Compressible particle-driven gravity currents

2001 ◽  
Vol 445 ◽  
pp. 305-325 ◽  
Author(s):  
MARY-LOUISE E. TIMMERMANS ◽  
JOHN R. LISTER ◽  
HERBERT E. HUPPERT
Keyword(s):  
Large Scale ◽  
Numerical Solutions ◽  
Volcanic Eruptions ◽  
Gravity Currents ◽  
Scale Height ◽  
Pyroclastic Flows ◽  
Water Model ◽  
Model Approximation ◽  
Particle Settling ◽  
Density Scale

Large-scale particle-driven gravity currents occur in the atmosphere, often in the form of pyroclastic flows that result from explosive volcanic eruptions. The behaviour of these gravity currents is analysed here and it is shown that compressibility can be important in flow of such particle-laden gases because the presence of particles greatly reduces the density scale height, so that variations in density due to compressibility are significant over the thickness of the flow. A shallow-water model of the flow is developed, which incorporates the contribution of particles to the density and thermodynamics of the flow. Analytical similarity solutions and numerical solutions of the model equations are derived. The gas–particle mixture decompresses upon gravitational collapse and such flows have faster propagation speeds than incompressible currents of the same dimensions. Once a compressible current has spread sufficiently that its thickness is less than the density scale height it can be treated as incompressible. A simple ‘box-model’ approximation is developed to determine the effects of particle settling. The major effect is that a small amount of particle settling increases the density scale height of the particle-laden mixture and leads to a more rapid decompression of the current.

Entraining gravity currents

2013 ◽  
Vol 731 ◽  
pp. 477-508 ◽  
Author(s):  
Christopher G. Johnson ◽  
Andrew J. Hogg
Keyword(s):  
Richardson Number ◽  
Solution Structure ◽  
Large Scale ◽  
Gravity Current ◽  
Gravity Currents ◽  
Similarity Solutions ◽  
Water Model ◽  
Experimental Measurements ◽  
Entrainment Rate ◽  
Long Time

AbstractEntrainment of ambient fluid into a gravity current, while often negligible in laboratory-scale flows, may become increasingly significant in large-scale natural flows. We present a theoretical study of the effect of this entrainment by augmenting a shallow water model for gravity currents under a deep ambient with a simple empirical model for entrainment, based on experimental measurements of the fluid entrainment rate as a function of the bulk Richardson number. By analysing long-time similarity solutions of the model, we find that the decrease in entrainment coefficient at large Richardson number, due to the suppression of turbulent mixing by stable stratification, qualitatively affects the structure and growth rate of the solutions, compared to currents in which the entrainment is taken to be constant or negligible. In particular, mixing is most significant close to the front of the currents, leading to flows that are more dilute, deeper and slower than their non-entraining counterparts. The long-time solution of an inviscid entraining gravity current generated by a lock-release of dense fluid is a similarity solution of the second kind, in which the current grows as a power of time that is dependent on the form of the entrainment law. With an entrainment law that fits the experimental measurements well, the length of currents in this entraining inviscid regime grows with time approximately as ${t}^{0. 447} $. For currents instigated by a constant buoyancy flux, a different solution structure exists in which the current length grows as ${t}^{4/ 5} $. In both cases, entrainment is most significant close to the current front.

Axisymmetric gravity currents in a rotating system: experimental and numerical investigations

2001 ◽  
Vol 447 ◽  
pp. 1-29 ◽  
Author(s):  
MARK A. HALLWORTH ◽  
HERBERT E. HUPPERT ◽  
MARIUS UNGARISH
Keyword(s):  
Flow Field ◽  
Shallow Water ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Salt Water ◽  
Gravity Currents ◽  
The Body ◽  
Water Model ◽  
Maximum Radius ◽  
Theoretical Predictions

The propagation at high Reynolds number of a heavy, axisymmetric gravity current of given initial volume over a horizontal boundary is considered in both rotating and non-rotating situations. The investigation combines experiments with theoretical predictions by both shallow-water approximations and numerical solutions of the full axisymmetric equations. Attention is focused on cases when the initial ratio of Coriolis to inertia forces is small. The experiments were performed by quickly releasing a known cylindrical volume of dense salt water of 2 m diameter at the centre of a circular tank of diameter 13 m containing fresh ambient water of typical depth 80 cm. The propagation of the current was recorded for different initial values of the salt concentration, the volume of released fluid, the ratio of the initial height of the current to the ambient depth, and the rate of rotation. A major feature of the rotating currents was the attainment of a maximum radius of propagation. Thereafter a contraction–relaxation motion of the body of fluid and a regular series of outwardly propagating pulses was observed. The frequency of these pulses is slightly higher than inertial, and the amplitude is of the order of magnitude of half the maximum radius. Theoretical predictions of the corresponding gravity currents were also obtained by (i) previously developed shallow-water approximations (Ungarish & Huppert 1998) and (ii) a specially developed finite-difference code based on the full axisymmetric Navier–Stokes equations. The ‘numerical experiments’ provided by this code are needed to capture details of the flow field (such as the non-smooth shape of the interface, the vertical dependence of the velocity field) which are not reproduced by the shallow-water model and are very difficult for, or outside the range of, accurate experimental measurement. The comparisons and discussion provide insight into the flow field and indicate the advantages and limitations of the verified simulation tools.

Particle settling from constant-flux surface gravity currents and a near-stationary particle-bearing layer

2021 ◽  
Vol 6 (6) ◽  
Author(s):  
Bruce R. Sutherland ◽  
Brianna Mueller ◽  
Brendan Sjerve ◽  
David Deepwell
Keyword(s):  
Gravity Currents ◽  
Surface Gravity ◽  
Particle Settling ◽  
Flux Surface ◽  
Constant Flux ◽  
Bearing Layer

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 Hunting for Information in Streamflow Signatures to Improve Modelled Drainage

Water ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 110
Author(s):  
Raphael Schneider ◽  
Simon Stisen ◽  
Anker Lajer Højberg
Keyword(s):  
Large Scale ◽  
Agricultural Land ◽  
Hydrological Cycle ◽  
Drainage System ◽  
Water Model ◽  
Generation Process ◽  
Hydrological Models ◽  
Drainage Patterns ◽  
Drain Flow ◽  
Set Up

About half of the Danish agricultural land is drained artificially. Those drains, mostly in the form of tile drains, have a significant effect on the hydrological cycle. Consequently, the drainage system must also be represented in hydrological models that are used to simulate, for example, the transport and retention of chemicals. However, representation of drainage in large-scale hydrological models is challenging due to scale issues, lacking data on the distribution of drain infrastructure, and lacking drain flow observations. This calls for more indirect methods to inform such models. Here, we investigate the hypothesis that drain flow leaves a signal in streamflow signatures, as it represents a distinct streamflow generation process. Streamflow signatures are indices characterizing hydrological behaviour based on the hydrograph. Using machine learning regressors, we show that there is a correlation between signatures of simulated streamflow and simulated drain fraction. Based on these insights, signatures relevant to drain flow are incorporated in hydrological model calibration. A distributed coupled groundwater–surface water model of the Norsminde catchment, Denmark (145 km2) is set up. Calibration scenarios are defined with different objective functions; either using conventional stream flow metrics only, or a combination with hydrological signatures. We then evaluate the results from the different scenarios in terms of how well the models reproduce observed drain flow and spatial drainage patterns. Overall, the simulation of drain in the models is satisfactory. However, it remains challenging to find a direct link between signatures and an improvement in representation of drainage. This is likely attributable to model structural issues and lacking flexibility in model parameterization.

scholarly journals Improved moist-convective rotating shallow water model and its application to instabilities of hurricane-like vortices

2018 ◽  
Author(s):  
LMD
Keyword(s):  
Tropical Cyclone ◽  
Shallow Water ◽  
Water Vapour ◽  
Large Scale ◽  
Precipitable Water ◽  
Water Model ◽  
Moist Convection ◽  
Shallow Water Model ◽  
Atmospheric Motions ◽  
Rotating Shallow Water

We show how the two-layer moist-convective rotating shallow water model (mcRSW), which proved to be a simple and robust tool for studying effects of moist convection on large-scale atmospheric motions, can be improved by including, in addition to the water vapour, precipitable water, and the effects of vaporisation, entrainment, and precipitation. Thus improved mcRSW becomes cloud-resolving. It is applied, as an illustration, to model the development of instabilities of tropical cyclone-like vortices.

scholarly journals Simulated climate variability in the region of Rapa Nui during the last millennium

2011 ◽  
Vol 7 (1) ◽  
pp. 381-395 ◽  
Author(s):  
C. Junk ◽  
M. Claussen
Keyword(s):  
Large Scale ◽  
Vegetation Change ◽  
Climate Model ◽  
Volcanic Eruptions ◽  
Easter Island ◽  
Ice Age ◽  
Vegetation Changes ◽  
Last Millennium ◽  
Climate Data ◽  
Climatic Fluctuations

Abstract. Easter Island, an isolated island in the Southeast Pacific, was settled by the Polynesians probably between 600 and 1200 AD and discovered by the Europeans in 1722 AD. While the Polynesians presumably found a profuse palm woodland on Easter Island, the Europeans faced a landscape dominated by grassland. Scientists have examined potential anthropogenic, biological and climatic induced vegetation changes on Easter Island. Here, we analyze observational climate data for the last decades and climate model results for the period 800–1750 AD to explore potential causes for a climatic-induced vegetation change. A direct influence of the ENSO phenomenon on the climatic parameters of Easter Island could not be found in the model simulations. Furthermore, strong climatic trends from a warm Medieval Period to a Little Ice Age or rapid climatic fluctuations due to large volcanic eruptions were not verifiable for the Easter Island region, although they are detectable in the simulations for many regions world wide. Hence we tentatively conclude that large-scale climate changes in the oceanic region around Easter Island might be too small to explain strong vegetation changes on the island over the last millennium.

scholarly journals The role of airborne volcanic ash for the surface ocean biogeochemical iron-cycle: a review

2009 ◽  
Vol 6 (4) ◽  
pp. 6441-6489 ◽  
Author(s):  
S. Duggen ◽  
N. Olgun ◽  
P. Croot ◽  
L. Hoffmann ◽  
H. Dietze ◽  
...  
Keyword(s):  
Large Scale ◽  
Volcanic Ash ◽  
Volcanic Eruptions ◽  
Research Field ◽  
Ash Deposition ◽  
Future Directions ◽  
Iron Cycle ◽  
Surface Ocean ◽  
Wide Range

Abstract. Iron is a key micronutrient for phytoplankton growth in the surface ocean. Yet the significance of volcanism for the marine biogeochemical iron-cycle is poorly constrained. Recent studies, however, suggest that offshore deposition of airborne ash from volcanic eruptions is a way to inject significant amounts of bio-available iron into the surface ocean. Volcanic ash may be transported up to several tens of kilometres high into the atmosphere during large-scale eruptions and fine ash may encircle the globe for years, thereby reaching even the remotest and most iron-starved oceanic areas. Scientific ocean drilling demonstrates that volcanic ash layers and dispersed ash particles are frequently found in marine sediments and that therefore volcanic ash deposition and iron-injection into the oceans took place throughout much of the Earth's history. The data from geochemical and biological experiments, natural evidence and satellite techniques now available suggest that volcanic ash is a so far underestimated source for iron in the surface ocean, possibly of similar importance as aeolian dust. Here we summarise the development of and the knowledge in this fairly young research field. The paper covers a wide range of chemical and biological issues and we make recommendations for future directions in these areas. The review paper may thus be helpful to improve our understanding of the role of volcanic ash for the marine biogeochemical iron-cycle, marine primary productivity and the ocean-atmosphere exchange of CO2 and other gases relevant for climate throughout the Earth's history.

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