Front dynamics and entrainment of finite circular gravity currents on an unbounded uniform slope

2016 ◽  
Vol 801 ◽  
pp. 322-352 ◽  
Author(s):  
N. Zgheib ◽  
A. Ooi ◽  
S. Balachandar
Keyword(s):  
Froude Number ◽  
Temporal Evolution ◽  
Gravity Current ◽  
Gravity Currents ◽  
Front Velocity ◽  
Acceleration Phase ◽  
Simple Method ◽  
Entrainment Coefficient ◽  
Converging Flow ◽  
Front Dynamics

We report on the dynamics of circular finite-release Boussinesq gravity currents on a uniform slope. The study comprises a series of highly resolved direct numerical simulations for a range of slope angles between $5^{\circ }$ and $20^{\circ }$. The simulations were fixed at Reynolds number $Re=5000$ for all slopes considered. The temporal evolution of the front is compared to available experimental data. One of the interesting aspects of this study is the detection of a converging flow towards the centre of the gravity current. This converging flow is a result of the finite volume of the release coupled with the presence of a sloping boundary, which results in a second acceleration phase in the front velocity of the current. The details of the dynamics of this second acceleration and the redistribution of material in the current leading to its development will be discussed. These finite-release currents are invariably dominated by the head where most of the mixing and ambient entrainment occurs. We propose a simple method for defining the head of the current from which we extract various properties including the front Froude number and entrainment coefficient. The Froude number is seen to increase with steeper slopes, whereas the entrainment coefficient is observed to be weakly dependent on the bottom slope.

scholarly journals Entrainment in Shallow Rotating Gravity Currents: A Modeling Study

2010 ◽  
Vol 40 (8) ◽  
pp. 1819-1834 ◽  
Author(s):  
Lars Umlauf ◽  
Lars Arneborg ◽  
Richard Hofmeister ◽  
Hans Burchard
Keyword(s):  
Froude Number ◽  
Gravity Current ◽  
Vertical Mixing ◽  
Spatial Separation ◽  
Gravity Currents ◽  
Transverse Jet ◽  
Entrainment Process ◽  
Set Up ◽  
Rotation Set ◽  
Bulk Parameters

Abstract The physics of shallow gravity currents passing through a rotating channel at subcritical Froude number is investigated here with a series of idealized numerical experiments. It is found that the combined effects of friction and rotation set up a complex transverse circulation that has some crucial implications for the entrainment process. A key component of this secondary circulation is a geostrophically balanced transverse jet in the interface that laterally drains fluid from the interface. This effect is shown to result in a strong cross-channel asymmetry and a spatial separation of the entrainment process: drained interfacial fluid is partly replaced by entrained ambient fluid on the deep side of the gravity current, whereas the downward mixing of buoyant fluid occurs on the shallow side. These results, closely corresponding to recent measurements in a shallow, channelized gravity current in the western Baltic Sea, illustrate that the description of entrainment as a strictly vertical mixing process with the help of local bulk parameters like the Froude number is not generally applicable in rotating gravity currents.

An analytical model of gravity currents in a stable atmosphere

2000 ◽  
Vol 420 ◽  
pp. 27-46 ◽  
Author(s):  
YIZHAK FELIKS
Keyword(s):  
Froude Number ◽  
Gravity Waves ◽  
Cold Front ◽  
Gravity Current ◽  
Gravity Currents ◽  
Structure Functions ◽  
Synoptic Wind ◽  
Advection Term ◽  
Nonlinear Advection ◽  
Nonlinear Gravity

An analytical solution to the nonlinear equations of motion and thermodynamic energy for gravity currents propagating in stable atmosphere is found. This solution differs from the previous analytical studies in several aspects. In our solution the head of the gravity current is a strong vortex and the dynamics are non-hydrostatic. The solution has two regimes: (i) a supercritical regime when the Froude number Fr = (c – U)/Na is larger than 1 – in this case the cold front is local; (ii) a subcritical regime when Fr is smaller than 1. Here, ahead of the front there is a disturbance of nonlinear gravity waves. The scale of the wave and its amplitude increase as the Froude number decreases.We found that the square of the speed of the gravity current (relative to the synoptic wind) is proportional to the mean drop of potential temperature over the front area times the front height a. The constant of proportionality is function of the environmental conditions. The thermal, velocity and vorticity fields can be described by non-dimensional structure functions of two numbers: pa = 1/Fr and ka. The amplitude of the structure functions is proportional to (c – U) 2/a for the thermal field, to (c – U) for the velocity field, and to (c – U)/a for the vorticity field.The propagation is studied in terms of the vorticity equation. The horizontal gradient of the buoyancy term always tends to propagate the cold front. The nonlinear advection term in most of the cases investigated here tends to slow the propagation of the gravity current. The propagation of the disturbance of nonlinear gravity waves ahead of the front in regime (ii) in most of the cases is due to the buoyancy term. The nonlinear advection term tends to slow the propagation when the synoptic wind blows in the direction opposite to that of the front propagation, and increase the propagation when the synoptic wind blows in the direction of propagation.

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

2015 ◽  
Vol 765 ◽  
pp. 544-575 ◽  
Author(s):  
Ayse Yuksel Ozan ◽  
George Constantinescu ◽  
Andrew J. Hogg
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Drag Coefficient ◽  
Gravity Current ◽  
Gravity Currents ◽  
Front Velocity ◽  
Release Time ◽  
Exchange Flow ◽  
Layer Model ◽  
Shallow Layer

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

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

2017 ◽  
Vol 831 ◽  
pp. 394-417 ◽  
Author(s):  
Jian Zhou ◽  
Claudia Cenedese ◽  
Tim Williams ◽  
Megan Ball ◽  
Subhas K. Venayagamoorthy ◽  
...  
Keyword(s):  
Volume Fraction ◽  
Gravity Current ◽  
Gravity Currents ◽  
Front Velocity ◽  
Circular Cylinders ◽  
Dimensional Parameter ◽  
Flow Interruption ◽  
Line Array ◽  
Through Flow ◽  
Array Density

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.

Rotational flow in gravity current heads

2005 ◽  
Vol 363 (1832) ◽  
pp. 1603-1623 ◽  
Author(s):  
J.N McElwaine
Keyword(s):  
Froude Number ◽  
Gravity Current ◽  
Gravity Currents ◽  
Rotational Flow ◽  
Arbitrary Angle ◽  
Von Karman ◽  
Von Kármán ◽  
A Current

The structure of gravity currents and plumes, in an unbounded ambient, on a slope of arbitrary angle is analysed. Inviscid, rotational flow solutions in a wedge are used to study the flow near the front of a current, and used to show that the Froude number is and the angle of the front to the slope is 60°. This extends the result of von Kármán (1940) to arbitrary slope angles and large internal current velocities. The predictions of the theory are briefly compared with experiments and used to explain the large negative (relative to ambient) pressures involved in avalanches.

scholarly journals Gravity currents and internal waves in a stratified fluid

2008 ◽  
Vol 616 ◽  
pp. 327-356 ◽  
Author(s):  
BRIAN L. WHITE ◽  
KARL R. HELFRICH
Keyword(s):  
Internal Waves ◽  
Wave Speed ◽  
Numerical Solutions ◽  
Gravity Current ◽  
Gravity Currents ◽  
Stratified Fluid ◽  
Front Speed ◽  
Long Wave ◽  
Conjugate State ◽  
Energy Conserving

A steady theory is presented for gravity currents propagating with constant speed into a stratified fluid with a general density profile. Solution curves for front speed versus height have an energy-conserving upper bound (the conjugate state) and a lower bound marked by the onset of upstream influence. The conjugate state is the largest-amplitude nonlinear internal wave supported by the ambient stratification, and in the limit of weak stratification approaches Benjamin's energy-conserving gravity current solution. When the front speed becomes critical with respect to linear long waves generated above the current, steady solutions cannot be calculated, implying upstream influence. For non-uniform stratification, the critical long-wave speed exceeds the ambient long-wave speed, and the critical-Froude-number condition appropriate for uniform stratification must be generalized. The theoretical results demonstrate a clear connection between internal waves and gravity currents. The steady theory is also compared with non-hydrostatic numerical solutions of the full lock release initial-value problem. Some solutions resemble classic gravity currents with no upstream disturbance, but others show long internal waves propagating ahead of the gravity current. Wave generation generally occurs when the stratification and current speed are such that the steady gravity current theory fails. Thus the steady theory is consistent with the occurrence of either wave-generating or steady gravity solutions to the dam-break problem. When the available potential energy of the dam is large enough, the numerical simulations approach the energy-conserving conjugate state. Existing laboratory experiments for intrusions and gravity currents produced by full-depth lock exchange flows over a range of stratification profiles show excellent agreement with the conjugate state solutions.

The Effect of Froude Number on Entrainment in Two-Dimensional Line Plumes

1981 ◽  
Vol 103 (3) ◽  
pp. 471-477 ◽  
Author(s):  
W. F. Phillips
Keyword(s):  
Froude Number ◽  
Large Distance ◽  
Universal Constant ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Development Length ◽  
High Discharge ◽  
Entrainment Coefficient ◽  
Theoretical Results

Theoretical results are presented which predict the entrainment coefficient in a forced plume as a function of the local Froude number. The model does not require any external specification of the velocity and temperature profiles. The Froude number for any plume, in a motionless isothermal ambient, approaches a universal constant, at a large distance above the source. However, it is shown here that the development length for the Froude number, in plumes with high discharge Froude number, is of the order of a few hundred times the discharge width.

scholarly journals Scaling for lobe and cleft patterns in particle-laden gravity currents

2013 ◽  
Vol 20 (1) ◽  
pp. 121-130 ◽  
Author(s):  
A. Jackson ◽  
B. Turnbull ◽  
R. Munro
Keyword(s):  
Granular Material ◽  
Froude Number ◽  
Particle Diameter ◽  
Granular Flows ◽  
Leading Edge ◽  
Air Entrainment ◽  
Gravity Currents ◽  
Laboratory Scale ◽  
Scale Model ◽  
Snow Avalanches

Abstract. Lobe and cleft patterns are frequently observed at the leading edge of gravity currents, including non-Boussinesq particle-laden currents such as powder snow avalanches. Despite the importance of the instability in driving air entrainment, little is known about its origin or the mechanisms behind its development. In this paper we seek to gain a better understanding of these mechanisms from a laboratory scale model of powder snow avalanches using lightweight granular material. The instability mechanisms in these flows appear to be a combination of those found in both homogeneous Boussinesq gravity currents and unsuspended granular flows, with the size of the granular particles playing a central role in determining the wavelength of the lobe and cleft pattern. When scaled by particle diameter a relationship between the Froude number and the wavelength of the lobe and cleft pattern is found, where the wavelength increases monotonically with the Froude number.

The Critical Densimetric Froude Number of Subaqueous Gravity Currents Can Be Non-Unity or Non-Existent

2009 ◽  
Vol 79 (7) ◽  
pp. 479-485 ◽  
Author(s):  
H. Huang ◽  
J. Imran ◽  
C. Pirmez ◽  
Q. Zhang ◽  
G. Chen
Keyword(s):  
Froude Number ◽  
Gravity Currents ◽  
Densimetric Froude Number

scholarly journals Axisymmetric three-dimensional gravity currents generated by lock exchange

2018 ◽  
Vol 851 ◽  
pp. 507-544 ◽  
Author(s):  
Roberto Inghilesi ◽  
Claudia Adduce ◽  
Valentina Lombardi ◽  
Federico Roman ◽  
Vincenzo Armenio
Keyword(s):  
Froude Number ◽  
Flow Rate ◽  
Rapid Development ◽  
Three Dimensional ◽  
Gravity Currents ◽  
Constant Flow ◽  
Axially Symmetric ◽  
Grashof Number ◽  
Constant Flow Rate ◽  
Dimensional Gravity

Unconfined three-dimensional gravity currents generated by lock exchange using a small dividing gate in a sufficiently large tank are investigated by means of large eddy simulations under the Boussinesq approximation, with Grashof numbers varying over five orders of magnitudes. The study shows that, after an initial transient, the flow can be separated into an axisymmetric expansion and a globally translating motion. In particular, the circular frontline spreads like a constant-flow-rate, axially symmetric gravity current about a virtual source translating along the symmetry axis. The flow is characterised by the presence of lobe and cleft instabilities and hydrodynamic shocks. Depending on the Grashof number, the shocks can either be isolated or produced continuously. In the latter case a typical ring structure is visible in the density and velocity fields. The analysis of the frontal spreading of the axisymmetric part of the current indicates the presence of three regimes, namely, a slumping phase, an inertial–buoyancy equilibrium regime and a viscous–buoyancy equilibrium regime. The viscous–buoyancy phase is in good agreement with the model of Huppert (J. Fluid Mech., vol. 121, 1982, pp. 43–58), while the inertial phase is consistent with the experiments of Britter (Atmos. Environ., vol. 13, 1979, pp. 1241–1247), conducted for purely axially symmetric, constant inflow, gravity currents. The adoption of the slumping model of Huppert & Simpson (J. Fluid Mech., vol. 99 (04), 1980, pp. 785–799), which is here extended to the case of constant-flow-rate cylindrical currents, allows reconciling of the different theories about the initial radial spreading in the context of different asymptotic regimes. As expected, the slumping phase is governed by the Froude number at the lock’s gate, whereas the transition to the viscous phase depends on both the Froude number at the gate and the Grashof number. The identification of the inertial–buoyancy regime in the presence of hydrodynamic shocks for this class of flows is important, due to the lack of analytical solutions for the similarity problem in the framework of shallow water theory. This fact has considerably slowed the research on variable-flow-rate axisymmetric gravity currents, as opposed to the rapid development of the knowledge about cylindrical constant-volume and planar gravity currents, despite their own environmental relevance.

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