A Laboratory Study of the Velocity Structure in an Intrusive Gravity Current

2000 ◽  
Author(s):  
Ryan J. Lowe
Keyword(s):  
Particle Tracking ◽  
Laboratory Experiments ◽  
Velocity Structure ◽  
Gravity Current ◽  
Current Theory ◽  
Head Region ◽  
Front Speed ◽  
Energy Conserving ◽  
The Stability ◽  
Lock Gate

Abstract Laboratory experiments were performed in which an intrusive gravity current was observed using shadowgraph and particle tracking methods. The intrusion was generated in a two-layer fluid with a sharp interface by mixing the fluid behind a vertical lock-gate and then suddenly withdrawing the gate from the tank. The purpose of the experiments is to determine the structure of the velocity field inside the intrusion as well as the stability characteristics of the interface. Soon after the removal of the lock-gate the speed of the front of the intrusive gravity current reached a constant speed. The observed structure of the flow inside the intrusion shows a “head region” where the flow is nearly uniform, followed by a region of intense mixing and high velocities and finally followed by another region of fairly uniform velocity with a speed slightly faster than the front speed. The results show that the maximum centerline velocity is about 50% greater than the front speed and corresponds to the position in the intrusion where the strongest Kelvin- Helmholtz billows form. Closer to the front, the relative flow within the head is weak, which explains why Benjamin’s (1968) energy-conserving gravity current theory accurately predicts the behavior of dissipative gravity currents.

A laboratory study of the velocity structure in an intrusive gravity current

2002 ◽  
Vol 456 ◽  
pp. 33-48 ◽  
Author(s):  
RYAN J. LOWE ◽  
P. F. LINDEN ◽  
JAMES W. ROTTMAN
Keyword(s):  
Velocity Field ◽  
Velocity Structure ◽  
Fluid Velocity ◽  
Gravity Current ◽  
Maximum Speed ◽  
Wake Region ◽  
Tail Region ◽  
Front Speed ◽  
Energy Conserving ◽  
Lock Gate

Laboratory experiments were performed in which an intrusive gravity current was observed using shadowgraph and particle tracking methods. The intrusion was generated in a two-layer fluid with a sharp interface by mixing the fluid behind a vertical lock gate and then suddenly withdrawing the gate from the tank. The purpose of the experiments was to determine the structure of the velocity field inside the intrusion and the stability characteristics of the interface. Soon after the removal of the lock gate, the front of the intrusive gravity current travelled at a constant speed close to the value predicted by theory for an energy-conserving gravity current. The observed structure of the flow inside the intrusion can be divided into three regions. At the front of the intrusion there is an energy-conserving head region in which the fluid velocity is nearly uniform with speed equal to the front speed. This is followed by a dissipative wake region in which large billows are present with their associated mixing and in which the fluid velocity is observed to be non-uniform and have a maximum speed approximately 50% greater than the front speed. Behind the wake region is a tail region in which there is very little mixing and the velocity field is nearly uniform with a speed slightly faster than the front speed.

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.

scholarly journals Gravity current propagation up a valley

2014 ◽  
Vol 762 ◽  
pp. 417-434 ◽  
Author(s):  
Catherine S. Jones ◽  
Claudia Cenedese ◽  
Eric P. Chassignet ◽  
P. F. Linden ◽  
Bruce R. Sutherland
Keyword(s):  
Numerical Simulations ◽  
Laboratory Experiments ◽  
Rectangular Channel ◽  
Gravity Current ◽  
Gravity Currents ◽  
Momentum Transport ◽  
Front Speed

AbstractThe advance of the front of a dense gravity current propagating in a rectangular channel and V-shaped valley both horizontally and up a shallow slope is examined through theory, full-depth lock–release laboratory experiments and hydrostatic numerical simulations. Consistent with theory, experiments and simulations show that the front speed is relatively faster in the valley than in the channel. The front speed measured shortly after release from the lock is 5–22 % smaller than theory, with greater discrepancy found in upsloping V-shaped valleys. By contrast, the simulated speed is approximately 6 % larger than theory, showing no dependence on slope for rise angles up to ${\it\theta}=8^{\circ }$. Unlike gravity currents in a channel, the current head is observed in experiments to be more turbulent when propagating in a V-shaped valley. The turbulence is presumably enhanced due to the lateral flows down the sloping sides of the valley. As a consequence, lateral momentum transport contributes to the observed lower initial speeds. A Wentzel–Kramers–Brillouin like theory predicting the deceleration of the current as it runs upslope agrees remarkably well with simulations and with most experiments, within errors.

scholarly journals Inhibition or Facilitation? Contrasted Inter-Specific Interactions in Sphagnum under Laboratory and Field Conditions

Plants ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 1554
Author(s):  
Chao Liu ◽  
Zhao-Jun Bu ◽  
Azim Mallik ◽  
Yong-Da Chen ◽  
Xue-Feng Hu ◽  
...  
Keyword(s):  
Field Experiment ◽  
Species Interactions ◽  
Laboratory Experiments ◽  
Resource Competition ◽  
Specific Interactions ◽  
Interaction Type ◽  
Negative Effects ◽  
Experiment Data ◽  
The Stability ◽  
Positive Effect

In a natural environment, plants usually interact with their neighbors predominantly through resource competition, allelopathy, and facilitation. The occurrence of the positive effect of allelopathy between peat mosses (Sphagnum L.) is rare, but it has been observed in a field experiment. It is unclear whether the stability of the water table level in peat induces positive vs. negative effects of allelopathy and how that is related to phenolic allelochemical production in Sphagnum. Based on field experiment data, we established a laboratory experiment with three neighborhood treatments to measure inter-specific interactions between Sphagnum angustifolium (Russ.) C. Jens and Sphagnum magellanicum Brid. We found that the two species were strongly suppressed by the allelopathic effects of each other. S. magellanicum allelopathically facilitated S. angustifolium in the field but inhibited it in the laboratory, and relative allelopathy intensity appeared to be positively related to the content of released phenolics. We conclude that the interaction type and intensity between plants are dependent on environmental conditions. The concentration of phenolics alone may not explain the type and relative intensity of allelopathy. Carefully designed combined field and laboratory experiments are necessary to reveal the mechanism of species interactions in natural communities.

Simple Leg Placement Strategy for a One Legged Running Model

2012 ◽  
Author(s):  
Timothy Sullivan ◽  
Justin Seipel
Keyword(s):  
Stance Phase ◽  
Energy State ◽  
Center Of Mass ◽  
Mass Movement ◽  
Legged Locomotion ◽  
Energy Conserving ◽  
Lower Torque ◽  
The Stability ◽  
Time Required ◽  
Torque Values

The Spring Loaded Inverted Pendulum (SLIP) model was developed to describe center of mass movement patterns observed in animals, using only a springy leg and a point mass. However, SLIP is energy conserving and does not accurately represent any biological or robotic system. Still, this model is often used as a foundation for the investigation of improved legged locomotion models. One such model called Torque Damped SLIP (TD-SLIP) utilizes two additional parameters, a time dependent torque and dampening to drastically increase the stability. Forced Damped SLIP (FD-SLIP), a predecessor of TD-SLIP, has shown that this model can be further simplified by using a constant torque, instead of a time varying torque, while still maintaining stability. Using FD-SLIP as a base, this paper explores a leg placement strategy using a simple PI controller. The controller takes advantage of the fact that the energy state of FD-SLIP is symmetric entering and leaving the stance phase during steady state conditions. During the flight phase, the touch down leg angle is adjusted so that the energy dissipation due to dampening, during the stance phase, compensates for any imbalance of energy. This controller approximately doubles the region of stability when subjected to velocity perturbations at touchdown, enables the model to operate at considerably lower torque values, and drastically reduces the time required to recover from a perturbation, while using less energy. Finally, the leg placement strategy used effectively imitates the natural human response to velocity perturbations while running.

scholarly journals Dynamic population stage structure due to juvenile–adult asymmetry stabilizes complex ecological communities

2021 ◽  
Vol 118 (21) ◽  
pp. e2023709118
Author(s):  
André M. de Roos
Keyword(s):  
Self Regulation ◽  
Interaction Network ◽  
Population Level ◽  
Stage Structure ◽  
Current Theory ◽  
Species Interaction ◽  
Interaction Matrix ◽  
Foraging Efficiency ◽  
Ecological Communities ◽  
The Stability

Natural ecological communities are diverse, complex, and often surprisingly stable, but the mechanisms underlying their stability remain a theoretical enigma. Interactions such as competition and predation presumably structure communities, yet theory predicts that complex communities are stable only when species growth rates are mostly limited by intraspecific self-regulation rather than by interactions with resources, competitors, and predators. Current theory, however, considers only the network topology of population-level interactions between species and ignores within-population differences, such as between juvenile and adult individuals. Here, using model simulations and analysis, I show that including commonly observed differences in vulnerability to predation and foraging efficiency between juvenile and adult individuals results in up to 10 times larger, more complex communities than observed in simulations without population stage structure. These diverse communities are stable or fluctuate with limited amplitude, although in the model only a single basal species is self-regulated, and the population-level interaction network is highly connected. Analysis of the species interaction matrix predicts the simulated communities to be unstable but for the interaction with the population-structure subsystem, which completely cancels out these instabilities through dynamic changes in population stage structure. Common differences between juveniles and adults and fluctuations in their relative abundance may hence have a decisive influence on the stability of complex natural communities and their vulnerability when environmental conditions change. To explain community persistence, it may not be sufficient to consider only the network of interactions between the constituting species.

scholarly journals The Influence of Grain Size Distribution on the Hydraulic Gradient for Initiating Backward Erosion

Water ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2644 ◽  
Author(s):  
Willem-Jan Dirkx ◽  
Rens Beek ◽  
Marc Bierkens
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Laboratory Experiments ◽  
Hydraulic Gradient ◽  
Concentrated Flow ◽  
Pipe Formation ◽  
Novel Method ◽  
Flow Through ◽  
The Stability

Backward erosion by piping is one of the processes that threaten the stability of river embankments in the Netherlands. During high river stages, groundwater flow velocities underneath the embankment increase as a result of the steepened hydraulic gradient. If a single outflow point exists or forms, the concentrated flow can entrain soil particles, leading to the formation of a subsurface pipe. The processes controlling this phenomenon are still relatively unknown due to their limited occurrence and because piping is a subsurface phenomenon. To study the initiation of piping, we performed laboratory experiments in which we induced water flow through a porous medium with a vertically orientated outflow point. In these experiments, we explicitly considered grain size variations, thus adding to the existing database of experiments. Our experiments showed that the vertical velocity needed for the initiation of particle transport can be described well by Stokes’ law using the median grain size. We combine this with a novel method to relate bulk hydraulic conductivity to the grain size distribution. This shows that knowledge of the grain size distribution and the location of the outflow point are sufficient to estimate the hydraulic gradient needed to initiate pipe formation in the experiment box.

Gravity currents and related phenomena

1968 ◽  
Vol 31 (2) ◽  
pp. 209-248 ◽  
Author(s):  
T. Brooke Benjamin
Keyword(s):  
Salt Water ◽  
Gravity Current ◽  
Circular Cross Section ◽  
Gravity Currents ◽  
Head Wave ◽  
Physical Problems ◽  
Energy Conserving ◽  
Fluid Theory ◽  
Hydrodynamical Problem ◽  
Upper Boundary

This paper presents a broad investigation into the properties of steady gravity currents, in so far as they can be represented by perfect-fluid theory and simple extensions of it (like the classical theory of hydraulic jumps) that give a rudimentary account of dissipation. As usually understood, a gravity current consists of a wedge of heavy fluid (e.g. salt water, cold air) intruding into an expanse of lighter fluid (fresh water, warm air); but it is pointed out in § 1 that, if the effects of viscosity and mixing of the fluids at the interface are ignored, the hydrodynamical problem is formally the same as that for an empty cavity advancing along the upper boundary of a liquid. Being simplest in detail, the latter problem is treated as a prototype for the class of physical problems under study: most of the analysis is related to it specifically, but the results thus obtained are immediately applicable to gravity currents by scaling the gravitational constant according to a simple rule.In § 2 the possible states of steady flow in the present category between fixed horizontal boundaries are examined on the assumption that the interface becomes horizontal far downstream. A certain range of flows appears to be possible when energy is dissipated; but in the absence of dissipation only one flow is possible, in which the asymptotic level of the interface is midway between the plane boundaries. The corresponding flow in a tube of circular cross-section is found in § 3, and the theory is shown to be in excellent agreement with the results of recent experiments by Zukoski. A discussion of the effects of surface tension is included in § 3. The two-dimensional energy-conserving flow is investigated further in § 4, and finally a close approximation to the shape of the interface is obtained. In § 5 the discussion turns to the question whether flows characterized by periodic wavetrains are realizable, and it appears that none is possible without a large loss of energy occurring. In § 6 the case of infinite total depth is considered, relating to deeply submerged gravity currents. It is shown that the flow must always feature a breaking ‘head wave’, and various properties of the resulting wake are demonstrated. Reasonable agreement is established with experimental results obtained by Keulegan and others.

Numerical simulations of lock-exchange compositional gravity current

2009 ◽  
Vol 635 ◽  
pp. 361-388 ◽  
Author(s):  
SENG KEAT OOI ◽  
GEORGE CONSTANTINESCU ◽  
LARRY WEBER
Keyword(s):  
High Resolution ◽  
Dissipation Rate ◽  
Friction Velocity ◽  
Gravity Current ◽  
Gravity Currents ◽  
Inviscid Limit ◽  
Grashof Number ◽  
Front Speed ◽  
Initial Volume ◽  
Bed Friction

Compositional gravity current flows produced by the instantaneous release of a finite-volume, heavier lock fluid in a rectangular horizontal plane channel are investigated using large eddy simulation. The first part of the paper focuses on the evolution of Boussinesq lock-exchange gravity currents with a large initial volume of the release during the slumping phase in which the front of the gravity current propagates with constant speed. High-resolution simulations are conducted for Grashof numbers $\sqrt {Gr}$ = 3150 (LGR simulation) and $\sqrt {Gr}$ = 126000 (HGR simulation). The Grashof number is defined with the channel depth h and the buoyancy velocity ub = $\sqrt {g'h}$ (g′ is the reduced gravity). In the HGR simulation the flow is turbulent in the regions behind the two fronts. Compared to the LGR simulation, the interfacial billows lose their coherence much more rapidly (over less than 2.5h behind the front), which results in a much faster decay of the large-scale content and turbulence intensity in the trailing regions of the flow. A slightly tilted, stably stratified interface layer develops away from the two fronts. The concentration profiles across this layer can be approximated by a hyperbolic tangent function. In the HGR simulation the energy budget shows that for t > 18h/ub the flow reaches a regime in which the total dissipation rate and the rates of change of the total potential and kinetic energies are constant in time. The second part of the paper focuses on the study of the transition of Boussinesq gravity currents with a small initial volume of the release to the buoyancy–inertia self-similar phase. When the existence of the back wall is communicated to the front, the front speed starts to decrease, and the current transitions to the buoyancy–inertia phase. Three high-resolution simulations are performed at Grashof numbers between $\sqrt {Gr}$ = 3 × 104 and $\sqrt {Gr}$ = 9 × 104. Additionally, a calculation at a much higher Grashof number ($\sqrt {Gr}$ = 106) is performed to understand the behaviour of a bottom-propagating current closer to the inviscid limit. The three-dimensional simulations correctly predict a front speed decrease proportional to t−α (the time t is measured from the release time) over the buoyancy–inertia phase, with the constant α approaching the theoretical value of 1/3 as the current approaches the inviscid limit. At Grashof numbers for which $\sqrt {Gr}$ > 3 × 104, the intensity of the turbulence in the near-wall region behind the front is large enough to induce the formation of a region containing streaks of low and high streamwise velocities. The streaks are present well into the buoyancy–inertia phase before the speed of the front decays below values at which the streaks can be sustained. The formation of the velocity streaks induces a streaky distribution of the bed friction velocity in the region immediately behind the front. This distribution becomes finer as the Grashof number increases. For simulations in which the only difference was the value of the Grashof number ($\sqrt {Gr}$ = 4.7 × 104 versus $\sqrt {Gr}$ = 106), analysis of the non-dimensional bed friction velocity distributions shows that the capacity of the gravity current to entrain sediment from the bed increases with the Grashof number. Past the later stages of the transition to the buoyancy–inertia phase, the temporal variations of the potential energy, the kinetic energy and the integral of the total dissipation rate are logarithmic.

Propagation of viscous currents on a porous substrate with finite capillary entry pressure

2016 ◽  
Vol 801 ◽  
pp. 65-90 ◽  
Author(s):  
Roiy Sayag ◽  
Jerome A. Neufeld
Keyword(s):  
Laboratory Experiments ◽  
Gravity Current ◽  
Fluid Pressure ◽  
Analytical Techniques ◽  
Gravity Currents ◽  
Porous Substrate ◽  
Entry Pressure ◽  
Self Similar ◽  
Capillary Entry Pressure ◽  
Theoretical Results

We study the propagation of viscous gravity currents over a thin porous substrate with finite capillary entry pressure. Near the origin, where the current is deep, propagation of the current coincides with leakage through the substrate. Near the nose of the current, where the current is thin and the fluid pressure is below the capillary entry pressure, drainage is absent. Consequently the flow can be characterised by the evolution of drainage and fluid fronts. We analyse this flow using numerical and analytical techniques combined with laboratory-scale experiments. At early times, we find that the position of both fronts evolve as $t^{1/2}$, similar to an axisymmetric gravity current on an impermeable substrate. At later times, the growing effect of drainage inhibits spreading, causing the drainage front to logarithmically approach a steady position. In contrast, the asymptotic propagation of the fluid front is quasi-self-similar, having identical structure to the solution of gravity currents on an impermeable substrate, only with slowly varying fluid flux. We benchmark these theoretical results with laboratory experiments that are consistent with our modelling assumption, but that also highlight the detailed dynamics of drainage inhibited by finite capillary pressure.

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