of time series using continuous wavelet transform scheme have been applied in order to identify characteristic scales, its duration, and localisation in time. The results of wavelet analysis have shown a great number of periodicities in time series at the inter-annual time scale when compared to the classical Fourier analysis. Additionally, wavelet coherence revealed the complex nature of the relationship between dissolved oxygen and hydrological variables dependent on the scale and localisation in time. Hence, the results presented in this paper may provide an alternative representation to a frequency analysis of time series.

Lagrangian Modelling of Saltating Sediment Transport: A Review

One hundred years of research on the saltation in rivers, both experimental and numerical, has allowed for a fairly good improvement of our knowledge of the physics of the saltation process. Lagrangian modelling has played a huge role in this field and has made it possible to apply the knowledge obtained in the analysis of processes associated with the movement of sediment particles. The present paper briefly reviews the current state-of-the-art of the Lagrangian modelling of saltating grains in open channels and highlights recent findings in three areas in which employment of the Lagrangian models of saltation improve our understanding of sediment transport in rivers, namely: initial motion of saltating grains, diffusion of particles and calculation of the bedload transport rate. The particular challenges in all of these research areas are discussed and future ways forward are presented.

Application of Lattice Boltzmann Method for Generation of Flow Velocity Field Over River Bed-Forms

In this chapter a Lattice Boltzmann Method (LBM) was presented as a relatively simple tool for generation of flow velocity field over river sand waves. The special attention was paid to the way of discretization of the presented equations. The choice of this method was conditioned by its advantages for modeling of complex geometries. Moreover, the computations with use of this method are easy to parallelize in contrast to the widely used models. The numerical results were compared with the available laboratory data and a reasonable agreement was found among the mean fluid velocity over the stoss, crest and trough of the considered fixed, triangular dune.