Propagation Of Gravity Currents Research Articles

Density-driven exchange flow propagating over an array of densified obstacles

The evolution of bottom-propagating gravity currents with the presence of an array of densified obstacles submerged in a channel is investigated using large-eddy simulations. Our attention is particularly focused on the flow transition of gravity currents over rough surfaces with extra resistance that provokes significant dissipative processes. Two geometric parameters of the roughness elements, namely, the submergence ratio of the obstacle D/H and the gap-spacing ratio λ/D between obstacles, govern their kinematic and dynamic effects on the propagation of gravity currents. Physically, D/H plays a significant role in the control of the current diversion, and λ/D regulates the flow pathway of gravity current propagation. The integrated measures show that two distinct flow morphologies are identified. For a low submergence ratio (D/H<0.15), an overtopping flow is formed in which the gravity current travels on the top of the array and undergoes an inconspicuous loss of buoyancy, subject to minimal vertical convective instability interacting with the underlying ambient fluid within the gap regions. For a sufficiently high submergence ratio (D/H≥0.15) and a certain gap spacing (2≤λ/D<4), an overrunning flow is formed in which the current rapidly decelerates to a buoyancy–inertia state and then transitions to a drag-dominated state with a gain in excessive drag, in which the front velocity is proportional to t−0.5. However, the simulation results show a turning point toward an increase in the gap spacing as λ/D≥4, that the maximum drag acting on the gravity current is measured when it impinges on the second obstacle of an array, and that the drag coefficient goes up by 10%–40%, depending on D/H. The propagation of the gravity current does not show a higher sensitivity to the retarding effect instead. Meanwhile, the promotion of energy conversion occurs because of the gravity current encountering the continuous climbing and plunging flow behavior between two adjacent obstacles in regular motions.

Exact Solutions for Gravity-Segregated Flows in Porous Media

The review is devoted to exact analytical solutions for quasi-2D gravity segregated flows or gravity currents in subterranean porous formations. The problems under consideration are quasi-linear. The driving forces are two components of the buoyancy—one exerting the bulk of the light fluid and one due to the curvilinearity of the interface between the fluids. In the case of homogeneous formation or where the seal slope is negligible, the transport equation is parabolic and allows for a wide set of self-similar solutions. In a large-scale approximation of the buoyancy domination, the governing equation is hyperbolic; the method of characteristics allows for a detailed analytical description of gravity current propagation with final accumulation in the geological trap. Analytical models for leakage via the caprock seal are also discussed. The work was completed by formulating some unsolved problems in segregated flows in porous media.

Gravity currents with large salinity in a gravel bed valley: an experimental study

Abstract In the current study experiments in a valley (a composite cross-sectional tank consisting of a rectangular upper cross section and a lower trapezoidal) were performed. The purpose of this research is to study the gravel bed in gravity currents with large salinity. The tank is separated in two parts by a vertical gate, which separates the fresh water with the gravel bed from the salt water with the impermeable bed. When the gate opens, a flow is created due to density difference. The salinity densities are large (from 1,050 to 1,090 kg/m3). These specific densities have been chosen to simulate liquid wastes that affect the environment. Compared to experiments in the same tank without a gravel bed, it is observed that the gravel bed reduces the propagation of currents and mainly reduces the current with the smallest density difference at the lowest height. The main conclusion of this study is that the kind of channel bed plays a key role in the propagation of gravity currents. The gravel bed affects significantly the velocity and the distance traveled by the currents in comparison with impermeable bed.

Lock-release gravity currents propagating over roughness elements

The influence of bottom roughness on the development of lock-release gravity currents is investigated through laboratory experiments using Particle Image Velocimetry. The bottom roughness is represented by arrays of vertical LEGO bricks with a constant spacing while varying lambda , the relative height of the roughness elements to the gravity current depth. Depending on lambda , the roughness elements may affect the gravity current propagation: for small lambda the current behaves like moving over a smooth bottom, while for larger lambda the propagation speed is reduced and the internal structure of the current, including both the head and the tail, is significantly modified. As lambda increases, stronger recirculation areas between the roughness elements develop interacting with the overlying layer and giving rise to small-scale vortical structures of opposite sign within the whole depth of the current. The additional drag force induced by the bottom roughness adds significant complexity to the flow dynamics and modifies the characteristics of the current.

Flow morphology in bottom-propagating gravity currents over immersed obstacles

The interaction of bottom-propagating gravity currents with immersed obstacles in the path of the lock-exchange configuration was numerically investigated based on large eddy simulations. The three-dimensional Navier–Stokes solver was quantitatively employed to resolve the flow structure of gravity currents and their dynamics during impact. The integral measure of analysis comprises the front condition, the energy budget, the turbulent mixing, and the force response. Some flow parameters involved in momentum and energy fluctuations are the fractional depth of volume release, relative density difference, and obstacle dimensions. A particular focus in this study was on the scale effect of obstacles (W/D, the aspect ratio of a cross-sectional obstacle with side length W to height D) that affect the propagation of gravity currents. Depending on integral measures of the simulation, the flow morphology could be demarcated for the condition W/D = 2 with different flow regimes in accordance with the reattachment of the current as the plunged front overflows and separates from the obstacle. For W/D > 2, as the current impinges on the obstacle, the plunged current front overtops and travels on the obstacle surface and consequently causes the entrainment without intense mixing to form a circulation zone at the downstream of the obstacle. Accordingly, the predicted drag forces acting on the downstream surface are reduced by ∼25% for W/D ≥ 4 comparing to the case of W/D = 0.5, which is beneficial to the structural stability of the barrier in practical aspect. Notably, the integrated analysis of gravity currents provides insights into physical mechanisms by identifying distinct propagation stages during transitions, including the impact stage, transient stage, and quasi-steady stage.

A model for the propagation of inertial gravity currents released from a two-layer stratified lock

Abstract

Impact of ambient stable stratification on gravity currents propagating over a submerged canopy

The structure and propagation of lock-release bottom gravity currents in a linearly stratified ambient with the presence of a submerged canopy are investigated for the first time using large-eddy simulations. The canopy density (i.e. the solid volume fraction), the strength of ambient stratification and the canopy height are varied to study their respective effects on the gravity current. Both denser canopies and stronger ambient stratification tend to switch the horizontal boundary along which the current propagates from the channel bed towards the canopy top (i.e. the through-to-over flow transition). It is found that the dilution of the current density is enhanced by denser canopies but is weakened by stronger ambient stratification. The non-monotonic relationship between front velocity and canopy density proposed by Zhou et al. (J. Fluid Mech., vol. 831, 2017, pp. 394–417) in homogeneous environments is also observed in stratified environments. However, as the ambient stratification is strengthened, the present study shows a shift of the turning point (beyond which increasing canopy density leads to faster current propagation) towards sparser canopies, accompanied by a more pronounced recovery of the front velocity. This is the combined action of three stratification-induced mechanisms: the promotion of through-to-over flow transition (less canopy drag), the upward displacement of current nose in a stably stratified water column (more buoyancy gain) and the weakening of current dilution (less buoyancy loss). Under stronger ambient stratification, the propagation of gravity currents shows a lower sensitivity to the retarding effect of the submerged canopy.

Comparison of different turbulence models in predicting cohesive fluid mud gravity current propagation

A numerical study of propagation of cohesive fluid mud gravity currents in the form of lock-exchange was done using the OpenFOAM open source toolbox. An Eulerian approach solution for three separate phases was developed by incorporating a rheological model to predict the front position of cohesive fluid mud gravity currents. The model also simulates features in the complete movement phases including slumping, self-similar, and viscous in which the dynamics of propagation are affected by the balance of viscous and buoyancy forces, and the inertia force is negligible. The influence of using different turbulence models containing sub-grid scale (SGS), modified SGS, detached eddy simulation (DES), delayed-detached eddy simulation (DDES), Launder-R eece-Rodi (LRR), and k-ɛ models on the accuracy of simulation results was evaluated by comparing with available experimental data. The results show that the selection of the proper turbulence model is one of the most important issues for this type of the numerical modeling. The more efficient turbulence model was suggested and tabulated for each stage of propagation and different selected concentrations of 1,045, 1,140, and 1,214 g/L. Although different turbulence models (except k-ɛ) lead to front propagation dynamic simulation results that are in good agreement with the experimental measurements in the early stage of propagation for low concentrations, only DES, SGS, and modified SGS are able to capture the Kelvin-Helmholtz instability vortex shapes at the dense fluid interface, which is the main characteristic of the gravity current through the slumping phase. The calculated accuracies of SGS and modified SGS in predicting gravity current propagation for the both self-similar and viscous phases also are slightly better than DES, DDES, and LRR model results. The results of this study confirmed the performance and efficiency of the modified SGS model in which the interaction coefficients between phases are calibrated for the numerical modeling of fluid mud gravity current propagation.

Quantification of turbulent mixing in colliding gravity currents

Collision between two identical counterflowing gravity currents was studied in the laboratory with the goal of understanding the fundamental turbulent mixing physics of flow collisions in nature, for example katabatic flows and thunderstorm outflows. The ensuing turbulent mixing is a subgrid process in mesoscale forecasting models, and needs to be parameterized using eddy diffusivity. Laboratory gravity currents were generated by simultaneously removing two identical locks, located at both ends of a long rectangular tank, which separated dense and lighter water columns with free surfaces of the same depth $H$. The frontal velocity $u_{f}$ and the velocity and density fields of the gravity currents were monitored using time-resolved particle image velocimetry and planar laser-induced fluorescence imaging. Ensemble averaging of identical experimental realizations was used to compute turbulence statistics, after removing inherent jitter via phase alignment of successive data realizations by iteratively maximizing the cross-correlation of each realization with the ensemble average. Four stages of flow evolution were identified: initial (independent) propagation of gravity currents, their approach while influencing one another, collision and resulting updraughts, and postcollision slumping of collided fluid. The collision stage, in turn, involved three phases, and produced the strongest turbulent mixing as quantified by the rate of change of density. Phase I spanned $-0.2\leqslant tu_{f}/H<0.5$, where collision produced a rising density front (interface) with strong shear and intense turbulent kinetic energy production ($t$ is a suitably defined time coordinate such that gravity currents make the initial contact at $tu_{f}/H=-0.2$). In Phase II ($0.5\leqslant tu_{f}/H<1.2$), the interface was flat and calm with negligible vertical velocity. Phase III ($1.2\leqslant tu_{f}/H<2.8$) was characterized by slumping which led to hydraulic bores propagating away from the collision area. The measurements included root mean square turbulent velocities and their decay rates, interfacial velocity, rate of change of fluid-parcel density, and eddy diffusivity. These measures depended on the Reynolds number $Re$, but appeared to achieve Reynolds number similarity for $Re>3000$. The eddy diffusivity $K_{T}$, space–time averaged over the spatial extent ($H\times H$) and the lifetime ($t\approx 3H/u_{f}$) of collision, was $K_{T}/u_{f}H=0.0036$ for $Re>3000$, with the area $A$ of active mixing being $A/H^{2}=0.037$.

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.

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.

Interaction between waves and gravity currents: description of turbulence in a simple numerical model

Effects of surface waves on gravity current propagation are studied by means of a numerical model. The adopted modeling approach couples a Boussinesq-type of model for surface waves and a gravity current model for stratified flows. In particular two different turbulence closure models are introduced which take into account subgrid turbulence and an additional depth-constant eddy-viscosity. The turbulence parameters are calibrated by means of experimental data on the time evolution of the heavy front, obtained both in the absence and in the presence of regular surface waves. Velocity fields, heavy and light front position, shear stresses, vorticity and entrainment calculated by the model are analyzed. The turbulence closure which includes both uniform and Smagorinsky type eddy viscosity allows a better description of the actual gravity current propagation. In particular, the results highlight the fact that the presence of the oscillatory motion causes, simultaneously, a reduction in turbulence and an increase in the mixing of heavy and light fluids. Such a result is in agreement with the experimental observations.

Influence of Regular Surface Waves on the Propagation of Gravity Currents: Experimental and Numerical Modeling

AbstractThe propagation of gravity currents is analyzed in the presence of regular surface waves, both experimentally and numerically, by using a full-depth lock-exchange configuration. Full-depth ...

Influence of Regular Surface Waves on the Propagation of Gravity Currents: Experimental and Numerical Modeling

Influence of Regular Surface Waves on the Propagation of Gravity Currents: Experimental and Numerical Modeling

On the propagation of viscous gravity currents of non-Newtonian fluids in channels with varying cross section and inclination

This paper presents a model for the laminar propagation of gravity currents of rheologically complex fluids over natural slopes. The study is motivated by the ubiquitous occurrence of gravity currents in environmental applications that are confined by channels that widen and have reduced slopes in the flow direction; typical examples are mud and lava flows. In these applications, many fluids exhibit nonlinear relationships between shear stress and shear rate, with or without the appearance of a yield stress. We consider Ostwald-de Waele and Herschel-Bulkley (HB) fluids. A power-law equation is used to capture the variations in the channel shape and slope in the flow direction. We study the motion of constant and time-dependent volumes of these fluids on smoothly varying topographies. Approximate similarity solutions are obtained for Ostwald-de Waele fluids, while for HB fluids, we use the methods of characteristics to compute front propagation. Constant volume and constant influx tests were conducted in a channel with a widening parabolic cross-section and an inclination decreasing downstream from ≈ 7° to ≈ 3.2°. The front position was measured continuously over time, and the current thickness and the surface velocity were recorded for a subset of experiments in some cross sections. The experimental study confirms the theoretical formulation, with a better agreement for constant influx than constant volume currents.

On the self-similar propagation of gravity currents through an array of emergent vegetation-like obstacles

Self-similar propagation of gravity currents through vegetation-like obstruction arrays was elucidated. We conducted a theoretical analysis by using an approximate model for one-layer and two-layer situations. This model incorporates a balance between the driving buoyancy (i.e., pressure) force and the resisting obstruction-induced drag force that is proportional to uλ (where u —speed in the layer and λ —a constant). We focused our attention on solutions with λ ≥ 1. We considered both gravity currents in a deep ambient fluid (including both continuous-flux release currents and constant-volume currents) and lock-exchange currents and demonstrated that a variety of such flows are governed by physically acceptable similarity solutions. For gravity currents in a deep ambient fluid, our theoretical analysis revealed four distinct classes of similarity solutions. Class I solutions predict gravity currents with a triangular profile (i.e., linear current interface with a constant negative slope) and a front/nose position that is a linear function of time. The physical presence of such self-similar currents was reported in recent experimental observations for currents sustained by a continuous-flux release source. We showed that theoretical predictions of Class I solutions capture the behavior of these experimental currents well. Class II solutions predict gravity currents with a non-linear profile/interface and a constant height at the source. Though physically acceptable, we could not relate this class of solutions to presently known currents. Class III solutions correspond to constant-volume currents and predict a linear increase of velocity within the current toward the nose. We discussed this class of similarity solutions using previously reported experimental observations of such currents. Class IV solutions cover the rest of the parameter domain for all other continuous-flux release gravity currents (except those that fall under Classes I-III). Next, using a two-layer variation of the model, we developed physically acceptable similarity solutions for lock-exchange currents (released by a full-depth gate). We confirmed our theoretical results by performing comparisons with previously reported experimental data for such currents. These comparisons, while showing a good qualitative agreement, revealed a quantitative ambiguity on the value of λ for the dependency of the obstruction-induced drag force on u. We also extended our similarity solutions for the currents in a deep ambient fluid to the axisymmetric geometry. We expect our similarity solutions to provide useful insights for both “deep” and lock-exchange type of gravity currents propagating through aquatic vegetation-like obstacles and a guidance for adequate design of relevant experiments.

Experiments on gravity currents down a ramp in unstratified and linearly stratified salt water environments

Gravity current propagation in the stratified environment is one of key research topics in atmosphere and marine sciences, etc. A series of experiments were conducted to investigate lock-release gravity currents down a ramp into different ambient environments. The front velocity of gravity currents in constant-density ambient increases rapidly at first, then stays nearly constant; the front velocity in linearly stratification environments increases firstly but then decreases gradually. This development process can be divided into three stages, namely, acceleration stage, deceleration stage and separation stage. The flow can be characterized by the relative stratification S , the Reynolds number Re and the Richardson number Ri 0. The front location, the front velocity and the velocity profile were analyzed by high speed camera. A particle image velocimetry (PIV) technique was applied to study the velocity field and vorticity field. The result showed that the counterclockwise vortexes appearing at the upper boundary were mainly due to Kelvin-Helmholtz instability and the clockwise vortexes in the lower boundary arose from the viscous forces in the boundary layer. This paper revealed the dynamic characteristics of gravity currents in constant-density ambient and linearly stratification respectively. The result can be applied in situations such as salinity intrusion of estuary and submarine turbidity currents, etc.

Numerical simulation of gravity current propagation in a compressible atmosphere

Numerical simulation of gravity current propagation in a compressible atmosphere

Chislennoe modelirovanie rasprostraneniya gravitatsionnogo techeniya v szhimaemoy atmosfere

Chislennoe modelirovanie rasprostraneniya gravitatsionnogo techeniya v szhimaemoy atmosfere

High-resolution simulations of downslope gravity currents in the acceleration phase

Gravity currents generated from an instantaneous buoyancy source propagating down a slope in the range of 0∘ ≤ θ < 90∘ have been investigated in the acceleration phase by means of high-resolution two-dimensional simulations of the incompressible Navier-Stokes equations with the Boussinesq approximation. Front velocity history shows that, after the heavy fluid is released from rest, the flow goes through the acceleration phase, reaching a maximum front velocity Uf,max, and followed by the deceleration phase. The existence of a maximum of Uf,max is found near θ = 40∘, which is supported by the improved theory. It is identified for the first time that the time of acceleration decreases as the slope angle increases, when the slope angle is approximately greater than 10∘, and the time of acceleration increases as the slope angle increases for gravity currents on lower slope angles. A fundamental difference in flow patterns, which helps explain the distinct characteristics of gravity currents on high and low slope angles using scaling arguments, is revealed. Energy budgets further show that, as the slope angle increases, the ambient fluid is more easily engaged in the gravitational convection and the potential energy loss is more efficiently converted into the kinetic energy associated with ambient fluid. The propagation of gravity currents on a slope is found to be qualitatively modified as the depth ratio, i.e., the lock height to channel height ratio, approaches unity. As the depth ratio increases, the conversion of potential energy loss into the kinetic energy associated with heavy fluid is inhibited and the conversion into the kinetic energy associated with ambient fluid is enhanced by the confinement of the top wall.