Lock-exchange Gravity Currents Research Articles

Head-on collision of gravity currents of unequal strengths: Large-eddy simulations and laboratory experiments

The collision of two counterflowing gravity currents with unequal strengths was investigated through large-eddy simulations and laboratory experiments. The collisions were initiated by releasing currents from two partial-depth locks at identical heights but with different densities, characterized by the reduced gravity ratio, γg. By varying γg, we elucidate the transport processes of colliding gravity currents, spanning from comparable driving strengths (γg=1.0) to markedly disparate driving strengths (γg≪1). Three distinct regimes of colliding gravity currents were identified based on kinematic features derived from integrated measures. For γg≥0.92, the collisions are driven by counterflowing gravity currents with comparable driving strengths, leading to nearly symmetrical collisions with negligible impact on evolved flow patterns. In the intermediate regime when 0.4<γg<0.92, the collisions are weakly asymmetric, characterized by differing contact surface steepness and insensitive maximum vertical displacement of ascending motions to γg. For γg≤0.4, strongly asymmetric collisions dominate, featuring minimal vertical convective fluxes in the collision region rather than typical colliding currents. In this flow regime, the denser fluid mass intrudes beneath the less dense one, akin to the propagation of intrusive lock-exchange gravity currents. Additionally, mixing rates over the entire flow domain were quantified using background potential energy calculations. The results reveal that intense diapycnal mixing is predominantly driven by stirring processes before collision, with the mixing rate increasing as γg decreases. From the collision stage onward, currents with the gain of inertia converge within the collided region and move upward with the distinct opposite effect of negative buoyancy. Notably, the mixing rate stabilizes regardless of convective process variations and decreases consistently as the currents slump away from the collision region.

Uncertainty of propagation and entrainment characteristics of lock-exchange gravity current

Uncertainty of propagation and entrainment characteristics of lock-exchange gravity current

Graphics processing unit accelerated lattice Boltzmann method simulations of dilute gravity currents

Lattice Boltzmann method models offer a novel framework for the simulation of high Reynolds number dilute gravity currents. The numerical algorithm is well suited to acceleration via implementation on massively parallel computer architectures. Here, we present two lattice Boltzmann method models of lock-exchange dilute gravity currents in which the largest turbulent length scales are directly resolved. The three-dimensional simulations are accelerated by exporting computations to a graphics processing unit and are validated against experiments and high-resolution simulations for Reynolds numbers up to 30 000. The lattice Boltzmann method models achieve equivalent accuracy to conventional large-eddy simulation models in the prediction of key flow properties. A conservative analysis of computational performance relative to conventional methods indicates that the presented framework reduces simulation times by two orders of magnitude. Therefore, it can be used as a foundation for the development of depth-resolving models that capture more of the complexity of environmental gravity currents.

Diapycnal mixing efficiency in lock-exchange gravity currents

An experimental measure of irreversible mixing efficiency, $R\phantom{\rule{0}{0ex}}{i}_{f}^{*}$, for a lock-exchange gravity current is presented. The results show that mixing efficiency increases and is sustained in the presence of strong stratification provided the flow energy is high. Following this, various turbulence regimes are mapped based on turbulent Froude number and turbulent Reynolds number. Additionally, $R\phantom{\rule{0}{0ex}}{i}_{f}^{*}$ is shown to have a strong dependence on turbulence regime and molecular effects induced by Prandtl number.

Gravity currents over fixed beds of monodisperse spheres

Abstract

Energetics and mixing efficiency of lock-exchange gravity currents using simultaneous velocity and density fields

A series of laboratory experiments on energy conserving gravity currents in a lock-exchange facility are conducted for a range of Reynolds numbers, $Re= \frac{U_Fh}{\nu} =$ 485-12270. The velocity and density fields are captured simultaneously using a PIV-PLIF system. A moving average method is employed to compute the mean field and a host of turbulence statistics, namely, turbulent kinetic energy ($K$), shear production ($P$), buoyancy flux ($B$), and energy dissipation ($\epsilon$) during the slumping phase of the current. The subsequent findings are used to ascertain the quantitative values of mixing efficiency, $Ri_{f}$, Ozmidov length-scale ($L_O$), Kolmogorov length-scale ($L_\kappa$), and eddy diffusivities of momentum ($\kappa_m$) and scalar ($\kappa_\rho$). Two different forms of $Ri_{f}$ are characterized in this study, denoted by $Ri_{f}^I=\frac{B}{P}$ and $Ri_{f}^{II}=\frac{B}{B+\epsilon}$. The results cover the entire diffusive regime (3 $<Re_b<$ 10) and a portion of the intermediate regime (10 $<Re_b<$ 50), where $Re_b=\frac{\epsilon}{\nu N^2}$ is the buoyancy Reynolds number that measures the level of turbulence in a shear-stratified flow. The values of $P$, $B$, and $\epsilon$ show a marked increase at the interface of the ambient fluid and the current, owing to the development of a shear-driven mixed layer. Based on the changes in the turbulence statistics and the length scales, it is inferred that the turbulence decays along the length of the current. The mixing efficiency monotonically increases in the diffusive regime ($Re_{b}<$10), and is found to have an upper bound of $Ri_{f}^{I}\approx$ 0.15 and $Ri_{f}^{II}\approx$ 0.2 in the intermediate regime. Using the values of $Ri_{f}$, the normalized eddy diffusivity of momentum is parameterized as $\frac{\kappa_m}{\nu.Ri_{g}}$=1.2$Re_{b}$ and normalized eddy diffusivity of scalar as $\frac{\kappa_{\rho}}{\nu}$=0.2$Re_{b}$

Mixing character in the head part of a gravity current

The mixing within a full depth lock-exchange gravity current was investigated experimentally with planar laser-induced fluorescence PLIF. The scalar edge of the gravity current was identified via an edge detection algorithm. A strong mixing region located along this edge was extracted from the flow field and analyzed. A dimensionless background potential energy was defined to characterize the local mixing rate in this region, which showed a two-stage behavior. In the section near the nose, mixing rate oscillates strongly under the influence of the lobe and cleft shifting, while in the upper part, the mixing rate grows gradually under the mechanism of billows rolling up.

Separation of particle-laden gravity currents down a slope in linearly stratified environments

Particle-laden gravity currents down a slope in stratified fluid are important processes in lake, estuary, and ocean environments. By conducting direct numerical simulations, this study investigates the detailed dynamic features of lock-exchange particle-laden gravity currents down a slope in linearly stratified environments. The front velocity, separation depth, water entrainment ratio, and energy budget are quantitatively analyzed. This evolutionary process can be divided into three stages, i.e., the acceleration stage, deceleration stage, and separation stage, if the relative stratification parameter is larger than unity. At the acceleration stage, as the collapse of the dense fluid leads to fast entrainment of ambient water into the current, the entrainment ratios have large values, while the settling velocity and the ambient stratification are shown to have less impact on both the entrainment ratios and the front velocity. At the deceleration stage, a larger slope angle, a weaker ambient stratification, and a smaller settling velocity bring a greater front velocity. At the separation stage, the head of the current leaves the slope and intrudes into the environment; meanwhile, the dense fluid at the body of the current also intrudes into the ambient water because the density contrast has largely been reduced due to water entrainment, particle settling, and the density increase in the ambient fluid. A predictive model is developed to determine the separation depth by considering the presence of particles. The fingerlike horizontal intrusions enhance the entrainment effect between the current and the ambient water. A stronger ambient stratification suppresses the conversion of the potential energy to the kinetic energy, while a larger settling velocity accelerates the conversion of the kinetic energy to the dissipated energy.

Residual-based variational multi-scale modeling for particle-laden gravity currents over flat and triangular wavy terrains

In this paper, a numerical formulation for simulating dilute particle-laden gravity currents at large Reynolds number (Re) is developed using a residual-based variational multi-scale formulation (RBVMS), in which the coupling between the velocity fine scales and density concentration equation residual is represented. The proposed formulation is utilized to simulate the lock-exchange particle-laden gravity currents at Re=10,000. Firstly, we validated the proposed formulation by simulating the gravity currents over flat terrain. Flow statistics are thoroughly compared against high-resolution simulation results such as DNS or experimental results in the literature. It shows the RBVMS formulation presented here can reproduce quite accurate results with much lower mesh resolution. Then, the particle-laden gravity currents over triangular wavy terrains with changing wave heights are simulated. The effect of the wave height on the flow statistics is investigated.

ТОЧНО РЕШАЕМАЯ МОДЕЛЬ ИНТРУЗИИ

The conformal-mapping approach (Bazant, Crowdy, 2005; Tanveer, 1993; Zakharov, Dyachenko, 1996; Yoshikawa, Balk, 1999, 2003) is used to formulate a minimal exactly solvable model for studying the lock-exchange gravity currents in an infinite horizontal channel (Simpson, 1999; Ungarish, 2009). The distinctive feature of such flows is a pressure jump which arises at the interface between two incompressible fluids of different densities at once after removing a lock gate. Because of this, the process of intrusion does not fit into Benjamin’s scenario (Benjamin, 1968) but rather is like propagation of two shock waves. This work was supported by the RFBR (Project No. 18-05-00831) and by the RAS Presidium Program «Nonlinear dynamics: fundamental problems and applications».

HYDRODYNAMIC MECHANISM OF TURBIDITY CURRENTS IN ESTUARY STRATIFICATIONS

Water stratification commonly exists in nature, such as thermocline in lakes and oceans and halocline in estuaries and oceans (He et al. 2017). Turbidity currents in estuary often encounter stratified sea water, which may significantly influence their propagation and deposition. This study presents high-resolution numerical simulations of lock-exchange gravity and turbidity currents in linear stratifications on a flat bed. Laboratory experiments are conducted to validate the numerical model and good agreements between numerical results and measurements are found. The evolution process, front velocity, internal wave, and entrainment ratio are analyzed based on the numerical results. For a gravity current in a strong stratification, its front velocity can be maintained as a near constant state for a long time after an initial acceleration period because of interactions between the current and internal waves. However, sedimentation of suspended particles due to the damping effect of ambient stratification on turbulence makes a turbidity current quickly lose its structure so the maintaining effect of the internal waves on its front velocity is quite weak. During the evolution process of a turbidity current, the ambient stratification is found to damp the turbulent structures, and front velocity. Stratification can also decrease the entrainment ratios between a gravity current and ambient water after the initial period, but it has an insignificant influence on the entrainment ratios of a turbidity current. This study provides a better understanding of gravity and turbidity currents in estuary stratifications.

Numerical modeling of lock-exchange gravity/turbidity currents by a high-order upwinding combined compact difference scheme

This study presents two-dimensional direct numerical simulations for sediment-laden current with higher density propagating forward through a lighter ambient water. The incompressible NavierStokes equations including the buoyancy force for the density difference between the light and heavy fluids are solved by a finite difference scheme based on a structured mesh. The concentration transport equations are used to explore such rich transport phenomena as gravity and turbidity currents. Within the framework of an Upwinding Combined Compact finite Difference (UCCD) scheme, rigorous determination of weighting coefficients underlies the modified equation analysis and the minimization of the numerical modified wavenumber. This sixth-order UCCD scheme is implemented in a four-point grid stencil to approximate advection and diffusion terms in the concentration transport equations and the first-order derivative terms in the Navier-Stokes equations, which can greatly enhance convective stability and increase dispersive accuracy at the same time. The initial discontinuous concentration field is smoothed by solving a newly proposed Heaviside function to prevent numerical instabilities and unreasonable concentration values. A two-step projection method is then applied to obtain the velocity field. The numerical algorithm shows a satisfying ability to capture the generation, development, and dissipation of the Kelvin-Helmholz instabilities and turbulent billows at the interface between the current and the ambient fluid. The simulation results also are compared with the data in published literatures and good agreements are found to prove that the present numerical model can well reproduce the propagation, particle deposition, and mixing processes of lock-exchange gravity and turbidity currents.

A conformal-mapping model for intrusion

The conformal-mapping approach is used to formulate a minimal exactly solvable model for studying the lock-exchange gravity currents in an infinite horizontal channel. The distinctive feature of such flows is a pressure jump which arises at the interface between two incompressible fluids of different densities at once after removing a lock gate. Because of this, the process of intrusion does not fit into Benjamin’s scenario but rather is like propagation of two shock waves. Being identical in shape and speed, they move in opposite directions along the upper and lower channel boundaries, reaching a steady state as t → ∞.

Front Velocity and Front Location of Lock-Exchange Gravity Currents Descending a Slope in a Linearly Stratified Environment

Gravity currents descending a slope in a linearly stratified environment can be frequently encountered in nature. However, few studies have quantitatively investigated the evolution process of lock-exchange gravity currents in such environments. A new set of analytical formulae is proposed by integrating both mass conservation and linear momentum equations to determine the front velocity and the front location of a downslope current. Based on the thermal theory, the formula considers the influence of ambient stratification by introducing a newly defined stratification coefficient in the acceleration stage. As for the deceleration stage, the formula is derived by adding a parameter that takes into account the density distribution of the ambient water. The transition point between the acceleration and deceleration stages and the maximum front velocity are also determined by the proposed formulae. Lock-exchange gravity current experiments are conducted in the flume with linear stratifications to provide data for the validation of the formulae. The comparisons between the calculated and measured data in terms of front location and front velocity show satisfactory agreements, which reveal that front velocity presents a rapid acceleration stage and then a deceleration stage in a linearly stratified ambient.

Front propagation of gravity currents on inclined bottoms in linearly stratified fluids

Gravity currents propagating on an inclined bottom into stratified environment can be frequently encountered in nature or engineering fields. However, theoretical analysis and simulations on the evolution process of lock-exchange gravity currents in such environments are still in lack of investigations. In this work, we derive a set of semi-empirical formulae to determine the frontal propagation speed in homogenous and linearly stratified ambient fluids. Two phases can be clearly observed in the propagation process, a relatively short acceleration phase followed by a deceleration phase. In the acceleration phase, the formula considers the influence of initial position and ambient stratification by introducing mass centroid coefficient (αp) and effective stratification coefficient (αs), respectively. In the deceleration phase, the formula is derived by adding the effective buoyancy parameter Bm′ and entrainment coefficient km, where km is eventually a function of the fraction of heavy fluid in the dense current head (χ) as it propagating down the ramp. We propose a simplified and efficient method to estimate the value of χ in various conditions, which has been previously assumed as a constant. A series of lock-exchange gravity current experiments were conducted in the tank with linear stratifications to validate the propagation theory. The comparisons between the calculated and measured front propagation speed show good agreement, which reveal that the front velocity exhibits a rapid acceleration stage followed by a deceleration stage in the linearly stratified ambience. The good agreement between measured and calculated data indicates that semi-empirical formulae are capable to predict the whole process of gravity current propagation using only measurable information prior to initiate gravity current experiments.

Entrainment and mixing in lock-exchange gravity currents using simultaneous velocity-density measurements

Gravity currents modify their flow characteristics by entraining ambient fluid, which depends on a variety of governing parameters such as the initial density, Δρ, the total initial height of the fluid, H, and the slope of the terrain, α, from where it is released. It is imperative to study the entrainment dynamics of a gravity current in order to have a clear understanding of mixing transitions that govern the flow physics, the velocity mixing layer thickness, δu, and the density mixing layer thickness, δρ. Experiments were conducted in a lock-exchange facility in which the dense fluid was separated from the ambient lighter fluid using a gate. As the gate is released instantaneously, an energy conserving gravity current is formed, for which the only governing parameter is the Reynolds number defined as Re=Uhν, where U is the front velocity of the gravity current and h is the height of the current. In our study, the bulk Richardson number (inverse of Froude number, Fr), Rib = g′HUb2 = 1, takes a constant value for all the experiments, with Ub being the bulk velocity of the current defined as Ub = g′H. Simultaneous particle image velocimetry and planar laser induced fluorescence measurement techniques are employed to get the velocity and density statistics. Using the buoyancy conservation equation, a new flux-based method was formulated for calculating the entrainment coefficient, EF, near the front and head of the propagating gravity current for a Reynolds number range of Re ≈ 485-12 270 used in our experiments. At the head of the current, the results show a mixing transition at Re ≈ 2700 that is attributed to the flow transitioning from weak Holmboe waves to Kelvin-Helmholtz instabilities, in the form of Kelvin-Helmholtz vortex rolls. Following this mixing transition, the entrainment coefficient continued to increase with increasing Reynolds number owing to the occurrence of three-dimensional Kelvin-Helmholtz billows that promote further small-scale local mixing. Such a mixing transition indicates that a fully turbulent state is not reached even at Re = 12 270 and the amount of entrainment and ensuing mixing depends on the type of flow instability and presence of small-scale secondary structures. The entrainment dynamics were further substantiated using the ratio of δu and δρ. It was observed that δuδρ decreases with increasing Re and reaches a constant value of δuδρ≈ 1 at high values of Re. This trend is in contrast to the entrainment coefficient EF, which never reaches a constant value even at high enough Re. This disparity could be explained by the fact that EF accounts for small-scale scalar mixing, which is not captured by the ratio of mixing layer thicknesses. Experimentally, it was also observed that the EF value near the front of gravity current was 2-9 times higher than the head value depending on the value of the Reynolds numbers. At low Reynolds numbers, the entrainment near the front is an order of magnitude higher than the head and the value decreases with increasing Re. This could be attributed to different modes of entrainment near the front (dominated by vortical structures) and the head (dominated by turbulent flux exchange triggered by the nature of the flow instability). The results from this study improve our understanding of entrainment dynamics and would be useful in developing empirical parameterizations for mixing in stratified flows.

Large Eddy Simulations of sediment entrainment induced by a lock-exchange gravity current

Abstract Large Eddy simulations of lock-exchange gravity currents propagating over a mobile reach are presented. The numerical setting allows to investigate the sediment pick up induced by the currents and to study the underlying mechanisms leading to sediment entrainment for different Grashof numbers and grain sizes. First, the velocity field and the bed shear-stress distribution are investigated, along with turbulent structures formed in the flow, before the current reaches the mobile bed. Then, during the propagation of the current above the erodible section of the bed the contour plots of the entrained material are presented as well as the time evolution of the areas covered by the current and by the sediment at this section. The numerical outcomes are compared with experimental data showing a very good agreement. Overall, the study confirms that sediment pick up is prevalent at the head of the current where the strongest turbulence occurs. Further, above the mobile reach of the bed, settling process seems to be of minor importance, with the entrained material being advected downstream by the current. Additionally, the study shows that, although shear stress is the main mechanism that sets particles in motion, turbulent bursts as well as vertical velocity fluctuations are also necessary to counteract the falling velocity of the particles and maintain them into suspension. Finally, the analysis of the stability conditions of the current shows that, from one side, sediment concentration gives a negligible contribution to the stability of the front of the current and from the other side, the stability conditions provided by the current do not allow sediments to move into the ambient fluid.

LES mesh resolution requirements for particledriven gravity currents

In this study we investigate the influence of grid resolution on a near-wall resolved LES model of a lock-exchange particle-driven gravity current. The simulations are performed using the finite volume Boussinesq code SnS with a Smagorinsky turbulence model for a buoyant Reynolds number of 60,000 on 4 grid sizes. According to previous studies, two-point correlations are most appropriate to estimate LES resolution. With the largest scales of the flow being resolved by more than 20 cells, well-resolved LES is obtained for grid resolutions of 1925×62×125 and finer. In addition, in order to apply the turbulence model correctly, we show that the velocity power spectrum densities provide useful information for the maximum cell size. The ratio of the subgrid scale viscosity to the molecular viscosity and the subgrid scale shear-stress to the resolved Reynolds stress show good convergence with grid refinement. The ratios vSGS / &lt;0.3 above the current and τSGS (u'v')ave &lt; 0.05 inside the mixing layer, are chosen as threshold values, based on our evaluation study.

Unconfined lock-exchange gravity currents with variable lock width: laboratory experiments and shallow-water simulations

ABSTRACTThe dynamics of unconfined gravity currents generated by a lock-exchange with different lock widths is considered. The gravity currents were generated by density differences caused by a salinity gradient and were realized both numerically and experimentally. Several runs were carried out in order to study the role played by the lock width in the current dynamics. Numerical simulations were performed with a new single-layer, 2D, shallow-water model, which accounts for the dilution of the gravity current due to the entrained ambient fluid. By the comparison between experimental and numerical results, the relevant role played by the entrainment in the propagation velocity of the front emerges, mainly for the cases with a narrow lock. The effect of the lock width on the current dynamics is also highlighted: the lock chocks the flow causing a localized loss of mechanical energy and a consequent deceleration of the flow. Results show that the smaller is the lock, the larger is the loss of energy.

On the propagation of gravity currents over and through a submerged array of circular cylinders

The propagation of full-depth lock-exchange bottom gravity currents past a submerged array of circular cylinders is investigated using laboratory experiments and large eddy simulations. Firstly, to investigate the front velocity of gravity currents across the whole range of array density $\unicode[STIX]{x1D719}$ (i.e. the volume fraction of solids), the array is densified from a flat bed ($\unicode[STIX]{x1D719}=0$) towards a solid slab ($\unicode[STIX]{x1D719}=1$) under a particular submergence ratio $H/h$, where $H$ is the flow depth and $h$ is the array height. The time-averaged front velocity in the slumping phase of the gravity current is found to first decrease and then increase with increasing $\unicode[STIX]{x1D719}$. Next, a new geometrical framework consisting of a streamwise array density $\unicode[STIX]{x1D707}_{x}=d/s_{x}$ and a spanwise array density $\unicode[STIX]{x1D707}_{y}=d/s_{y}$ is proposed to account for organized but non-equidistant arrays ($\unicode[STIX]{x1D707}_{x}\neq \unicode[STIX]{x1D707}_{y}$), where $s_{x}$ and $s_{y}$ are the streamwise and spanwise cylinder spacings, respectively, and $d$ is the cylinder diameter. It is argued that this two-dimensional parameter space can provide a more quantitative and unambiguous description of the current–array interaction compared with the array density given by $\unicode[STIX]{x1D719}=(\unicode[STIX]{x03C0}/4)\unicode[STIX]{x1D707}_{x}\unicode[STIX]{x1D707}_{y}$. Both in-line and staggered arrays are investigated. Four dynamically different flow regimes are identified: (i) through-flow propagating in the array interior subject to individual cylinder wakes ($\unicode[STIX]{x1D707}_{x}$: small for in-line array and arbitrary for staggered array; $\unicode[STIX]{x1D707}_{y}$: small); (ii) over-flow propagating on the top of the array subject to vertical convective instability ($\unicode[STIX]{x1D707}_{x}$: large; $\unicode[STIX]{x1D707}_{y}$: large); (iii) plunging-flow climbing sparse close-to-impermeable rows of cylinders with minor streamwise intrusion ($\unicode[STIX]{x1D707}_{x}$: small; $\unicode[STIX]{x1D707}_{y}$: large); and (iv) skimming-flow channelized by an in-line array into several subcurrents with strong wake sheltering ($\unicode[STIX]{x1D707}_{x}$: large; $\unicode[STIX]{x1D707}_{y}$: small). The most remarkable difference between in-line and staggered arrays is the non-existence of skimming-flow in the latter due to the flow interruption by the offset rows. Our analysis reveals that as $\unicode[STIX]{x1D719}$ increases, the change of flow regime from through-flow towards over- or skimming-flow is responsible for increasing the gravity current front velocity.