Rotational flow in gravity current heads

McElwaine, J. N.

doi:10.1098/rsta.2005.1597

Cited by 28 publications

(39 citation statements)

References 7 publications

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“…As the current moves down the slope this front crescent spreads and flattens out and then becomes unstable. The spreading is to be expected, because there is no steady flow possible with a curved front where the pressure in the ambient fluid balances the hydrostatic spreading forces [McElwaine, 2005]. This instability as the flow front flattens is probably related to the well known, but poorly understood, lobe and cleft instability.…”

Section: Resultsmentioning

confidence: 99%

“…[49] The nature of the pressure field on the center line through a gravity current is discussed in detail by McElwaine [2005]. The main result is that the pressure along the surface through the center of the flow is …”

Section: Comparison With Dynamic Theory For the Air Flowmentioning

confidence: 99%

“…Typical signals from the snow-air experiments are shown in Figure 8. The positive pressure in front of the avalanche is that of a dipole [McElwaine and Nishimura, 2001;McElwaine, 2005], which is to leading order 1 2 r a u…”

Section: Air Pressurementioning

confidence: 99%

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Experiments on the non‐Boussinesq flow of self‐igniting suspension currents on a steep open slope

Turnbull¹,

McElwaine²

2008

J. Geophys. Res.

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[1] Pyroclastic flows from volcanoes, dust storms in the desert, and submarine turbidity currents are all gravity currents of particles in suspension occurring in nature. Powder snow avalanches are one such flow where the density difference between the suspended particles and the interstitial air is high and the particles carry a significant proportion of the flow's momentum. This means that the Boussinesq approximation, where density differences are considered negligible in inertia terms, is not valid. Aspects of such flows, such as their internal structure and the transition from a dense flow to a suspension current are not well understood. Repeatable laboratory experiments are necessary for a better understanding of the underlying physics. Up to now, an experiment has not been designed with the correct similarity criteria for modeling powder snow avalanches. We have addressed this by designing and analyzing the results from a new experimental model of powder snow avalanches that had three distinctive features. Fine, dry snow was used to form suspension currents in air. The high density ratio of powder snow avalanches was preserved so that the currents are non-Boussinesq. Our experiments started with a dense current that then self-ignited, undergoing the transition to a suspension current. The shape and position of the current was tracked with two video cameras, and the air flow measured with a high-frequency response pressure transducer mounted in the base. We show how the air pressure data closely match theory and reveal whether a current is primarily dense or suspended.

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Section: Resultsmentioning

confidence: 99%

Section: Comparison With Dynamic Theory For the Air Flowmentioning

confidence: 99%

See 1 more Smart Citation

Experiments on the non‐Boussinesq flow of self‐igniting suspension currents on a steep open slope

Turnbull¹,

McElwaine²

2008

J. Geophys. Res.

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“…Note that the pressure is not constant at the free boundary, but this does not violate the Bernoulli relation since the radial velocity becomes infinite along the streamline ψ 0 = 0: the velocity components in the moving frame are u = c 0 g (θ ) and v = −c 0 g(θ ). This singularity can be removed by considering appropriate boundary conditions at the free surface: as suggested by McElwaine [46], the intrusion of a high-speed gravity current entails the motion of the ambient fluid, which means that there is a more complicated relation between the surge and its environment. As shown by McElwaine [46], the singularity in the u and p solutions drops out when the stream function has a highly pronounced dependence on r : typically, we should impose ψ 0 = c 0 r m g(θ ) with m > 2; the case m = 2 corresponds to constant vorticity [23].…”

Section: Refined Analysis Of the Front Structurementioning

confidence: 99%

“…The angle χ is here only imposed by mass balance, whereas in finite-volume gravity currents investigated by McElwaine [46], the angle is controlled by dynamic conditions at the interface with the surrounding fluid.…”

Section: Patchingmentioning

confidence: 99%

Existence and features of similarity solutions for non-Boussinesq gravity currents

Ancey

Cochard

Rentschler

et al. 2007

Physica D: Nonlinear Phenomena

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In this paper, the flow dynamics of gravity currents on a horizontal plane is investigated from a theoretical point of view by seeking similarity solutions. The current is generated by unleashing a varying volume of heavy fluid within an ambient fluid of much lower density. Unlike earlier investigators, we assume that the ambient fluid exerts no significant resisting action on the current, and therefore the flow depth is expected to drop to zero at the front in the absence of friction. In this context, the shallow-water equations are highly appropriate for computing the mean velocity and flow depth of the current. The boundary condition imposed at the front leads to technical mathematical difficulties. Indeed, unlike in the Boussinesq case, no regular solution to the shallow-water equations satisfies the downstream condition, but when the flow is supercritical at the channel inlet, it is possible to construct a piecewise solution by patching a regular solution to an exceptional solution, which represents the head behavior. To better understand this result and make sure that the result is physically relevant, we consider the Navier-Stokes equations within the high-Reynolds-number limit. Approximate similarity solutions can be worked out, which support our earlier analysis on the shallow-water equations. While the flow body is self-similar and weakly rotational, the head is not self-similar, but tends toward a self-similarity shape at long times. It is characterized by a strong vorticity, a straight free surface, and a nonuniform velocity profile, which becomes flatter and flatter with time.

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Frontal dynamics of powder snow avalanches

2013

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[1] We analyze frontal dynamics of dilute powder snow avalanches sustained by rapid blow-out behind the front. Such material injection arises as a weakly cohesive snow cover is fluidized by the very pore pressure gradient that the particle cloud induces within the snowpack. We model cloud fluid mechanics as a potential flow consisting of a traveling source of denser fluid thrust into a uniform airflow. Stability analysis of a mass balance involving snow cover and powder cloud yields relations among scouring depth, frontal height, speed, mixed-mean density, and impact pressure when the frontal region achieves a stable growth rate. We compare predictions with field measurements, show that powder clouds cannot reach steady frontal speed on a uniform snowpack with constant cloud width and derive a criterion for cloud ignition. Because static pressure is continuous across the mean air-cloud interface and deviatoric stresses are negligible, frontal acceleration is insensitive to local slope, but instead arises from a deficit of flow-induced suction in the wake. We calculate how far a powder cloud travels until its frontal mixed-mean density becomes stable, and show how topographic spread can hasten its collapse.

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Rotational flow in gravity current heads

Cited by 28 publications

References 7 publications

Experiments on the non‐Boussinesq flow of self‐igniting suspension currents on a steep open slope

Experiments on the non‐Boussinesq flow of self‐igniting suspension currents on a steep open slope

Existence and features of similarity solutions for non-Boussinesq gravity currents

Frontal dynamics of powder snow avalanches

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