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 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.

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.

Gravity currents over fractured substrates in a porous medium

2007 ◽  
Vol 584 ◽  
pp. 415-431 ◽  
Author(s):  
DAVID PRITCHARD
Keyword(s):  
Porous Medium ◽  
Steady State ◽  
Gravity Current ◽  
Gravity Currents ◽  
Limited Extent ◽  
Form Part ◽  
Long Time ◽  
Self Similar ◽  
Steady State Solutions ◽  
A Current

We consider the behaviour of a gravity current in a porous medium when the horizontal surface along which it spreads is punctuated either by narrow fractures or by permeable regions of limited extent. We derive steady-state solutions for the current, and show that these form part of a long-time asymptotic description which may also include a self-similar ‘leakage current’ propagating beyond the fractured region with a length proportional to t1/2. We discuss the conditions under which a current can be completely trapped by a permeable region or a series of fractures.

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.

scholarly journals On the baroclinic instability of axisymmetric rotating gravity currents with bottom slope

2000 ◽  
Vol 408 ◽  
pp. 149-177 ◽  
Author(s):  
PAUL F. CHOBOTER ◽  
GORDON E. SWATERS
Keyword(s):  
Numerical Simulations ◽  
Linear Stability ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Laboratory Data ◽  
Gravity Current ◽  
Gravity Currents ◽  
Finite Amplitude ◽  
Rotating System ◽  
A Current

The baroclinic stability characteristics of axisymmetric gravity currents in a rotating system with a sloping bottom are determined. Laboratory studies have shown that a relatively dense fluid released under an ambient fluid in a rotating system will quickly respond to Coriolis effects and settle to a state of geostrophic balance. Here we employ a subinertial two-layer model derived from the shallow-water equations to study the stability characteristics of such a current after the stage at which geostrophy is attained. In the model, the dynamics of the lower layer are geostrophic to leading order, but not quasi-geostrophic, since the height deflections of that layer are not small with respect to its scale height. The upper-layer dynamics are quasi-geostrophic, with the Eulerian velocity field principally driven by baroclinic stretching and a background topographic vorticity gradient.Necessary conditions for instability, a semicircle-like theorem for unstable modes, bounds on the growth rate and phase velocity, and a sufficient condition for the existence of a high-wavenumber cutoff are presented. The linear stability equations are solved exactly for the case where the gravity current initially corresponds to an annulus flow with parabolic height profile with two incroppings, i.e. a coupled front. The dispersion relation for such a current is solved numerically, and the characteristics of the unstable modes are described. A distinguishing feature of the spatial structure of the perturbations is that the perturbations to the downslope incropping are preferentially amplified compared to the upslope incropping. Predictions of the model are compared with recent laboratory data, and good agreement is seen in the parameter regime for which the model is valid. Direct numerical simulations of the full model are employed to investigate the nonlinear regime. In the initial stage, the numerical simulations agree closely with the linear stability characteristics. As the instability develops into the finite-amplitude regime, the perturbations to the downslope incropping continue to preferentially amplify and eventually evolve into downslope propagating plumes. These finally reach the deepest part of the topography, at which point no more potential energy can be released.

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