Gravity Current Head Research Articles

Impact force of non-Boussinesq gravity-current head against a circular cylinder above the seabed

We study the impact force of the gravity-current head on a circular cylinder above the seabed for the non-Boussinesq effect using a large-eddy simulation model well validated against laboratory data. Most existing studies of the gravity current were for the slight density difference between the current and the ambient fluid, assuming the density is constant using the Boussinesq approximation. The aim of the present study, however, is about gravity current of significant density difference. We detail the coherent turbulence structure of the gravity current and the transient oscillation of the impact force on the cylinder over a range of density differences varying from (ρs−ρa)/ρa=0.02 to 2 for the elevation relative to the diameter of the cylinder E/D=0.05, 0.4 and 1.0. The velocity and vorticity field in the current show a gravity-current head separating from the primary current driven by excess pressure at the back, with a structural similarity almost independent of the density difference. The gravity-current head’s frontal and wake velocities are determined from the numerical simulations and related to the buoyancy speed. The impact force on the cylinder rises to a peak immediately after the arrival of the gravity-current head. We propose a set of new drag and lift coefficients using a gravity-driven pressure as a reference for the impact force of the non-Boussinesq current. The peak impact force, made dimensionless by the gravity-driven pressure, is found to be relatively independent of the density difference, regardless of how large the current density may be.

On the merging and splitting processes in the lobe-and-cleft structure at a gravity current head

High-resolution simulations are performed for gravity currents propagating on a no-slip boundary to study the merging and splitting processes in the lobe-and-cleft structure at a gravity current head. The simulations reproduce the morphological features observed in the laboratory and provide more detailed flow information to elucidate the merging and splitting processes. Our mean lobe width$\tilde {b}$and mean maximum lobe width$\tilde {b}_{max}$satisfy the empirical relationships$\tilde {b}/\tilde {d}=7.4 Re^{-0.39}_f$and$\tilde {b}_{max}/\tilde {d}=12.6 Re^{-0.38}_f$, respectively, over the front Reynolds number in the range$383 \le Re_f \le 3267$, where the front Reynolds number is defined as$Re_f= \tilde {u}_f \tilde {d} / \tilde {\nu }, \tilde {u}_f$is the front velocity,$\tilde {d}$is the height of the gravity current head and$\tilde {\nu }$is the fluid kinematic viscosity. When measured in terms of the viscous length scale$\tilde {\delta }_\nu = \tilde {\nu }/\tilde {u}^*$, where$\tilde {u}^*$is the shear velocity at the gravity current head, the mean lobe width and the mean maximum lobe width increase with increasing front Reynolds number and asymptotically approach$126 \tilde {\delta }_\nu$and$230 \tilde {\delta }_\nu$at$Re_f=3267$, respectively. The vortical structure inside a lobe has an elongated tooth-like shape and a pair of counter-rotating streamwise vortices are positioned on the left- and right-hand sides of each cleft. For the merging process, it requires the interaction of three tooth-like vortices and the middle tooth-like vortex breaks up and reconnects with the two neighbouring tooth-like vortices. Therefore, a cleft may continually merge with another neighbouring cleft but may never disappear. For the splitting process, even before the new cleft appears, a new born streamwise vortex is created by the parent vortex of opposite orientation and the parent vortex can be either the left part or the right part of the existing tooth-like vortex inside the splitting lobe. The new born streamwise vortex then induces the other counter-rotating streamwise vortex as the new cleft develops. The initiation of the splitting process can be attributed to the Brooke–Hanratty mechanism reinforced by the baroclinic production of vorticity. Depending on the orientation of the parent vortex, the resulting new cleft after the splitting process can shift laterally in the positive or negative spanwise direction along the leading edge of the gravity currents as the lobe-and-cleft structure moves forward in the streamwise direction. For gravity currents propagating on a no-slip boundary, the lobe-and-cleft structure is self-sustaining and the manifestations of the merging and splitting processes are in accord with reported laboratory observations.

Continuous and discontinuous gravity currents in open-channel embayments.

Embayments, as major storage zones in riverine environments, could be surrounded by gravity currents associated with industrial pollution, heavy impurities, and sewage. The accumulated contaminated matter in embayments significantly impairs aquatic habitats and influences the embayment performance. In this study, the three-dimensional vortical structures of continuous and discontinuous gravity currents in channels connected to an embayment are investigated by solving unsteady Reynolds-averaged Navier-Stokes with algebraic Reynolds stress model (ASM) which has been improved by the buoyancy effects. The lateral embayment with different configurations is simulated to investigate the exchange processes of the dense fluid between the lateral embayment and main stream. The accuracy and consistency of the developed model are checked using the experimental data of continuous and discontinuous gravity currents in the straight channel and mass exchange in the lateral embayment. The findings have revealed that the agreement between measured and simulated flow and concentration fields is reasonable. The current head propagation of the continuous gravity current inside the embayment is similar to the discontinuous gravity current head propagation. At early time, the continuous gravity current leads to rapid diffusion of the concentration in the embayment and main channel downstream. In the discontinuous gravity current with the embayment aspect ratio equal to 1.0, the dense fluid firstly fills the lateral embayment as the most volume of the dense fluid is trapped and then it flushes out into the main channel. The geometric aspect ratio of the lateral cavity slightly affects the exchange coefficient between the main channel and lateral cavity. The time-averaged exchange coefficient is 0.33 in the continuous gravity current.

Propagation of a continuously supplied gravity current head down bottom slopes

We present a combined theoretical-experimental investigation of the downslope propagation of a gravity current sustained by a source. The current propagates first on a horizontal bottom, then on a downslope. We focus on the case when the current at the ridge (point where donwslope begins) has a stable interface (Ri>0.25) and is critical with F=1, where Ri and F are the bulk Richardson and flow Froude numbers. We derive the equations that govern the nose propagation and speed using a shallow-water (SW) model, in which the nose is a jump matched to characteristics emitted at the ridge. This provides a self-contained prediction for the speed of propagation uN and position ξN of the nose. The predicted uN increases with time and distance ξ from the ridge. Since Ri decreases with ξ in the tail behind the nose, appearance of instabilities at a certain traveled distance determines the domain of validity of the SW solution. A good agreement is reported with various experiments with different initial conditions at the ridge and slope angles (both fixed and changing with distance from the ridge). It is shown that the nose velocity is always less than the maximum velocity within the current head, which corresponds to the speed of the characteristics released at the ridge that catch on the current head.

Interaction between an inclined gravity current and a pycnocline in a two-layer stratification

A series of laboratory experiments were conducted to investigate the characteristics of a dense gravity current flowing down an inclined slope into a quiescent two-layer stratification. The presence of the pycnocline causes the gravity current to split and intrude into the ambient at two distinct levels of neutral buoyancy, as opposed to the classical description of gravity currents in stratified media as being either a pure underflow or interflow. The splitting behaviour is observed to be dependent on the Richardson number ( ) of the gravity current, formulated as the ratio of the excess density and the ambient stratification. For low , underflow is more dominant, while at higher interflow is more dominant. As increases, however, we find that the splitting behaviour eventually becomes independent of . Additionally, we have also identified two different types of waves that form on the pycnocline in response to the intrusion of the gravity current. An underflow-dominated regime causes a pycnocline displacement where the speed of the wave crest is locked to the gravity current, whereas an interflow-dominated regime launches an internal wave that moves much faster than the gravity current head or interfacial intrusion.

Interaction of a downslope gravity current with an internal wave

We investigate the interaction of a downslope gravity current with an internal wave propagating along a two-layer density jump. Direct numerical simulations confirm earlier experimental findings of a reduced gravity current mass flux, as well as the partial removal of the gravity current head from its body by large-amplitude waves (Hogg et al., Environ. Fluid Mech., vol. 18 (2), 2018, pp. 383–394). The current is observed to split into an intrusion of diluted fluid that propagates along the interface and a hyperpycnal current that continues to move downslope. The simulations provide detailed quantitative information on the energy budget components and the mixing dynamics of the current–wave interaction, which demonstrates the existence of two distinct parameter regimes. Small-amplitude waves affect the current in a largely transient fashion, so that the post-interaction properties of the current approach those in the absence of a wave. Large-amplitude waves, on the other hand, perform a sufficiently large amount of work on the gravity current fluid so as to modify its properties over the long term. The ‘decapitation’ of the current by large waves, along with the associated formation of an upslope current, enhance both viscous dissipation and irreversible mixing, thereby strongly reducing the available potential energy of the flow.

An Analysis of Two-Dimensional Stratified Gravity Current Flow using Open FOAM

Direct numerical simulations (DNSs) of two-dimensional stratified gravity-current are simulated using OpenFOAM. Three different aspect ratio, h0/l0 (where h0 is the height of the dense fluid and l0 is the length of the dense fluid) are simulated with stratification ranging from 0 (homogenous ambient) to 0.2 with a constant Reynolds number (Re) of 4000. The stratificationof the ambient air is determined by the density difference between the bottom and the top walls of the channel (ρb- ρ0, where ρb is the density at the bottom of the domain and ρ0 is the density at the top). The magnitude of the stratification (S=ԑb/ԑ) can be determined by calculating the reduced density differences of the bottom fluid with the ambient fluid (ԑb = (ρb- ρ0)/ ρ0) and the dense fluid with the ambient fluid (ԑ = (ρc-ρ0)/ ρ0, where ρc represents the density of the dense fluid). The configuration of the simulation is validated with a test case from Birman, Meiburg & Ungraish and the contour and front velocity (propagation speed) were in good agreement. The gravity current flow in the stratified ambient is analyzed qualitatively and compared with the gravity current in the homogenous ambient. Gravity current in homogenous ambient (S=0) and weak stratification (S=0.2) are supercritical flow where the flow is turbulent and Kelvin-Helmholtz (K-H) billow formed behind the gravity current head. The front location of the gravity is reduced as the stratification increase and denotes that the front velocity of the gravity current is reduced by the stratification.

A two-dimensional inviscid model of the gravity-current head by Lagrangian block simulation

A two-dimensional inviscid model of the gravity-current head produced by the release of a relatively small volume of dense fluid from behind a tall lock gate is constructed by Lagrangian block simulation. Three numerical experiments are conducted for the lock’s height-to-length aspect ratios H/Lo = 8, 4 and 2. The front speeds obtained by the simulations agree with the laboratory observation for a similar range of aspect ratios. The floor velocity in the wake behind these heads is found to be greater than their front speed. The high floor velocity is caused by the impingement of the coherent wake vortex on the floor. It is a condition that permits these gravity-current heads to maintain their structural integrity so that the fine sediments can travel with the head over long distances on the ocean floor. The structural coherence of the current head depends on the lock aspect ratio. The gravity-current head produced by the release from the lock with the highest aspect ratio of H/Lo = 8 is most coherent and relatively has the greatest floor velocity and the least trailing current behind the head.

Direct numerical simulation of double-diffusive gravity currents

This paper presents three-dimensional direct numerical simulations of laboratory-scale double-diffusive gravity currents. Flow is governed by the incompressible Navier-Stokes equations under the Boussinesq approximation, with salinity and temperature coupled to the equations of motion using a nonlinear approximation to the UNESCO equation of state. The effects of vertical boundary conditions and current volume are examined, with focus on flow pattern development, current propagation speed, three-dimensionalization, dissipation, and stirring and mixing. It was observed that no-slip boundaries cause the gravity current head to take the standard lobe-and-cleft shape and encourage both a greater degree and an earlier onset of three-dimensionalization when compared to what occurs in the case of a free-slip boundary. Additionally, numerical simulations with no-slip boundary conditions experience greater viscous dissipation, stirring, and mixing when compared to similar configurations using free-slip conditions.

Inside the head and tail of a turbulent gravity current

Gravity currents are an important buoyancy-driven flow in environmental, geophysical and industrial settings. Turbulence and mixing is commonplace in these flows, but is typically overlooked in theoretical models and predictions. Sher & Woods (J. Fluid Mech., vol. 784, 2015, pp. 130–162) have quantified the velocity and density structure in turbulent gravity currents by combining high-quality experimental data with new theory. Their insights are set to stimulate significant advances in the area.

Gravity current flow over sinusoidal topography in a two-layer ambient

We report upon a laboratory experimental study of dense full- and partial-depth locks released gravity currents propagating through a two-layer ambient and over sinusoidal topography of amplitude A and wavelength λ. Attention is restricted to a Boussinesq flow regime and the initial (or slumping) stage of motion. Because of the presence of the topography, the lower layer depth and channel depth vary in the downstream direction by as much as ±52% and ±40%, respectively. Despite such large variations, the instantaneous gravity current front speed typically changes by only a small amount from its average value, Ū. We conclude that the reason for this unexpected observation is a counterbalancing between the contraction/expansion of the channel on one hand and along-slope variations of the buoyancy force on the other hand. Compared to the case of gravity current flow over a horizontal surface, the topography has a retarding effect on Ū; we characterize the variation of Ū with the following parameters: A, A/λ, the interface height, the height of gravity current fluid inside the lock, and the layer densities as characterized by S ≡ (ρ1 − ρ2)/(ρ0 − ρ2) where ρ0 is the gravity current density, ρ1 is the lower ambient layer density, and ρ2 is the upper ambient layer density. The topography also alters the structure of the gravity current head by inducing large-scale Kelvin-Helmholtz (K-H) vortices directly downstream of regions of significant shear. These vortices are transient flow features; after formation and saturation, they relax at which point gravity current fluid sloshes back and forth in the topographic troughs. A simple geometric model is presented that prescribes the minimum number of topographic peaks a gravity current fluid will overcome. As in the horizontal bottom case, the forward advance of the gravity current can excite a downstream-propagating interfacial disturbance, which is more prominent for larger S. We identify when the gravity current front will travel faster (supercritical flow) or slower (subcritical flow) than the interfacial disturbance based on S and A/λ. Unlike in the horizontal-bottom case, however, we typically also observe interfacial oscillations far ahead of the gravity current front. These have wavelength approximately equal to λ and are due to spatial variations in the speed of the ambient return flow.

Gravity currents over a rigid and emergent vegetated slope

Lock-exchange experiments are conducted to investigate the effects of emergent vegetation on gravity currents flowing down a slope. Rigid and emergent cylinders are used to represent vegetation such as reeds in aquatic environments. The results show that the head of gravity currents without cylinders forms a semi-elliptic shape, similar to the flat bed case. For the slope-induced gravity, however, the head of gravity currents gradually grows and accelerates. A steeper slope without cylinders causes the evident entrainment and subsequent energy dissipation of gravity currents with ambient fluid. When the cylinder population becomes denser, developments of the head become slower, and the semi-elliptic head can be only seen at the very front end. As the density reaches 6.9%, the interface between the saltwater and freshwater performs an inclined straight line, corresponding to the pervious theoretical derivation. The gravity current event could go through two different routes under the similar toe speeds. The current head without cylinders grows along the downslope path, and the enrollment and mixing with ambient fluid could occur at the edge of the head; while the currents within dense cylinders (∼6.9%) has a nearly constant thickness and a smaller and more streamlined head at the very front end. As the cylinder density increases, the front speed of gravity currents transforms from acceleration to deceleration phases. The experimental results reveal that the head would accelerate over the downslope course if the cylinder density is less than 2%.

Dynamics of the head of gravity currents

The present work experimentally investigates the dynamics of unsteady gravity currents produced by lock-release of a saline mixture into a fresh water tank. Seven different experimental runs were performed by varying the density of the saline mixture in the lock and the bed roughness. Experiments were conducted in a Perspex flume, of horizontal bed and rectangular cross section, and recorded with a CCD camera. An image analysis technique was applied to visualize and characterize the current allowing thus the understanding of its general dynamics and, more specifically, of the current head dynamics. The temporal evolution of both head length and mass shows repeated stretching and breaking cycles: during the stretching phase, the head length and mass grow until reaching a limit, then the head becomes unstable and breaks. In the instants of break, the head aspect ratio shows a limit of 0.2 and the mass of the head is of the order of the initial mass in the lock. The average period of the herein called breaking events is seen to increase with bed roughness and the spatial periodicity of these events is seen to be approximately constant between runs. The rate of growth of the mass at the head is taken as a measure to assess entrainment and it is observed to occur at all stages of the current development. Entrainment rate at the head decreases in time suggesting this as a phenomenon ruled by local buoyancy and the similarity between runs shows independence from the initial reduced gravity and bed roughness.

Experiments on gravity currents propagating on different bottom slopes

AbstractExperiments for gravity currents generated from an instantaneous buoyancy source propagating on an inclined boundary in the slope angle range ${0}^{\circ } \leq \theta \leq {9}^{\circ } $ are reported. While the flow patterns for gravity currents on $\theta = {6}^{\circ } , {9}^{\circ } $ are qualitatively different from those on $\theta = {0}^{\circ } $, similarities are observed in the acceleration phase for the flow patterns between $\theta = {2}^{\circ } $ and $\theta = {6}^{\circ } , {9}^{\circ } $ and in the deceleration phase, the patterns for gravity currents on $\theta = {2}^{\circ } $ are found similar to those on $\theta = {0}^{\circ } $. Previously, it was known that the front location history in the deceleration phase obeys a power-relationship, which is essentially an asymptotic form of the solution to thermal theory. We showed that this power-relationship applies only in the early stage of the deceleration phase, and when gravity currents propagate into the later stage of the deceleration phase, viscous effects become more important and the front location data deviate from this relationship. When the power-relationship applies, it is found that at $\theta = {9}^{\circ } $, ${u}_{f} {({x}_{f} + {x}_{0} )}^{1/ 2} / {{ B}_{0}^{\prime } }^{1/ 2} \approx 2. 8{ 8}_{- 0. 17}^{+ 0. 19} $, which changes to $2. 8{ 6}_{- 0. 13}^{+ 0. 13} $ at $\theta = {6}^{\circ } $, $2. 5{ 4}_{- 0. 07}^{+ 0. 08} $ at $\theta = {2}^{\circ } $, and $1. 5{ 1}_{- 0. 07}^{+ 0. 07} $ on a horizontal boundary, where ${u}_{f} $ is the front velocity, $({x}_{f} + {x}_{0} )$ is the front location measured from the virtual origin, and ${ B}_{0}^{\prime } $ is the released buoyancy. Our results indicate that in the slope angle range ${6}^{\circ } \leq \theta \leq {9}^{\circ } $, the asymptotic relationship between the front velocity and front location in the deceleration phase is not sensitive to the variation of slope angle. In the late deceleration phase when the front location data deviate from the power-relationship, we found that the flow patterns for $\theta = {6}^{\circ } , {9}^{\circ } $ are dramatically different from those for $\theta = {0}^{\circ } , {2}^{\circ } $. For high slope angles, i.e. $\theta = {6}^{\circ } , {9}^{\circ } $, the edge of the gravity current head experiences a large upheaval and enrolment by ambient fluid towards the end of the deceleration phase, while for low slope angles, i.e. $\theta = {0}^{\circ } , {2}^{\circ } $, the gravity current head maintains a more streamlined shape without violent mixing with ambient fluid throughout the course of gravity current propagation. Our findings indicate two plausible routes to the finale of a gravity current event.

Power-law for gravity currents on slopes in the deceleration phase

The power-law for gravity currents on slopes is essentially an asymptotic form of the solution of thermal theory developed in Beghin, Hopfinger, and Britter (J. Fluid Mech. 107 (1981) 407–422), when the gravity current is sufficiently far into the deceleration phase. The power-law not only describes the long-term front location versus time relationship but also provides a useful means to estimate the buoyancy contained in the gravity current head. However, the hypothesis that gravity current is sufficiently far into the deceleration phase is hardly satisfied in experiments. In this paper, we re-formulated the power-law, considering the influence of bottom friction, and supplement the formulation by proposing a correct version of the power-law. When the gravity current is not sufficiently far into the deceleration phase, we showed that the power-law still robustly describes the front location versus time relationship, but the amount of heavy fluid in the head can be easily underestimated. The underestimation of heavy fluid in the head also depends on where the gravity current is in the deceleration phase. Therefore, a correction factor is suggested according to the location of gravity current. The amount of heavy fluid in the head, when estimated by the power-law, should be understood as the ‘effective’ buoyancy in driving the gravitational convection and is deemed as a lower limit for the estimation of buoyancy contained in the head.

Gravity Currents Propagating on Sloping Boundaries

AbstractThree-dimensional direct numerical simulations of gravity currents on different bottom slopes are presented in this paper. After the buoyancy closed in a lock is instantaneously released, the produced gravity currents go through an acceleration phase followed by a deceleration phase. In the acceleration phase, the tail current connects to and feeds buoyancy into the head for all cases considered here. The maximum buoyancy contained in the head, reached at the end of the acceleration phase, increases as the bottom slope increases. The maximum buoyancy in the head never reaches the total released buoyancy, and a significant portion of released heavy fluid is left in the tail current. In the deceleration phase, the tail current continues to join the head as the gravity currents propagate for lower slope angles (θ=0.2, and 4°), but the head disconnects the joining tail current for higher slope angles (θ=6, 8, and 10°). The gravity current head loses contained buoyancy less rapidly in the deceleration ...

Gravity Currents from Instantaneous Sources Down a Slope

Gravity currents from instantaneous sources down a slope were modeled with classic thermal theory, which has formed the basis for many subsequent studies. Considering entrainment of ambient fluid and conservation of total buoyancy, thermal theory predicted the height, length, and velocity of the gravity current head. In this study, the problem with direct numerical simulations was re-investigated, and the results compared with thermal theory. The predictions based on thermal theory are shown to be appropriate only for the acceleration phase, not for the entire gravity current motion. In particular, for the current head forms on a 10° slope produced from an instantaneous buoyancy source, the contained buoyancy in the head is approximately 58% of the total buoyancy at most and is not conserved during the motion as assumed in thermal theory. In the deceleration phase, the height and aspect ratio of the head and the buoyancy contained within it may all decrease with downslope distance. Thermal theory relies o...

Response of buoyant plumes to transient discharges investigated using an adaptive solver

The behavior of buoyant plumes driven by variable momentum inputs were examined using an adaptive Navier‐Stokes solver (Gerris). Boundary conditions were representative of an idealized stratified, coastal environment. Salinity ranged from 5 to 30 in the top 5 m of the water column to replicate the strong vertical gradients experienced in fjord environments. Two‐dimensional simulations examined the response of the buoyant plume driven by zero, steady, and variable momentum fluxes. The behavior was quantified in terms of the characteristic features of a buoyant plume, the thickness of the nose (or head of gravity current), and the trailing tail. Both the nose and tail of the plume were substantially thicker for the variable momentum run, whereas elongation and thinning of the plume was evident for the steady and zero momentum inputs. Furthermore, an order of magnitude difference in available potential energy was found for the variable momentum run. Validation of the Boussinesq approximation initially utilized the classic lock‐exchange experiment with excellent agreement to previous numerical and theoretical experiments. Frontal speeds of the gravity current converged toward the theoretical value of Benjamin (1968). The adaptive mesh permitted lock‐exchange simulations at Reynolds number (Re) of ∼10,500 and are some of the highest Re runs to date. Moreover, improved computational efficiency was achieved using the adaptive solver with simulations completed in 20% of the time they took on a static, high‐resolution grid.

Three-Dimensional Unsteady RANS Modeling of Discontinuous Gravity Currents in Rectangular Domains

Discontinuous gravity currents in rectangular channels are modeled numerically by solving the 3D unsteady Reynolds- averaged Navier-Stokes URANS equations closed with a buoyancy corrected low-Reynolds number LRN k- model using second- order accurate finite-volume numerics. It is shown that, on moderately fine computational meshes with 10 6 grid nodes and with careful modeling of the near-wall flow, the URANS model can capture the essential large-scale 3D dynamics of gravity current flows, which previously had been resolved only by DNS and/or large-eddy simulation LES on very fine computational meshes. These 3D dynamics include the onset of the well-known lobe-and-cleft instability at the current head, the onset of large-scale Kelvin-Helmholtz billows at the head of the gravity current, and the breakdown of the interfacial billows in the rear part of the current head due to intense three- dimensional mixing. The computed results underscore the importance of careful modeling of the near wall flow in URANS simulations. The standard k- model with wall functions fails to capture the aforementioned complex 3D dynamics, which are only resolved by the LRN k- model on grids that resolve the near-wall region. Furthermore, numerical experiments show that including in the simulation the lateral no-slip end walls of the channel has a profound effect on the accuracy of the computed solutions. End-wall effects enhance the three-dimensionality of the flow, result in increased mixing of the dense and the ambient fluids behind the head of gravity currents, and yield results in good agreement with measurements. On the other hand, when end-wall effects are omitted, by imposing periodicity in the spanwise direction, three-dimensional mixing is suppressed and the breakdown of interfacial billows is significantly underestimated. Grid sensitivity studies are also carried out using three successively refined meshes and show that the URANS LRN model yields grid- converged solutions at affordable computational resources. As URANS modeling requires only a fraction of the computational cost of DNS or LES with near-wall resolution, the present results underscore the potential of unsteady statistical turbulence models for predicting and elucidating the physics of gravity current flows in complex geometries and at Reynolds numbers of engineering relevance.

A numerical study of the frontal region of gravity currents propagating on a free-slip boundary

We investigate numerically the three-dimensional flow near the head of gravity currents propagating along a free-slip boundary. The simulations show that two states are possible: a high-mixing state, where the flow departs from the analytic inviscid solution 0.5 channel heights downstream of the front location, and with characteristics similar to the ones observed for purely two-dimensional simulations; and a low-mixing state, where billows are weaker and appear further downstream. To access the high-mixing state, it is necessary to add a source of perturbation upstream of the head in the form of turbulence. At high values of the Reynolds number, the intensity of rms turbulent fluctuations necessary to switch to the high-mixing state is small (0.5% of the speed of propagation) and may explain why the low-mixing state has so far eluded experimental detection. In the low-mixing state, the flow becomes three-dimensional near the front due to centrifugal instabilities caused by the curved streamlines. This instability of the outer flow is coupled to overturning instabilities that develop within the heavy fluid in the head, and suppresses the formation of billows. This complex behavior, which feeds on the interplay of streamline curvature and stratification, should be considered a good model to understand how instabilities occur in other types of strongly nonlinear stratified flows.