Intrusive 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.

Presence of Holmboe waves in particle-laden intrusive gravity current

The present study evaluates the prevalence of Holmboe waves in an intrusive gravity current (IGC) containing particles, employing large Eddy simulation (LES). Holmboe waves, a type of stratified shear layer-generated wave, are characterised by a relatively thin density interface compared to the thickness of the shear layer. The study demonstrates the occurrence of secondary rotation, wave stretching over time, and fluid ejection at the interface between the IGC and a lower gravity current (LGC). Results indicate that, aside from J and R, the density difference between the IGC and the LGC has an impact on Holmboe instability. However, a reduction in the density difference does not manifest consistently in the frequency, growth rate, and phase speed, though it does cause an increase in the wavelength. It is important to note that small particles do not affect the Holmboe instability of the IGC, while larger particles cause the current to become unstable and vary the characteristics of Holmboe instability. Moreover, an increase in the particle diameter size results in an increment in the wavelength, growth rate, and phase speed; but is accompanied by a decrease in frequency. Additionally, the enlargement of the bed slope angle makes the IGC more unstable, encouraging the growth of Kelvin–Helmholtz waves; however, this causes Holmboe waves to disappear on inclined beds. Finally, a range for the instabilities of both Kelvin–Helmholtz and Holmboe is provided.

Direct numerical simulations of intrusive density- and particle-driven gravity currents

In the present study, mesopycnal flows are investigated using direct numerical simulations. In particular, intrusive density- and particle-driven gravity currents in the lock exchange setup are simulated with the high-order finite-difference framework Xcompact3d. To account for the settling velocity of particles, a customized Fick's law for the particle-solution species is used with an additional term incorporating a constant settling velocity proportional to the concentration of particles. A general energy budget equation is presented, for which the energy can migrate across the domain's boundaries. The relevant main features of intrusive gravity currents, such as front velocity, energy exchanges, sedimentation rate, deposit profile, and deposit map are discussed with the comparison between two- and three-dimensional simulations. In particular, the influence of the Grashof number, the interface thickness, the energy exchanges, the sedimentation process, and how the presence of more than one particle fraction may change the flow dynamics are investigated. The results are in good agreement with previous experiments and theoretical work, in particular for the prediction of the front velocity. For the particle-driven case, the suspended mass evolution along with the sedimentation rate suggests the occurrence of three different stages. In the first stage after the lock release, the particle mixture tends to suspend itself due to gravitational forces. Once most of the particle-mixture mass is suspended, the current intrudes while increasing its velocity, reaching its kinetic energy peak. In the last stage, the particles are deposited at a nearly constant sedimentation rate. As a result, the front velocity constantly decelerates.

Intruding gravity currents and re-circulation in a rotating frame: Laboratory experiments

We present experimental results of rotating downslope gravity currents performed at the Coriolis Platform in Grenoble, France. A novel experimental design to produce the downslope gravity flow has been employed using an axisymmetric configuration and a uniform flow injection that enabled the study of the long-term evolution of surface baroclinic vortices and of the gravity current, monitoring at the same time the evolution of the global circulation and the vorticity produced in the central deep area. The structure of the current, its relevant scales, and the characteristics of the generated surface vortices fairly agree with previous results in the literature in smaller scale installations. Discrepancies are attributable to the influence of both topographic Rossby waves and viscous effects that are much reduced in the Coriolis platform. Rotating intrusive gravity currents in a two-layer stratified ambient behave very differently from dense currents following the bottom slope. Substantial differences appear for the induced global circulation, which depend on the nature of the intrusion, with a strong influence of the rotation rate. In particular, intruding gravity currents give rise to a strong turbulent environment at intermediate and bottom depths in the central area, with submesoscale vortices (i.e., with a typical size smaller than the Rossby deformation radius) and a large variety of scales. In contrast, when the dense current follows the bottom slope, no significant vorticity production in the bottom and intermediate layers is reported. This clearly suggests that bottom boundary layers detaching from the boundary and propagating toward the ambient interior as in intrusive currents give an important contribution to the turbulence dynamics.

PLUME-MoM-TSM 1.0.0: a volcanic column and umbrella cloud spreading model

Abstract. In this paper, we present a new version of PLUME-MoM, a 1-D integral volcanic plume model based on the method of moments for the description of the polydispersity in solid particles. The model describes the steady-state dynamics of a plume in a 3-D coordinate system, and a modification of the two-size moment (TSM) method is adopted to describe changes in grain size distribution along the plume, associated with particle loss from plume margins and with particle aggregation. For this reason, the new version is named PLUME-MoM-TSM. For the first time in a plume model, the full Smoluchowski coagulation equation is solved, allowing us to quantify the formation of aggregates during the rise of the plume. In addition, PLUME-MOM-TSM allows us to model the phase change of water, which can be either magmatic, added at the vent as liquid from external sources, or incorporated through ingestion of moist atmospheric air. Finally, the code includes the possibility to simulate the initial spreading of the umbrella cloud intruding from the volcanic column into the atmosphere. A transient shallow-water system of equations models the intrusive gravity current, allowing computation of the upwind spreading. The new model is applied first to the eruption of the Calbuco volcano in southern Chile in April 2015 and then to a sensitivity analysis of the upwind spreading of the umbrella cloud to mass flow rate and meteorological conditions (wind speed and humidity). This analysis provides an analytical relationship between the upwind spreading and some observable characteristic of the volcanic column (height of the neutral buoyancy level and plume bending), which can be used to better link plume models and volcanic-ash transport and dispersion models.

Large eddy simulations of solitons colliding with intrusions

The dynamics of lock-release Intrusive Gravity Currents (IGCs) generating Internal Solitary Waves (ISWs) are investigated by three-dimensional large eddy simulations. We set the numerical, laboratory-scale domain in order to release a uniform fluid in multi-layer, stratified ambient, exciting pycnocline displacements. By adopting different initial settings, we analyzed the influence of the ambient stratification on both IGCs and ISWs features. We present the main flow dynamics and the time evolution of IGC and ISW front and trough positions, respectively. During the simulations, the ISW is allowed to reach the vertical wall at the end of the domain, and it undergoes reflection. We then analyzed the interaction between the IGC and the reflected ISW: the wave is observed to accelerate as it is pushed upwards by the intrusion, which, in turns, flows below the ISW, decelerating. By analyzing instantaneous velocity fields and flow rates, we found that during this interaction, the ISW increases its celerity in response of the reduced area available for its propagation, partially occupied by the intrusion, and because the velocity field in the IGC interface surroundings acts to facilitate the ISW passage.

Intrusions and solitons: Propagation and collision dynamics

Triggering and evolution of internal solitary waves (ISWs) generated by intrusive gravity currents (IGCs) propagating into a stratified ambient fluid is analyzed by laboratory experiments. After the release of a fluid of uniform density, intermediate with respect to the upper (lower-density) and lower (higher-density) layers in the channel, the IGC develops and flows downstream, intruding into the pycnocline. Near the IGC leading front, the compression of the upper layer generates ISWs: they gradually separate from the current that propagates slower. Shoaling downstream over a uniform sloping boundary, solitons break and partially reflect. We investigate the dynamics of the interaction between the reflected ISWs and the incoming IGC. During the engage, an increase in the ISW celerity occurs, leading the celerity of the reflected waves to be even larger than the incident wave. Our analysis shows how both ISWs and IGCs can significantly change their features as they experience a change of the density structure in the water column. This is expected to occur, for example, in stratified small-scale basins, where river plumes intrude the seasonal thermocline. The radial ISWs, originated by IGCs, can then be reflected by the adjacent bottom bathymetry, spreading against the intrusive current from which they are generated.

Application of Circular Bubble Plume Diffusers to Restore Water Quality in a Sub-Deep Reservoir.

Circular bubble plume diffusers have been confirmed as an effective technology for the restoration of the deep water system, but have never been applied in sub-deep water system. In this study, circular bubble plume diffusers were used, for the first time, to restore water quality in the Aha Reservoir, a typical sub-deep reservoir in Southwest China. Axisymmetric intrusive gravity currents were formed with a horizontal radius of 250 m at the equilibrium depth and the intrusion of oxygen-enriched water occurred within the depth of 10–14 m, while thermal stratification remained intact. A total of 95% of the imported oxygen was dissolved, but most was consumed by organic matter and other reduced substances within the hypolimnion. The oxygen consumption of organic matter, NH4+ and remaining reduced materials, accounted for 41.4–52.5%, 25% and 13.3–24.4% of the total imported oxygen, respectively. Compared with the control sites, dissolved oxygen level in the hypolimnion increased 3–4 times, and concentrations of NH4+, total Fe and total Mn were reduced by 15.5%, 45.5% and 48.9%, respectively. A significant decrease in total phosphorus and nitrogen concentrations was observed in the experimental zone (0.04–0.02 mg/L and 1.9–1.7 mg/L, respectively). This indicates that circular bubble plumes have great potential for oxygenation of the hypolimnion and improving water quality in the sub-deep water system. Nevertheless, further efforts are needed to improve the discrete bubble model to elaborate the oxygen transmission dynamics and the plume formation processes in sub-deep water systems, incorporating oxygen consumption processes.

Intrusive gravity currents propagating into two-layer stratified ambients: Vorticity modeling

Intrusive gravity currents propagating into two-layer stratified ambients: Vorticity modeling M. A. Khodkar, M. M. Nasr-Azadani and E. Meiburg Department of Mechanical Engineering University of California at Santa Barbara Santa Barbara, CA 93106. Email: mkhodkar@umail.ucsb.edu Abstract A simplified model is developed for intrusive gravity currents propagating along the interface of a two- layer stratified ambient. The model is based on the conservation of mass and vorticity, and it does not require any empirical closure assumptions. A parametric study conducted with this model reproduces the correct behavior in various limits, and is consistent with previously reported experimental observations. Specifically, it predicts the formation of equilibrium intrusions when the intrusion density equals the depth-weighted mean density of the two ambient layers. It furthermore demonstrates the existence of non- smooth limits under certain conditions. An energy analysis shows that under non-equilibrium conditions the intrusion gains energy. The predictions by the parametric study are furthermore compared to two- dimensional DNS results, and very good agreement is observed with regard to all flow properties. 1. Introduction Intrusions represent a special class of gravity currents that propagate horizontally into a stratified ambient at intermediate depths. They occur in a variety of atmospheric and oceanic situations, where they can influence the dynamics of such flows as sea breeze fronts, river plumes and powder snow avalanches. Fig1. Schematic of an intrusion produced via a lock-release process: a) at the initial state, where all the fluids are at rest, b) when the gate is removed and a quasisteady, symmetric intrusion forms and c) when (𝜌 𝑙 𝑑 𝑙 + 𝜌 𝑢 𝑑 𝑢 )/𝐻 < 𝜌 𝑐 and a quasisteady, non-symmetric intrusion emerges.

Numerical simulations of intrusive gravity currents interacting with a bottom-mounted obstacle in a continuously stratified ambient

In this study, the flow dynamics of intrusive gravity currents past a bottom-mounted obstacle were investigated using highly resolved numerical simulations. The propagation dynamics of a classic intrusive gravity current was first simulated in order to validate the numerical model with previous laboratory experiments. A bottom-mounted obstacle with a varying non-dimensional height of $$\tilde{D}=D/H$$ , where D is the obstacle height and H is the total flow depth, was then added to the problem in order to study the downstream flow pattern of the intrusive gravity current. For short obstacles, the intrusion re-established itself downstream without much distortion. However, for tall obstacles, the downstream flow was found to be a joint effect of horizontal advection, overshoot-springback phenomenon, and associated Kelvin-Helmholtz instabilities. Analysis of the numerical results show that the relationship between the downstream propagation speed and the obstacle height can be subdivided into three regimes: (1) a retarding regime ( $$\tilde{D}$$ $$\approx $$ 0–0.3) where a 30 % increase in obstacle height leads to a 20 % reduction in propagation speed, simply due to the obstacle’s retarding effect; (2) an impounding regime ( $$\tilde{D}$$ $$\approx $$ 0.3–0.6) where the additional 30 % increase in obstacle height only leads to a further (negligible) 5 % reduction in propagation speed, due to the accelerating effect of upstream impoundment and downstream enhanced mixing; and (3) a choking regime ( $$\tilde{D}$$ $$\approx $$ 0.6–1.0) where the propagation speed is dramatically reduced due to the dominance of the obstacle’s blocking effect. The obstacle thickness was found to be irrelevant in determining the downstream propagation speed at least for the parameter range explored in this study. The present work highlights the significance of topographic effects in stratified flows with horizontal pressure forcing.

The instantaneous Froude number and depth of unsteady gravity currents

We have studied two-dimensional and three-dimensional gravity currents with Reynolds number 22,600. We present a definition for h c , a spatially varying characteristic depth of an unsteady current which can be used to determine an appropriate current head height h H . We also propose a robust method for the determination of the front speed u c and a characteristic measure of the available buoyancy in the head g′ c . The proposed definitions and methods are robust in the sense that the quantities (h c , u c and g′ c ) computed from the instantaneous flow fields show a largely continuous behaviour in time despite the unsteady nature of the flow. We show that the Froude number calculated from these variables, , remains constant throughout the constant-velocity and the self-similar regimes. We also investigate the dependence of the Froude number on the ratio of the current depth to the channel depth and compare our results with the theories of Nokes et al. [(2008). The front condition for intrusive gravity currents. J. Hydraulic Res. 46(6), 788–801] and Shin et al. [(2004). Gravity currents produced by lock exchange. J. Fluid Mech. 521, 1–34].

Numerical simulation of particle-driven gravity currents

Particle-driven gravity currents frequently occur in nature, for instance as turbidity currents in reservoirs. They are produced by the buoyant forces between fluids of different density and can introduce sediments and pollutants into water bodies. In this study, the propagation dynamics of gravity currents is investigated using the FLOW-3D computational fluid dynamics code. The performance of the numerical model using two different turbulence closure schemes namely the renormalization group (RNG) \({k-\epsilon}\) scheme in a Reynold-averaged Navier-Stokes framework (RANS) and the large-eddy simulation (LES) technique using the Smagorinsky scheme, were compared with laboratory experiments. The numerical simulations focus on two different types of density flows from laboratory experiments namely: Intrusive Gravity Currents (IGC) and Particle-Driven Gravity Currents (PDGC). The simulated evolution profiles and propagation speeds are compared with laboratory experiments and analytical solutions. The numerical model shows good quantitative agreement for predicting the temporal and spatial evolution of intrusive gravity currents. In particular, the simulated propagation speeds are in excellent agreement with experimental results. The simulation results do not show any considerable discrepancies between RNG \({k-\epsilon}\) and LES closure schemes. The FLOW-3D model coupled with a particle dynamics algorithm successfully captured the decreasing propagation speeds of PDGC due to settling of sediment particles. The simulation results show that the ratio of transported to initial concentration Co/Ci by the gravity current varies as a function of the particle diameter ds. We classify the transport pattern by PDGC into three regimes: (1) a suspended regime (ds is less than about 16 μm) where the effect of particle deposition rate on the propagation dynamics of gravity currents is negligible i.e. such flows behave like homogeneous fluids (IGC); (2) a mixed regime (16 μm 40 μm) where the PDGC rapidly loses its forward momentum due to fast deposition. The present work highlights the potential of the RANS simulation technique using the RNG \({k-\epsilon}\) turbulence closure scheme for field scale investigation of particle-driven gravity currents.

A new view of the dynamics, stability and longevity of volcanic clouds

Powerful explosive volcanic eruptions inject ash high into the atmosphere, which spreads to form umbrella clouds. Identifying key physical processes governing the dynamics, stability and longevity of umbrella clouds is central to assessing volcanic hazards as well as the nature of volcanic forcings on climate. Here we present a series of laboratory experiments producing turbulent particle-laden jets and subsequent axisymmetric intrusive gravity currents into a stratified environment. Our experiments reproduce many of the main dynamical regimes observed during the formation of an explosive volcanic column, and highlight new dynamics for the umbrella cloud. Theoretical predictions of column collapse from a simple model of a turbulent jet are in good agreement with experimental observations as well as previous studies. Depending on the flow intensity, the strength of the initial environmental density stratification and the particle concentration at the source, resulting umbrella clouds can, however, evolve through a series of new regimes as a result of the dynamics of particle sedimentation within these flows as well as from their bases. Using scaling theory we show that during cloud spreading, internal sedimentation drives the growth and intermittent overturn of thin, gravitationally unstable “particle boundary layers” (PBLs) as particle-rich plumes. This PBL-driven convection can have remarkable effects ranging from progressive dilution of clouds to their catastrophic overturn and collapse. In natural eruptions, whether the dynamics of PBLs play a major role in particle sedimentation depends on the grain size distribution inside the cloud and on eruption column height. In general, particles larger than ~60μm–1mm are expected to settle individually, whereas finer particles will accumulate PBLs resulting in the formation of armless mammatus clouds or dangerous gravity currents at much larger distances from the volcanic vent than ever considered before. Such dynamics is apparent in observations of numerous modern eruptions and is inferred from the deposits of historic and prehistoric eruptions for where there exist appropriate data. Consideration of the consequences of these phenomena for problems such as volcanic hazards to humans and climate change may, thus, be very important in the assessment of future eruptions.

The lifecycle of axisymmetric internal solitary waves

Abstract. The generation and evolution of solitary waves by intrusive gravity currents in an approximate two-layer fluid with equal upper- and lower-layer depths is examined in a cylindrical geometry by way of theory and numerical simulations. The study is limited to vertically symmetric cases in which the density of the intruding fluid is equal to the average density of the ambient. We show that even though the head height of the intrusion decreases, it propagates at a constant speed well beyond 3 lock radii. This is because the strong stratification at the interface supports the formation of a mode-2 solitary wave that surrounds the intrusion head and carries it outwards at a constant speed. The wave and intrusion propagate faster than a linear long wave; therefore, there is strong supporting evidence that the wave is indeed nonlinear. Rectilinear Korteweg-de Vries theory is extended to allow the wave amplitude to decay as r-p with p=½ and the theory is compared to the observed waves to demonstrate that the width of the wave scales with its amplitude. After propagating beyond 7 lock radii the intrusion runs out of fluid. Thereafter, the wave continues to spread radially at a constant speed, however, the amplitude decreases sufficiently so that linear dispersion dominates and the amplitude decays with distance as r-1.

A steady-state model for asymmetric intrusive gravity currents in a linearly stratified ambient

The behavior of the steady intrusive gravity current of thickness h and density ρc which propagates with speed U at the neutral buoyancy level of a long horizontal channel of height H into a stratified ambient fluid whose density increases linearly from ρo to ρb is investigated. The intrusive and the ambient fluids are assumed to be asymmetric with respect to the neutral-buoyancy level. The Boussinesq, high-Reynolds number two-dimensional configuration is considered. Long’s model combined with the flow-force balance over the width of the channel and the pressure balances over a density current are used to obtain the desired results. It is shown that the intrusion velocity decreases with decreasing the asymmetry of the system and approaches its minimum for the symmetric configuration (however, the difference of speed between asymmetric and symmetric configurations shows no significant differences).

Intrusive gravity currents between two stably stratified fluids

We present an experimental and numerical study of one stratified fluid propagating into another. The two fluids are initially at rest in a horizontal channel and are separated by a vertical gate which is removed to start the flow. We consider the case in which the two fluids have the same mean densities but have different, constant, non-zero buoyancy frequencies. In this case the fluid with the smaller buoyancy frequency flows into the other fluid along the mid-depth of the channel in the form of an intrusion and two counter-flowing gravity currents of the fluid with the larger buoyancy frequency flow along the top and bottom boundaries of the channel. Working from the available potential energy of the system and measurements of the intrusion thickness, we develop an energy model to describe the speed of the intrusion in terms of the ratio of the two buoyancy frequencies. We examine the role of the stratification within the intrusion and the two gravity currents, and show that this stratification plays an important role in the internal structure of the flow, but has only a secondary effect on the speeds of the exchange flows.

Intrusive gravity currents from finite-length locks in a uniformly stratified fluid

Gravity currents intruding into a uniformly stratified ambient are examined in a series of finite-volume full-depth lock-release laboratory experiments and in numerical simulations. Previous studies have focused on gravity currents which are denser than fluid at the bottom of the ambient or on symmetric cases in which the intrusion is the average of the ambient density. Here, we vary the density of the intrusion between these two extremes. After an initial adjustment, the intrusions and the internal waves they generate travel at a constant speed. For small departures from symmetry, the intrusion speed depends weakly upon density relative to the ambient fluid density. However, the internal wave speed approximately doubles as the waves change from having a mode-2 structure when generated by symmetric intrusions to having a mode-1 structure when generated by intrusions propagating near the bottom. In the latter circumstance, the interactions between the intrusion and internal waves reflected from the lock-end of the tank are sufficiently strong and so the intrusion stops propagating before reaching the end of the tank. These observations are corroborated by the analysis of two-dimensional numerical simulations of the experimental conditions. These reveal a significant transfer of available potential energy to the ambient in asymmetric circumstances.

The dynamics of steady, partial‐depth intrusive gravity currents

Experiments of intrusive gravity currents generated by lock exchange offer insights into atmospheric and oceanic flows. However, whereas many previous investigations have considered the full‐depth’ lock exchange problem, in which the intermediate density fluid initially spans the entire channel depth, less is known about ‘partial‐depth’ releases, which represent a more appropriate analogue to environmental flows where the inceptive, localized interfacial mixing is relatively weak and/or the upper and lower ambient layers are of significant vertical expanse. Here, we consider this circumstance using a combination of experimental, (two‐dimensional) numerical and analytical techniques with a particular focus on equilibrium flow for which there is no auxiliary concentration or dilution of the active scalar, and the interface ahead of the intrusion remains approximately horizontal. In this case, the initial (steady) speed of propagation, U, can be well‐predicted by adapting a shallow‐water model for gravity currents that employs as its front condition the relationship of Benjamin (1968). When, in the initial state, the upper and lower halves of the density field are (stretched) mirror images of one another, the front travels at constant speed beyond 10 lock lengths, as was noted in the case of full‐depth lock releases by Sutherland et al. (2004) and Sutherland and Nault (2007). However, when this symmetry is broken either by altering the relative depth of either ambient layer or by changing the intrusion density, the flow begins to decelerate after travelling as few as three lock lengths.

The front condition for intrusive gravity currents

A mathematical model is developed for a high Reynolds number, quasi-steady, intrusive gravity current propagating into a two-layer ambient fluid. The model is based on inviscid, irrotational flow theory, and is used to predict the rate of advance of the current front as a function of its head height. The key underlying assumptions of the model are that the local conditions at the head determine its speed of propagation, and that the upstream portion of the head is well approximated by an inviscid, irrotational flow. In order to provide a complete set of boundary conditions it is assumed that the ambient flow over the top of the head is horizontal, but not uniform. An upper bound solution is derived and is compared with a full solution generated with an optimisation based Boundary Element Method technique. The upper bound solution is shown to be entirely adequate for relative current heights greater than 0.3. The results from two experimental programmes provide support for the model predictions, and particle tracking velocimetry measurements indicate that the assumption of horizontal flow over the head is reasonable.

On axisymmetric intrusive gravity currents: The approach to self-similarity solutions of the shallow-water equations in a stratified ambient

The axisymmetric intrusion of a fixed volume of fluid, which is released from rest and then propagates radially at the neutral buoyancy level in a deep linearly stratified ambient fluid is investigated. The SW equations representing the high-Reynolds number motion are used. For the long-time motion an analytical similarity solution indicates propagation with t 1 / 3 , but the shape is peculiar: the intrusion propagates like a ring and the inner domain contains a thin tail of clear ambient fluid. To avoid accumulation of numerical errors the problem was reformulated in terms of new variables and solved by finite-difference scheme. It is shown that the initial-value problem tends to the similarity prediction. Comparison with the non-stratified case is presented. It was found that for the non-stratified case there is a similar “tail-ring” stage of propagation, however this stage is only a transient to a different self-similar shape.