Dynamics Of Particle-laden Gravity Currents Propagating On Different Slopes In Stratified Environments

A gravity current is the flow driven by the density difference when two or more fluids zith similar specific gravity contact with each other.Gravity currents are frequently encountered in geophysical environments and engineering practices,such as reservoirs,lakes,estuaries,and oceans.However,it is still unclear how the ambient stratification,bed slope,and particle settling influence the dynamic behaviors,like evolution process,water entrainment,and energy budget.In this study,laboratory experiments,theoretical analysis,and direct numerical simulation(DNS)are carried out to investigate lock-exchange particle-free and particle-laden gravity currents iin stratified and unstratified environments on different slopes.The dynamic behaviors,including the front location,the front velocity,turbulent structures,the entrainment ratio,the energy budget,and the mechanism of long-distance propagation,are investigated in detail.The influence of stratified environment,slope angle,and sediment settling on the dynamics of the current is discussed.The dynamic mechanism and influence factors of the motion of the current are revealed.The main results and conclusions of this work are as follows:(1)By conducting PIV experiments and theoretical analysis,this study reveals the evolution process of lock-exchange downslope gravity currents in linearly stratified environments,pointing out that the ambient stratification has a damping effect on the evolution process.The propagation process of a lock-exchange gravity current down a slope in linearly stratified environments can be divided as an acceleration stage,a deceleration stage,and a separation stage during which the current leaves the slope and intrudes into the ambient environment horizontally.The ambient stratification would damp the turbulent structures and vorticities.A new set of analytical formulae is proposed to deterline the front velocity and the front location of the downslope current.Velocity profiles in the body part of the gravity current are well predicted by two equations with three fitted parameters obtained by using the present experimental data.An improved equation is proposed to predict the separation depth where the horizontal intrusion happens.(2)A mathematical model to describe the evolution process of lock-exchange gravity currents in different environments is established based on DNS and two-component material transport equation.The initially discontinuous concentration field at the intertace is smoothed by solving a Heaviside function with the Level-set method to prevent numerical instabilities.The third-order QUICK and the six-order UCCD schemes are implemented to approximate the governing equations.An immersed boundary method is applied to handle the complex bottom topography.The present model can precisely capture the temporal and spatial variations ot turbulent structures and concentration fields during the evolution of the current.(3)Based on the DNS model,this study investigates particle-laden gravity currents down a slope in uniform ambient water,and reveals the influencing mechanism.Between the rapid acceleration stage and the deceleration stage,the front velocity gradually changes from a slight decrease to increase with a greater slope angle.The critical slope is about 10°.A dynamic reference plane is proposed to describe the energy budget.The normalized potential energy continuously decreases.The normalized kinetic energy tends to sharply increase tirst.then remain nearly constant,and finally decrease.The water entrainment effect is most dominant at the very beginning due to the collapsing effect.The bed slope has a non-linear effect on the bulk entrainment ratio.The entrainment ratios barely change with the settling velocity of the suspended particle.(4)Based on the DNS model,this study illustrates the dynamics of particle-laden gravity currents in differently ambient stratifications and the influence mechanism.The sedimentation of suspended particles means that a particle-laden gravity current quickly loses momentum.Consequently,the propagation distance ot the near-constant state of the particle-laden current on a flat bed cannot be maintained to 10 lock lengths.After the acceleration stage,stratifhcation can decrease the entrainment ratio between a particle-free gravity current and the ambient water.Howexver,the entrainment ratio of a particle-laden gravity current barely changes with ambient stratitications because the suppression of ambient stratification on water entrainment is compromised by the enhancement of suspended particle settling on entrainment.During the evolution of a particle-laden current,the conversion of potential to kinetic energy is suppressed by ambient stratification,and the conversion of kinetic energy to dissipated energy is accelerated by particle settling.At the acceleration stage of particle-laden gravity currents down a slope in a linearly stratified environment,the slope angle,the settling velocity,and ambient stratification are found to have little influence on the front velocity.In the deceleration stage,a weaker stratification and a smaller settling velocity bring a larger front velocity.By considering the density decrease due to particle sedimentation and water entrainment,the numerical model can precisely predict the separation process of the cun'ent at the neutral level.At the separation stage,the main mechanism determining the entrainment ratio is the horizontal intrusions at different depths,which significantly increase the entrainment effect between the current and the ambient water.(5)This study provides a new perspective on the transition of hyperpycnal flows into saline particle-laden currents at estuaries,which permits longer runout lengths than might be otherwise expected.The new mechanism relies on the differential turbulent diffusion of salt and sediment,and in contrast to albient saltwater entrainment it enables the salinification of the freshwater current without diluting the sediment concentration field by a corresponding amount.Consequently,the bulk density of the current increases and the sediment can be kept suspended,which make the current have the potential to propagate for a longer distance.