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

Experimental Studies of Sedimentation Basin Dynamics

1977 ◽  
Vol 12 (1) ◽  
pp. 77-90
Author(s):  
J.F. Cordoba-Molina ◽  
P.L. Silveston ◽  
R. R. Hudgins
Keyword(s):  
Dynamic Response ◽  
Froude Number ◽  
Flow Model ◽  
Experimental Studies ◽  
Densimetric Froude Number ◽  
Number Range ◽  
The Real ◽  
Highly Correlated ◽  
Sedimentation Basins ◽  
Simple Flow

Abstract A simple Flow Model is proposed to describe the dynamic response of sedimentation basins. The response predicted by this model is linear as opposed to the real response of the basin which is nonlinear. However, the real response of the basin is highly correlated with its densimetric Froude number, and as a consequence our linear model effectively predicts the response of the basin in a restricted densimetric Froude Number range. Our experiments show that the response of the basin becomes more sluggish and erratic as the densimetric Froude number decreases.

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.

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.

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.

scholarly journals Origin of the scaling laws of sediment transport

2017 ◽  
Vol 473 (2197) ◽  
pp. 20160785 ◽  
Author(s):  
Sk Zeeshan Ali ◽  
Subhasish Dey
Keyword(s):  
Sediment Transport ◽  
Froude Number ◽  
Scaling Laws ◽  
Scaling Law ◽  
Bedload Transport ◽  
Inertial Range ◽  
Channel Width ◽  
Densimetric Froude Number ◽  
Relative Roughness ◽  
Contraction Ratio

In this paper, we discover the origin of the scaling laws of sediment transport under turbulent flow over a sediment bed, for the first time, from the perspective of the phenomenological theory of turbulence. The results reveal that for the incipient motion of sediment particles, the densimetric Froude number obeys the ‘(1 +  σ )/4’ scaling law with the relative roughness (ratio of particle diameter to approach flow depth), where σ is the spectral exponent of turbulent energy spectrum. However, for the bedforms, the densimetric Froude number obeys a ‘(1 +  σ )/6’ scaling law with the relative roughness in the enstrophy inertial range and the energy inertial range. For the bedload flux, the bedload transport intensity obeys the ‘3/2’ and ‘(1 +  σ )/4’ scaling laws with the transport stage parameter and the relative roughness, respectively. For the suspended load flux, the non-dimensional suspended sediment concentration obeys the ‘ − Z ’ scaling law with the non-dimensional vertical distance within the wall shear layer, where Z is the Rouse number. For the scour in contracted streams, the non-dimensional scour depth obeys the ‘4/(3 −  σ )’, ‘−4/(3 −  σ )’ and ‘−(1 +  σ )/(3 −  σ )’ scaling laws with the densimetric Froude number, the channel contraction ratio (ratio of contracted channel width to approach channel width) and the relative roughness, respectively.

Subsurface Ice Transport at a Transversally Towed Ship Model

2017 ◽  
Author(s):  
Li Zhou ◽  
Rüdiger U. Franz von Bock und Polach ◽  
Xu Bai
Keyword(s):  
Froude Number ◽  
Densimetric Froude Number ◽  
Ship Model ◽  
Drift Speed ◽  
Ice Accumulation ◽  
Underwater Cameras ◽  
Low Froude Number ◽  
Broken Ice ◽  
Level Ice ◽  
Ice Floes

The subsurface transport of ice along the underwater body of a ship hull or a structure may cause damages to appendages. In order to investigate the conditions under which the ice accumulation occurs, a series of model tests was carried out in the ice basin of Aalto University. The used ship model was towed laterally against the ice with one side breaking level ice. The transport of broken ice floes broken off from the intact ice sheet has been has been monitored with underwater cameras. Both the model drift speed, respectively the ice drift speed, and the ice thickness are found to affect ice accumulation process. The Densimetric Froude number is introduced as measured to determine whether ice floes will accumulate on the upstream of the hull. It is found that ice accumulation is triggered at relatively low Froude number.

The instantaneous Froude number and depth of unsteady gravity currents

2013 ◽  
Vol 51 (4) ◽  
pp. 432-445 ◽  
Author(s):  
Hafiz J. Anjum ◽  
Jim N. Mcelwaine ◽  
Colm-cille P. Caulfield
Keyword(s):  
Froude Number ◽  
Gravity Currents

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.

Evaluation of Sediment Gradation Effects on Clear-Water Pier Scour with Densimetric Froude Number

2020 ◽  
Vol 146 (12) ◽  
pp. 04020133
Author(s):  
Nian-Sheng Cheng ◽  
Maoxing Wei ◽  
Yesheng Lu ◽  
Yee-Meng Chiew
Keyword(s):  
Froude Number ◽  
Clear Water ◽  
Pier Scour ◽  
Densimetric Froude Number
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