Lock-exchange Gravity Currents Research Articles

Lattice Boltzmann simulations of gravity currents

This paper is aimed at assessing the ability of the Lattice-Boltzmann Method (LBM) in reproducing the fundamental features of lock-exchange gravity currents. Both two- and three-dimensional numerical simulations are presented at different Reynolds numbers (1000≤Re≤30,000). Turbulence has been accounted for by implementing an equivalent Large Eddy Simulation (LES) model in the LBM framework. The advancement of the front position and the front velocity obtained by LBM numerical simulations are compared with laboratory experiments appositely performed with similar initial and boundary conditions and with previous results from literature, revealing that the dynamics of the gravity current as a whole is correctly reproduced. Lobes and clefts instabilities arising in three-dimensional simulations and the entrainment parameter are also analysed and comparisons with previous studies are presented.

Lock-exchange gravity currents over rough bottoms

In nature, density driven currents often flow over or within a bottom roughness: a sea breeze encountering tall buildings, a shallow flow encountering aquatic vegetation, or a dense oceanic current flowing over a rough bottom. Laboratory experiments investigating the mechanisms by which bottom roughness enhances or inhibits entrainment and dilution in a lock-exchange dense gravity current have been conducted. The bottom roughness has been idealized by an array of vertical, rigid cylinders. Both spacing (sparse vs. dense configuration) and height of the roughness elements compared with the height of the current have been varied. Two-dimensional density fields have been obtained. Experimental results suggest that enhancement of the entrainment/dilution of the current can occur due to two different mechanisms. For a sparse configuration, the dense current propagates between the cylinders and the entrainment is enhanced by the vortices generated in the wake of the cylindrical obstacles. For a dense configuration, the dense current rides on top of the cylinders and the dilution is enhanced by the onset of convective instability between the dense current above the cylinders and the ambient lighter water between the cylinders. For low values of the ratio of the cylinder to lock height \(\lambda \) the dense current behavior approaches that of a current over a smooth bottom, while the largest deviations from the smooth bottom case are observed for large values of \(\lambda \).

Effect of surface waves on full depth lock exchange gravity currents hydrodynamics

Effect of surface waves on full depth lock exchange gravity currents hydrodynamics

Double-diffusive lock-exchange gravity currents

Double-diffusive lock-exchange gravity currents in the fingering regime are explored via two- and three-dimensional Navier–Stokes simulations in the Boussinesq limit. Even at modest Reynolds numbers, for which single-diffusive gravity currents remain laminar, double-diffusive currents are seen to give rise to pronounced small-scale fingering convection. The front velocity of these currents exhibits a non-monotonic dependence on the diffusivity ratio and the initial stability ratio. Strongly double-diffusive currents lose both heat and salinity more quickly than weakly double-diffusive ones, and they lose salinity more quickly than heat, so that the density difference driving them increases. This differential loss of heat and salinity furthermore results in the emergence of strong local density maxima and minima along the top and bottom walls in the gate region, which in turn promote the formation of secondary, counterflowing currents along the walls. These secondary currents cause the flow to develop a three-layer structure. The late stages of the flow are dominated by currents flowing oppositely to the original ones. Three-dimensional simulation results are consistent with the trends observed in a two-dimensional parametric study. A detailed analysis of the energy budget demonstrates that strongly double-diffusive currents can release several times their initially available potential energy, and convert large amounts of internal energy into mechanical energy via scalar diffusion. Scaling arguments based on the simulation results suggest that even low Reynolds number double-diffusive gravity currents are governed by a balance of buoyancy and turbulent drag.

Entrainment and mixing in unsteady gravity currents

ABSTRACTEntrainment 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.

Mixing in lock-release gravity currents propagating up a slope

Lock-exchange gravity currents propagating up a slope are investigated by large eddy simulations, focusing on the entrainment and mixing processes occurring between the dense current and the ambient fluid. Relevant parameters, such as the aspect ratio of the initial volume of dense fluid in the lock R, the angle between the bottom boundary and the horizontal direction θ and the depth aspect ratio ϕ, are varied. The numerical results are compared with laboratory experiments and a good agreement is found. Entrainment and mixing in a lock-release gravity current are studied using different entrainment parameters and an energy budget method. The entrainment is found to depend on both Froude, Fr, and Reynolds, Re, numbers. In addition, the dependence of both entrainment and mixing on the parameters varied is discussed. The entrainment decreases with increasing steepness of the bottom and R. Irreversible mixing is not affected by the varied parameters during the slumping phase, while during the successive phases of motion, it is found to decrease with the increase of θ and R. Low entrainment and mixing occur for ϕ < 1.

Curved boundaries in multi-layer Shallow Water Lattice Boltzmann Methods: bounce back versus immersed boundary

The Lattice Boltzmann Method has been successfully applied to solve Multilayer Shallow Water models for the simulation of gravity currents generated by laboratory lock exchange experiments in regular geometries. When complex boundaries are to be modelled, several approaches are feasible. In this work two types of boundary conditions are analyzed and compared in the simulation of lock exchange gravity currents impacting on vertical obstacles. The first one belongs to the common group of bounce back approaches; the second one is an adaptation of the immersed boundary technique to the Shallow Water dynamics. The analysis is carried out comparing accuracy against experimental data. Efficiency is also taken into account. Results show that the computational overhead introduced by the Immersed Boundary technique is not counterbalanced by a gain in accuracy for the considered kind of obstacles.

开闸式异重流锋速转变的一个判据

Gravity currents, which occur whenever fluid of one density flows primarily horizontally into a fluid of different density, are widespread in natural and industrial systems. Experimental results for lock-exchange gravity currents in a channel of rectangular cross-section are presented. High-speed particle image velocimetry and laser-induced fluorescence in refractive index-matched gravity currents were used to study the spatial and temporal resolution of flow structures. As previously reported, the resulting gravity current, if viscous effects are negligible, passes through two distinct phases. The transition from the first to the second phase is observed to be rather abrupt and occurs when a disturbance generated at the endwall overtakes the front. We discover that the streamwise velocity profiles oscillate during this short stage. Furthermore, the relevance between the oscillation and the disturbance are discussed. This oscillation phenomenon can be used as a criterion for the transition of the front velocity in lock-exchange gravity currents.

Lock-exchange gravity currents propagating in a channel containing an array of obstacles

AbstractLarge eddy simulation (LES) is used to investigate the evolution of Boussinesq gravity currents propagating through a channel of height$H$containing a staggered array of identical cylinders of square cross-section and edge length$D$. The cylinders are positioned with their axes horizontal and perpendicular to the (streamwise) direction along which the lock-exchange flow develops. The effects of the volume fraction of solids,${\it\phi}$, the Reynolds number and geometrical parameters describing the array of obstacles on the structure of the lock-exchange flow, total drag force acting on the gravity current, front velocity and global energy budget are analysed. Simulation results show that the currents rapidly transition to a state in which the extra resistance provided by the cylinders strongly retards the motion and dominates the dissipative processes. A shallow layer model is also formulated and similarity solutions for the motion are found in the regime where the driving buoyancy forces are balanced by the drag arising from the interaction with the cylinders. The numerical simulations and this shallow layer model show that low-Reynolds-number currents transition to a drag-dominated regime in which the resistance is linearly proportional to the flow speed and, consequently, the front velocity,$U_{f}$, is proportional to$t^{-1/2}$, where$t$is the time measured starting at the gate release time. By contrast, high-Reynolds-number currents, for which the cylinder Reynolds number is sufficiently high that the drag coefficient for most of the cylinders can be considered constant, transition first to a quadratic drag-dominated regime in which the front speed determined from the simulations is given by$U_{f}\sim t^{-0.25}$, before undergoing a subsequent transition to the aforementioned linear drag regime in which$U_{f}\sim t^{-1/2}$. Meanwhile, away from the front, the depth-averaged gravity current velocity is proportional to$t^{-1/3}$, a result that is in agreement with the shallow water model. It is suggested that the difference between these two is due to mixing processes, which are shown to be significant in the numerical simulations, especially close to the front of the motion. Direct estimation of the drag coefficient$C_{D}$from the numerical simulations shows that the combined drag parameter for the porous medium,${\it\Gamma}_{D}=C_{D}{\it\phi}(H/D)/(1-{\it\phi})$, is the key dimensionless grouping of variables that determines the speed of propagation of the current within arrays with different$C_{D},{\it\phi}$and$D/H$.

Lock-exchange gravity currents with a low volume of release propagating over an array of obstacles

The study discusses, based on high-resolution 3-D large eddy simulation results, the evolution of lock-exchange Boussinesq gravity currents with a low volume of release (LVR) propagating over an array of identical two-dimensional (2-D) obstacles (large roughness features in the form of dunes and ribs corresponding to eroded substrates) in a rectangular horizontal channel. The study analyzes the effect of the shape and height of the roughness elements and scale effects between Reynolds numbers at which most laboratory experiments of lock-exchange currents are conducted and Reynolds numbers closer to field-scale currents in geophysical applications on the temporal variation of the front velocity, mixing, and flow structure within the gravity current. The temporal evolution of the flow instabilities (e.g., Kelvin-Helmholtz billows, forward and backward propagating interfacial waves forming as a result of the interaction of the front of the current with the obstacles) and bed friction velocity distributions are analyzed during the different stages of the evolution of the current. The focus is on the later stages of the propagation of LVR currents, after the transition to the self-similar drag-dominated regime has started. The differences between the evolution and structure of gravity currents with a low and a high volume of release are highlighted.

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.

LES of lock-exchange compositional gravity currents: a brief review of some recent results

Three-dimensional 3-D Large eddy simulation (LES) has become a powerful tool to investigate evolution and structure of gravity currents, especially for cases (e.g., high Reynolds number flows, flows with massive separation) where 3-D Direct numerical simulation using non-dissipative viscous solvers is computationally too expensive. In this paper we briefly review some important results obtained based on high-resolution 3-D LES of bottom-propagating compositional Boussinesq currents in lock-exchange configurations. LES was used to provide a detailed description of the structure of the current, to discuss the role of the large-scale coherent structures, and to predict the evolution of the front velocity over the different stages of the current propagation. Three main types of lock-exchange flows are considered: (1) currents with a high volume of release (HVR) and a low volume of release (LVR) propagating in a channel with a smooth horizontal bed; (2) HVR and LVR currents propagating in a horizontal channel containing a porous layer; and (3) currents propagating in a horizontal channel containing an array of bottom obstacles (2-D dunes and ribs). The simulations are performed using non-dissipative numerical algorithms and sub-grid scale models that predict a zero eddy viscosity in regions where the turbulence is negligible. Experimental data is used to validate LES predictions. LES results show that in most cases the evolution of the front velocity is consistent with that predicted based on shallow-flow theory. LES flow fields are then used to estimate important quantities (e.g., bed friction velocity, sediment entrainment capacity) that are very difficult to obtain from experiments and to understand how the structure and evolution of the current change because of the additional drag induced by obstacles present within the channel or at the channel bed. The paper also discusses how the evolution and structure of the current change as the Reynolds number is increased to values that are relevant for gravity currents encountered in geosciences and environmental engineering applications.

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.

Lock-exchange gravity currents with a high volume of release propagating over a periodic array of obstacles

Large eddy simulations are employed to investigate the structure and evolution of a bottom-propagating compositional gravity current in a rectangular horizontal plane channel containing a series of identical large-scale obstacles (dunes and square ribs) at the channel bottom. Simulation results show that below a certain value of the additional drag force per unit streamwise length induced by the bottom obstacles (low drag cases), the gravity current propagating over an array of obstacles transitions to a regime where the average front velocity is close to constant. Past its initial stages, the total kinetic energy, Ek, increases in time proportional to t1/3, where t is the time since release. This behaviour is similar to the slumping phase observed for currents propagating over a flat bed, with the exception that in the latter case the temporal increase of Ek during the later stages of the slumping phase is much faster (Ek ~ t). Simulation results also show that above certain value of the drag force per unit streamwise length induced by the obstacles (high drag cases), the slumping phase can be very short. In this case, similar to currents propagating in a porous medium, the current transitions to a drag-dominated regime in which the front velocity decays proportionally to tβ, with β = −0.28, once the discharge of lock fluid at the position of the lock gate becomes close to constant in time.

Viscous lock-exchange in rectangular channels

In a viscous lock-exchange gravity current, which describes the reciprocal exchange of two fluids of different densities in a horizontal channel, the front between two Newtonian fluids spreads as the square root of time. The resulting diffusion coefficient reflects the competition between the buoyancy-driving effect and the viscous damping, and depends on the geometry of the channel. This lock-exchange diffusion coefficient has already been computed for a porous medium, a two-dimensional (2D) Stokes flow between two parallel horizontal boundaries separated by a vertical height H and, recently, for a cylindrical tube. In the present paper, we calculate it, analytically, for a rectangular channel (horizontal thickness b and vertical height H) of any aspect ratio (H/b) and compare our results with experiments in horizontal rectangular channels for a wide range of aspect ratios (1/10 to 10). We also discuss the 2D Stokes–Darcy model for flows in Hele-Shaw cells and show that it leads to a rather good approximation, when an appropriate Brinkman correction is used.

TURBINS: An immersed boundary, Navier–Stokes code for the simulation of gravity and turbidity currents interacting with complex topographies

An accurate, three-dimensional Navier–Stokes based immersed boundary code called TURBINS has been developed, validated and tested, for the purpose of simulating density-driven gravity and turbidity currents propagating over complex topographies. The code is second order accurate in space and third order in time, uses MPI, and employs a domain decomposition approach. It makes use of multigrid preconditioners and Krylov iterative solvers for the systems of linear equations obtained by the finite difference discretization of the governing equations. TURBINS utilizes the direct forcing variant of the immersed boundary approach and enforces the no-slip boundary condition via the first grid point inside the solid, which yields very accurate wall shear stress results. The results of test simulations are discussed for uniform flow around a circular cylinder, and for two- and three-dimensional lock-exchange gravity currents.

Numerical simulations of lock-exchange compositional gravity current

Compositional gravity current flows produced by the instantaneous release of a finite-volume, heavier lock fluid in a rectangular horizontal plane channel are investigated using large eddy simulation. The first part of the paper focuses on the evolution of Boussinesq lock-exchange gravity currents with a large initial volume of the release during the slumping phase in which the front of the gravity current propagates with constant speed. High-resolution simulations are conducted for Grashof numbers $\sqrt {Gr}$ = 3150 (LGR simulation) and $\sqrt {Gr}$ = 126000 (HGR simulation). The Grashof number is defined with the channel depth h and the buoyancy velocity ub = $\sqrt {g'h}$ (g′ is the reduced gravity). In the HGR simulation the flow is turbulent in the regions behind the two fronts. Compared to the LGR simulation, the interfacial billows lose their coherence much more rapidly (over less than 2.5h behind the front), which results in a much faster decay of the large-scale content and turbulence intensity in the trailing regions of the flow. A slightly tilted, stably stratified interface layer develops away from the two fronts. The concentration profiles across this layer can be approximated by a hyperbolic tangent function. In the HGR simulation the energy budget shows that for t > 18h/ub the flow reaches a regime in which the total dissipation rate and the rates of change of the total potential and kinetic energies are constant in time. The second part of the paper focuses on the study of the transition of Boussinesq gravity currents with a small initial volume of the release to the buoyancy–inertia self-similar phase. When the existence of the back wall is communicated to the front, the front speed starts to decrease, and the current transitions to the buoyancy–inertia phase. Three high-resolution simulations are performed at Grashof numbers between $\sqrt {Gr}$ = 3 × 104 and $\sqrt {Gr}$ = 9 × 104. Additionally, a calculation at a much higher Grashof number ($\sqrt {Gr}$ = 106) is performed to understand the behaviour of a bottom-propagating current closer to the inviscid limit. The three-dimensional simulations correctly predict a front speed decrease proportional to t−α (the time t is measured from the release time) over the buoyancy–inertia phase, with the constant α approaching the theoretical value of 1/3 as the current approaches the inviscid limit. At Grashof numbers for which $\sqrt {Gr}$ > 3 × 104, the intensity of the turbulence in the near-wall region behind the front is large enough to induce the formation of a region containing streaks of low and high streamwise velocities. The streaks are present well into the buoyancy–inertia phase before the speed of the front decays below values at which the streaks can be sustained. The formation of the velocity streaks induces a streaky distribution of the bed friction velocity in the region immediately behind the front. This distribution becomes finer as the Grashof number increases. For simulations in which the only difference was the value of the Grashof number ($\sqrt {Gr}$ = 4.7 × 104 versus $\sqrt {Gr}$ = 106), analysis of the non-dimensional bed friction velocity distributions shows that the capacity of the gravity current to entrain sediment from the bed increases with the Grashof number. Past the later stages of the transition to the buoyancy–inertia phase, the temporal variations of the potential energy, the kinetic energy and the integral of the total dissipation rate are logarithmic.