Potential-flow instability theory and alluvial stream bed forms

2000 ◽  
Vol 418 ◽  
pp. 101-117 ◽  
Author(s):  
S. E. COLEMAN ◽  
J. D. FENTON
Keyword(s):  
Sediment Transport ◽  
Potential Flow ◽  
Flow Model ◽  
Flow Instability ◽  
Phase Lag ◽  
Flow Conditions ◽  
Local Flow ◽  
Flow Models ◽  
Flow Systems ◽  
Bed Waves

The present work constitutes a reassessment of the role of potential-flow analyses in describing alluvial-bed instability. To facilitate the analyses, a new potential-flow description of unsteady alluvial flow is presented, with arbitrary phase lags between local flow conditions and sediment transport permitted implicitly in the flow model. Based on the present model, the explicit phase lag between local sediment transport rate and local flow conditions adopted for previous potential-flow models is shown to be an artificial measure that results in model predictions that are not consistent with observed flow system behaviour. Previous potential-flow models thus do not provide correct descriptions of alluvial flows, and the understanding of bed-wave mechanics inferred based upon these models needs to be reassessed. In contrast to previous potential-flow models, the present one, without the use of an explicit phase lag, predicts instability of flow systems of rippled or dune-covered equilibrium beds. Instability is shown to occur at finite growth rates for a range of wavelengths via a resonance mechanism occurring for surface waves and bed waves travelling at the same celerity. In addition, bed-wave speeds are predicted to decrease with increasing wavelength, and bed waves are predicted to grow and move at faster rates for flows of larger Froude numbers. All predictions of the present potential-flow model are consistent with observations of physical flow systems. Based on the predicted unstable wavelengths for a given alluvial flow, it is concluded that bed waves are not generated from plane bed conditions by any potential-flow instability mechanism. The predictions of instability are nevertheless consistent with instances of accelerated wave growth occurring for flow systems of larger finite developing waves. Potential-flow description of alluvial flows should, however, no longer form the basis of instability analyses describing bed-form (sand-wavelet) generation from flat bed conditions.

Study of the Response of PW Traffic Flow Model to a Bottleneck on a Circular Road and its Suitability for Heterogeneous Traffic Conditions

2021 ◽  
Vol 9 (4) ◽  
pp. 460-463
Keyword(s):  
Fluid Flow ◽  
Traffic Flow ◽  
Flow Model ◽  
Equation Model ◽  
Heterogeneous Traffic ◽  
Flow Conditions ◽  
Flow Models ◽  
Traffic Conditions ◽  
Model Response ◽  
Traffic Flow Models

The traffic flow conditions in developing countries are predominantly heterogeneous. The early developed traffic flow models have been derived from fluid flow to capture the behavior of the traffic. The very first two-equation model derived from fluid flow is known as the Payne-Whitham or PW Model. Along with the traffic flow, this model also captures the traffic acceleration. However, the PW model adopts a constant driver behavior which cannot be ignored, especially in the situation of heterogeneous traffic.This research focuses on testing the PW model and its suitability for heterogeneous traffic conditions by observing the model response to a bottleneck on a circular road. The PW model is mathematically approximated using the Roe Decomposition and then the performance of the model is observed using simulations.

Data Center Airflow Prediction With an Enhanced Potential Flow Model

2013 ◽  
Author(s):  
James W. VanGilder ◽  
Xuanhang (Simon) Zhang ◽  
Christopher M. Healey
Keyword(s):  
Data Center ◽  
Potential Flow ◽  
Data Centers ◽  
Flow Model ◽  
Computational Effort ◽  
Temperature Estimation ◽  
Flow Models ◽  
Physics Potential ◽  
Empirical Tests ◽  
Potential Flow Model

Potential flow models (PFM) have been implemented for a variety of applications, including data center airflow and temperature estimation. As an approximate solution to the data center room physics, potential flow models have great value in their simplicity and the limited computational effort required providing estimates. However, potential flow models lack the ability to capture the effects of buoyancy, which can affect airflow patterns within data centers. We show how this effect can be simulated within PFM; resulting in a model we call Enhanced PFM (EPFM). This model is only marginally more complex to implement than PFM and retains much of the properties of the original PFM, specifically its simplicity and stability. Solution time, about double that of PFM, is still only a small fraction of that of CFD, while empirical tests show a marked improvement in the prediction of key data center temperatures.

scholarly journals A dynamic bidirectional coupled surface flow model for flood inundation simulation

2021 ◽  
Vol 21 (2) ◽  
pp. 497-515
Author(s):  
Chunbo Jiang ◽  
Qi Zhou ◽  
Wangyang Yu ◽  
Chen Yang ◽  
Binliang Lin
Keyword(s):  
Flow Model ◽  
Wave Theory ◽  
Surface Flow ◽  
Flood Inundation ◽  
Flow Conditions ◽  
Local Flow ◽  
Benchmark Tests ◽  
Proposed Model ◽  
The World ◽  
Future Management

Abstract. Flood disasters frequently threaten people and property all over the world. Therefore, an effective numerical model is required to predict the impacts of floods. In this study, a dynamic bidirectional coupled hydrologic–hydrodynamic model (DBCM) is developed with the implementation of characteristic wave theory, in which the boundary between these two models can dynamically adapt according to local flow conditions. The proposed model accounts for both mass and momentum transfer on the coupling boundary and was validated via several benchmark tests. The results show that the DBCM can effectively reproduce the process of flood propagation and also account for surface flow interaction between non-inundation and inundation regions. The DBCM was implemented for the floods simulation that occurred at Helin Town located in Chongqing, China, which shows the capability of the model for flood risk early warning and future management.

Mathematical modelling of salt purification by recrystallization. A cross-current flow model and its comparison with the countercurrent arrangement

1986 ◽  
Vol 51 (11) ◽  
pp. 2489-2501
Author(s):  
Benitto Mayrhofer ◽  
Jana Mayrhoferová ◽  
Lubomír Neužil ◽  
Jaroslav Nývlt
Keyword(s):  
Flow Model ◽  
Current Flow ◽  
Countercurrent Flow ◽  
Flow Models ◽  
Multi Stage ◽  
Stage Crystallization ◽  
The Cross ◽  
Current Flows ◽  
Set Up ◽  
Cross Current

A model is derived for a multi-stage crystallization with cross-current flows of the solution and the crystals being purified. The purity of the product is compared with that achieved in the countercurrent arrangement. A suitable function has been set up which allows the cross-current and countercurrent flow models to be compared and reduces substantially the labour of computation for the countercurrent arrangement. Using the recrystallization of KAl(SO4)2.12 H2O as an example, it is shown that, when the cross-current and countercurrent processes are operated at the same output, the countercurrent arrangement is more advantageous because its solvent consumption is lower.

scholarly journals A conceptual model of flow to the Waikoropupu Springs, NW Nelson, New Zealand, based on hydrometric and tracer (<sup>18</sup>O, Cl,<sup>3</sup>H and CFC) evidence

2008 ◽  
Vol 12 (1) ◽  
pp. 1-19 ◽  
Author(s):  
M. K. Stewart ◽  
J. T. Thomas
Keyword(s):  
New Zealand ◽  
Flow Model ◽  
Sea Water ◽  
Quantitative Description ◽  
Water Volume ◽  
Deep Aquifer ◽  
Submarine Springs ◽  
Recharge Sources ◽  
Flow Systems ◽  
New Evidence

Abstract. The Waikoropupu Springs, a large karst resurgence 4 km from the coast, are supplied by the Arthur Marble Aquifer (AMA) underlying the Takaka Valley, South Island, New Zealand. New evidence on the recharge sources in the catchment, combined with previous results, is used to establish a new recharge model for the AMA. Combined with the oxygen-18 mass balance, this yields a quantitative description of the inputs and outputs to the aquifer. It shows that the Main Spring is sourced mainly from the karst uplands (74%), with smaller contributions from the Upper Takaka River (18%) and valley rainfall (8%), while Fish Creek Spring contains mostly Upper Takaka River water (50%). In addition, much of the Upper Takaka River contribution to the aquifer (58%) bypasses the springs and is discharged offshore via submarine springs. The chemical concentrations of the Main Spring show input of 0.5% of sea water on average, which varies with flow and derives from the deep aquifer. Tritium measurements spanning 40 yr, and CFC-11 measurements, give a mean residence time of 8 yr for the Main Spring water using the preferred two-component model. Our conceptual flow model, based on the flow, chloride, oxygen-18 and age measurements, invokes two different flow systems with different recharge sources to explain the flow within the AMA. One system contains deeply penetrating old water with mean age 10.2 yr and water volume 3 km3, recharged from the karst uplands. The other, at shallow levels below the valley floor, has much younger water with mean age 1.2 yr and water volume 0.4 km3, recharged by Upper Takaka River and valley rainfall. The flow systems contribute in different proportions to the Main Spring, Fish Creek Springs and offshore springs. Their very different behaviours, despite being in the same aquifer, are attributed to the presence of a diorite intrusion below the surface of the lower valley, which diverts the deep flow towards the Waikoropupu Springs and allows much of the shallow flow to pass over the intrusive and escape via submarine springs.

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