Claudia Adduce

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...

Mixing in a density-driven current flowing down a slope in a rotating fluid

We discuss laboratory experiments investigating mixing in a density-driven current flowing down a sloping bottom, in a rotating homogenous fluid. A systematic study spanning a wide range of Froude, 0.8 <F r <10, and Reynolds, 10 <R e <1400, numbers was conducted by varying three parameters: the bottom slope; the flow rate; and the density of the dense fluid. Different flow regimes were observed, i.e. waves (non-breaking and breaking) and turbulent regimes, while changing the above parameters. Mixing in the density-driven current has been quantified within the observed regimes, and at different locations on the slope. The dependence of mixing on the relevant non-dimensional numbers, i.e. slope, Fr and Re ,i s discussed. The entrainment parameter, E, was found to be dependent not only on Fr , as assumed in previous studies, but also on Re. In particular, mixing increased with increasing Fr and Re. For low Fr and Re, the magnitude of the mixing was comparable to mixing in the ocean. For large Fr and Re, mixing was comparable to that observed in previous laboratory experiments that exhibited the classic turbulent entrainment behaviour.

A new parameterization for entrainment in overflows

Abstract Dense overflows entrain surrounding waters at specific locations, for example, sills and constrictions, but also along the descent over the continental slope. The amount of entrainment dictates the final properties of these overflows, and thus is of fundamental importance to the understanding of the formation of deep water masses. Even when resolving the overflows, coarse resolution global circulation and climate models cannot resolve the entrainment processes that are often parameterized. A new empirical parameterization is suggested, obtained using an oceanic and laboratory dataset, which includes two novel aspects. First, the parameterization depends on both the Froude number (Fr) and Reynolds number of the flow. Second, it takes into account subcritical (Fr < 1) entrainment. A weak, but nonzero, entrainment can change the final density and, consequently, the depth and location of important water masses in the open ocean. This is especially true when the dense current follows a long path over ...

Analysis of lock-exchange gravity currents over smooth and rough beds

Gravity currents produced by full-depth lock-release of saline water into a fresh water tank are studied focusing on the influence of the initial density of the saline mixture in the lock and the bed roughness on gravity current kinematics. Temporal evolution of the current front position and front velocity are analysed and related to different phases of the current. Time–space evolution of current depth-averaged density and current height are assessed as well. Roughness of the channel bed plays an important role in the current kinematics, particularly in decreasing the front velocity due to extra drag at the bed. The analysis of Froude numbers, estimated with the initial and local reduced gravity and established with different length scales of the current, allow for the definition of the important variables and current dynamics of each phase of the current development.

Entrainment and mixing in unsteady gravity currents

ABSTRACT Entrainment and mixing in lock-exchange gravity currents are investigated by large eddy simulations. Nine cases are analysed, varying the initial excess density driving the motion and the aspect ratio r of the initial water depth to the lock length. Laboratory experiments are also performed and a fair agreement between numerical simulations and measurements is found. Mixing between the gravity current and the ambient fluid, in both the slumping and self-similar phases, is studied for a range of entrainment parameters, gravity current fractional area and using an energy budget method. The entrainment is found to increase as r decreases. The occurrence of irreversible mixing is detected during the entire development of the flow, i.e. both in the slumping and self-similar phases. A higher amount of mixing is observed as r decreases and the initial excess density increases.

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

Image analysis technique applied to lock-exchange gravity currents

An image analysis technique is used to estimate the two-dimensional instantaneous density field of unsteady gravity currents produced by full-depth lock-release of saline water. An experiment reproducing a gravity current was performed in a 3.0 m long, 0.20 m wide and 0.30 m deep Perspex flume with horizontal smooth bed and recorded with a 25 Hz CCD video camera under controlled light conditions. Using dye concentration as a tracer, a calibration procedure was established for each pixel in the image relating the amount of dye uniformly distributed in the tank and the greyscale values in the corresponding images. The results are evaluated and corrected by applying the mass conservation principle within the experimental tank. The procedure is a simple way to assess the time-varying density distribution within the gravity current, allowing the investigation of gravity current dynamics and mixing processes.