Giampiero Sciortino

Gravity Currents Produced by Lock Exchanges: Experiments and Simulations with a Two-Layer Shallow-Water Model with Entrainment

This paper presents the investigation of gravity currents by both laboratory experiments and a mathematical model. Eleven lock-exchange experiments, in which lock position, the initial current height, and density varied, were carried out to test the model validity and to compare laboratory results with previous expressions found in the literature. A two-layer shallow-water model was used to simulate all the runs. This model is new if compared with previous shallow-water models used to simulate gravity currents, because it accounts for both the entrainment and the free surface. A modified Turners formula is used to model the entrainment between the two fluids. The developed shallow-water models with and without entrainment are also compared, showing a better agreement when mixing is accounted for. Also, the effect of the free surface is shown by comparing the developed two-layer shallow-water model with a free surface and two different single-layer models with a rigid-lid approximation. Laboratory experiments and model simulations, accounting for both the entrainment and the free surface, are in good agreement. Front velocities, measured during the slumping phase, were compared with both predicted ones and previous expressions found in the literature, showing in most of the cases better result when the developed model is used. DOI: 10.1061/(ASCE)HY.1943-7900.0000484.

Experimental and numerical simulation of three-dimensional gravity currents on smooth and rough bottom

The dynamics of a three-dimensional gravity current is investigated by both laboratory experiments and numerical simulations. The experiments take place in a rectangular tank, which is divided into two square reservoirs with a wall containing a sliding gate of width b. The two reservoirs are filled to the same height H, one with salt water and the other with fresh water. The gravity current starts its evolution as soon as the sliding gate is manually opened. Experiments are conducted with either smooth or rough surface on the bottom of the tank. The bottom roughness is created by gluing sediment material of different diameters to the surface. Five diameter values for the surface roughness and two salinity conditions for the fluid are investigated. The mathematical model is based on shallow-water theory together with the single-layer approximation, so that the model is strictly hyperbolic and can be put into conservative form. Consequently, a finite-volume-based numerical algorithm can be applied. The Godu...

A fully nonlinear model for sloshing in a rotating container

In this paper a theoretical and experimental analysis of sloshing in 2D and 3D free-surface configurations is performed. In particular, the case of a tank rotating around a horizontal axis has been considered. The fluid is assumed to be incompressible and inviscid. A fully nonlinear mathematical model is defined by applying the variational method to the sloshing. The damping of gravity waves has been accounted by introducing a suitable dissipation function from which generalized dissipative forces are derived. A modal decomposition is then adopted for the unknowns and a dynamical system is derived to describe the evolution of the physical system. An experimental technique has been applied to select the leading modes, whose evolution characterizes the physical process, i.e. captures the most of the kinetic energy of the process. A very good agreement between experimental and numerical results confirms the validity of the methodological approach followed.

Gravity currents flowing upslope: Laboratory experiments and shallow-water simulations

This paper investigates the dynamics of lock-release gravity currents propagating upslope by laboratory experiments and shallow-water simulations. Both the interface between the dense and the ambient fluid and the instantaneous velocity field were measured by image analysis. Different runs were carried out by varying the initial density of the lock fluid and the bed upslope. As a gravity current moves upslope, the dense layer becomes thinner, and an accumulation region of dense fluid in the initial part of the tank occurs. The current speed decreases as the bed upslope increases, and for the highest up sloping angles, the gravity current stops before reaching the end of the tank. A new two-layer shallow-water model is developed and benchmarked against laboratory experiments. The present model accounts for the mixing between the two layers, the free surface, and the space-time variations of the density. The effect of the horizontal density gradient in the simulation of gravity currents is investigated by c...

A two-layer shallow water model for 3D gravity currents

A two-layer, shallow-water model for three-dimensional (3D) gravity currents is proposed. The formulation results from the shallow-water-equations for two layers of immiscible liquids, subjected by the rigid-lid condition, so that the upper surface of the lighter layer remains perfectly flat during the motion. The arising pressure must be determined by solving the equations of motion, which is no problem for two-dimensional and axisymmetric gravity currents because the pressure is easily eliminated. In 3D gravity currents, the pressure is determined by solving a Poisson equation, together with momentum and mass balance equations. By means of a suitable scaling and a perturbation expansion, the equations are uncoupled from each other so that the problem is considerably simplified. Numerical results are compared with 3D lock-exchange release experiments. A comparison between numerical and experimental results of the gravity current indicates a fairly good agreement, whereas the results concerning the upper layer field variables shows that the numerical results are consistent with the experiments.

Scour due to a horizontal turbulent jet : Numerical and experimental investigation

In this paper both numerical and experimental investigations of local scour downstream of a sill followed by a rigid apron are presented. Nine laboratory experiments were carried out in clear water scour conditions, with different values of discharge. At the end of each run, velocity measurements both on the apron and on the scour hole were performed by ultrasonic Doppler velocimetry. A mathematical-numerical model was developed, simulating local scour downstream of a sill followed by an apron. The model uses information related both to the measured velocity fields and to the physical and mechanical properties of the sand constituting the mobile bed. The mathematical structure of the model consists of a second order partial differential parabolic equation whose unknown is the shape of the mobile bed. The numerical integration of this nonlinear equation, with suitable boundary conditions, is in agreement with the measured scour profiles at the end of the run. Upon comparing experimental and numerical data, a similar temporal evolution of the maximum scour depth is observed

Experimental and theoretical investigation on the sloshing of a two-liquid system with free surface

In this paper a theoretical and experimental investigation is performed on the sloshing of a two-liquid system with both separation and free surface. The experimental configuration consists of an oscillating tank filled with two layers of immiscible liquids. The mathematical model is obtained by applying the Lagrangian variational approach to the potential formulation of the fluid motion, and a dynamical system which describes the dynamics of motion is derived. In order to account for the damping of the motion, generalized dissipative forces are considered. For this purpose, the logarithmic decrement coefficients are estimated by means of a wavelet analysis performed on the experimental free oscillations of the fluid system. Numerical integration of the mathematical model gives results which are in a fair agreement with the experimental results.

Interfacial gravity waves in a two-fluid system

Abstract In this work a theoretical and experimental investigation is performed on the sloshing of two immiscible liquid layers inside of a closed square-section tank. By applying a variational approach to the potential formulation of the fluid motion, a nonlinear dynamical system is derived applying the Lagrange equations to the Lagrangian of motion defined in terms of suitable generalised coordinates. These coordinates are the time depending coefficients of the modal expansions adopted for the separation surface of the two fluids and for the velocity potentials of the fluid layers. Dissipative effects are taken into account by considering generalised dissipative forces derived by a dissipative model extensively treated in the paper. Numerical integration of the dynamical system furnish solutions which well reproduce the examined experimental configurations.

On the effect of the intrinsic viscosity in a two-layer shallow water lattice Boltzmann model of axisymmetric density currents

In this work, a numerical assessment of the suitability of a Single Relaxation Time (SRT) Lattice Boltzmann Method (LBM) model to simulate axisymmetric gravity currents is carried out. The model results are compared with both experimental data and other numerical models. The particular SRT formulation employed is known to converge, in the limit of low Knudsen number, to the two-layer 2D Shallow Water Equations (SWEs) set with a viscosity term featuring a closed theoretical formulation. Even with the lowest viscosity achievable by the method, its effect is shown to become important in most of the cases analysed, thus posing some serious constraints on possible application of the single relaxation time LBM method to simulate the lock-release generated-type gravity currents analysed here. The comparison with classical numerical models shows that the the viscous effects in the LBM model can be well reproduced employing coefficients derived from the above-mentioned theoretical formulation.

Modified Einstein Sediment Transport Method to Simulate the Local Scour Evolution Downstream of a Rigid Bed

AbstractThe present study consists of a new mathematical-numerical modeling formulation to simulate the spatial and temporal scour development downstream of a rigid bed for both a noncohesive sediment bed and a cohesive sediment mixture with relatively small percentage of cohesive material. Laboratory tests were conducted in a rectangular tilting flume having a recessed box filled with the selected bed sediments and placed downstream of a rigid rough bed. The scour pattern was accurately acquired with a three-dimensional laser scanner at various time instants. The numerical code was calibrated through the scour profile data obtained under steady-state flow condition and then validated on the basis of scour patterns acquired under both steady and unsteady flow conditions (symmetric and asymmetric hydrographs). Contrary to most previous studies conducted with an issuing jet, the present study’s experiments were performed under non–strictly uniform flow conditions. The numerical model utilized information co...