Włodzimierz Czernuszenko

Properties of the dead-zone model of longitudinal dispersion in rivers

The dead zone equations were solved with the use of the Laplace transform technics. The solution was a base to derive the three moments of the pollution concentration distribution in a river. They differ from the moments published so far, because they were calculated from the solution of the pure boundary problem. This approach is easier to apply in calculations of the pollution concentration distributions and it covers a wider range of cases when we deal with natural field data. Main features of the model equations were analysed from the point of view of the theory of dynamic systems. The transfer function was derived and analysed as well as the frequency-response function. The dispersion relation for the dead zone equations was also obtained and analysed for different parameters of the model.

Experimental and numerical validation of the dead-zone model for longitudinal dispersion in rivers

Experimental results of longitudinal dispersion in rivers are discussed in the light of new findings with respect to the “dead-zone” theory. Both the experiments made by authors as well as some literature results are taken into consideration. The dead-zone model parameters, namely the relative dead-zone volume, penetration time of the tracer into dead-zones, constant mean flow velocity and dispersion coefficient, are obtained with the use of the nonlinear least square technique applied to the image functions of concentration time-distributions. The statistical moments of the concentration time distributions as functions of distance are also analyzed. Expressions for statistical moments, recently obtained by authors, are found to agree well with both experimental and computational results.

Water quality hazards and dispersion of pollutants

Mixing Models for Water Quality Management in Rivers: Continuous and Instantaneous Pollutant Releases.- Three-Dimensional Model of Flow and Mixing Processes in Open Channels.- Horizontal Mixing in Shallow Flows.- On the Theoretical Prediction of Longitudinal Dispersion Coefficients in a Compound Channel.- Application of a Transient Storage Model to Meandering Channel Studies of Solute Transport and Dispersion.- Experimental Study of Travel Times in a Small Stream.- Migration of Floating Particles in a Compound Channel.- Persistence of Skewness of Concentration Distribution.- Moments and Analytical Solution of Coupled Equation Describing Transport of Pollutants in Rivers.- Influence of Hyporheic Exchange on Solute Transport in a Highly Hydropower Regulated River.- Models of Hyporheic Contamination by Non Reactive Solutes, Metals and Colloids.- The Flow in Groyne Fields.

Modeling of three-dimensional velocity field in open channel flows

A comparatively simple model for calculation of the three-dimensional, stationary velocity field is presented. The model is able to calculate the streamwise velocity distribution as well as the secondary flow in a cross-section of regular channel. The Reynolds equations are closed by a new anisotropic turbulence model which consists of two sub-models: one for the shear stresses and the other for normal stresses. The numerical solution of the parabolic approximation of the model equations gives reasonably good secondary flow patterns as well as the longitudinal velocity distribution in the channel cross-section.

Some Properties of Lagrangian Modeling of Saltating Grains Over Movable Bed

The two-dimensional Lagrangian model of saltating grains is developed to simulate the particles’ movement over movable bed and for provision of some properties of this kind of modeling. Stochastic method of the particle’s collision with the channel bed is applied to identify and quantify the effects of the so-called cohesion coefficient on the particles behavior. The relationships between this coefficient and the coefficients of friction, restitution and an angle of collision are also presented. It is shown that the cohesion coefficient may be used to determinate the amount of momentum transferred by moving particles to the bottom and vice versa and controlling of its value may allow for the calculation of the velocity of moving bed.

Numerical Verification of Log-Law in Flows with Pressure Gradient

The chapter deals with 3D rough turbulent flows with pressure gradient in a straight open channel with regular bed roughness. The bed of the channel is characterized by roughness elements which are supposed to be uniform in size and form a regular surface of the bed. Turbulence structure above viscous sub-layer for such a roughness type is assumed to be homogenous in horizontal plane. Due to numerous experiments, this type of flow with zero pressure gradient is known to match the logarithmic law (log-law). So a question arises if it can be extended to flows with non-zero pressure gradient, and second, what are parameters of the log-law. An open channel turbulent flow is described by the Reynolds equations with simple turbulent model, which has eddy viscosities described by an enhanced mixing length hypothesis. The Reynolds equations with the continuity equation for steady, parabolic 3D turbulent flow in an open channel are solved for accelerating and decelerating flows. For these types of flow the additive parameter \(B\) of the log-law is calculated and results are discussed.