scholarly journals Approximation zones of the Saint-Venant equations f flood routing with overbank flow

2000 ◽  
Vol 4 (2) ◽  
pp. 251-260 ◽  
Author(s):  
R. Moussa ◽  
C. Bocquillon
Keyword(s):  
Momentum Equation ◽  
Flood Routing ◽  
Wave Number ◽  
Linear Perturbation ◽  
Dimensionless Wave Number ◽  
Overbank Flow ◽  
Saint Venant Equations ◽  
Linear Perturbation Theory ◽  
Wave Models ◽  
Flooded Area

Abstract. The classification of river waves as gravity, diffusion or kinematic waves, corresponds to different forms of the momentum equation in the Saint-Venant system. This paper aims to define approximation zones of the Saint-Venant equations for flood routing in natural channels with overbank flow in the flooded area. Using linear perturbation theory, the different terms in the Saint-equations were analysed as a function of the balance between friction and inertia. Then, using non-dimensionalised variables, flood waves were expressed as a function of three parameters: the Froude number of the steady uniform flow, a dimensionless wave, number of the unsteady component of the motion and the ratio between the flooded area zone width and the main channel width. Finally, different theoretical cases, corresponding to different flooded area zone widths were analysed and compared. Results show that, when the width of the flooded area increases, the domain of application of the diffusive wave and the inematic wave models is restricted. Keywords: Saint-Venant equations; river waves; overbank flow

One-dimensional hydrodynamic model accounting for tidal effect

2012 ◽  
Vol 43 (1-2) ◽  
pp. 113-122 ◽  
Author(s):  
Xiaoqin Zhang ◽  
Weimin Bao ◽  
Simin Qu ◽  
Zhongbo Yu
Keyword(s):  
Hydrodynamic Model ◽  
Dynamic Effect ◽  
Momentum Equation ◽  
Tidal Effect ◽  
Flood Routing ◽  
One Dimensional ◽  
Tidal Rivers ◽  
Saint Venant Equations ◽  
Tidal Reach ◽  
The One

Tidal effect has a significant impact on flood routing in tidal rivers, conceptually taking on a resistant effect during flood tide and a dynamic effect during ebb tide. Two expressions were developed to reflect the tidal effect in this study, which consisted of the tidal wave velocity, the change rate of tidal level and the change in channel width. By incorporating the expressions into the momentum equation of the one-dimensional (1D) Saint-Venant equations, we propose that there are two types of momentum equations accounting for tidal effect. Based on the continuity equation and proposed momentum equations, two types of 1D hydrodynamic model for tidal rivers (namely the SVN-1 and -2 models) were constructed. In the case study, these models were applied to the tidal reach of the Qiantang River in China. The simulation results show that the SVN-1 and -2 models can obtain better accuracy than the SVN model based on the standard Saint-Venant equations, and that the SVN-1 model performs better than the SVN-2 model. Furthermore, the SVN-1 model can effectively capture water-level fluctuation, indicating that the expression employed is capable of accounting for tidal effect.

scholarly journals Comparison of numerical schemes of river flood routing with an inertial approximation of the Saint Venant equations

RBRH ◽  
2018 ◽  
Vol 23 (0) ◽  
Author(s):  
Alice César Fassoni-Andrade ◽  
Fernando Mainardi Fan ◽  
Walter Collischonn ◽  
Artur César Fassoni ◽  
Rodrigo Cauduro Dias de Paiva
Keyword(s):  
Numerical Stability ◽  
Flood Routing ◽  
Computational Time ◽  
Numerical Schemes ◽  
Time Step ◽  
Simple Formulation ◽  
One Dimensional ◽  
Saint Venant Equations ◽  
Original Scheme ◽  
The One

ABSTRACT The one-dimensional flow routing inertial model, formulated as an explicit solution, has advantages over other explicit models used in hydrological models that simplify the Saint-Venant equations. The main advantage is a simple formulation with good results. However, the inertial model is restricted to a small time step to avoid numerical instability. This paper proposes six numerical schemes that modify the one-dimensional inertial model in order to increase the numerical stability of the solution. The proposed numerical schemes were compared to the original scheme in four situations of river’s slope (normal, low, high and very high) and in two situations where the river is subject to downstream effects (dam backwater and tides). The results are discussed in terms of stability, peak flow, processing time, volume conservation error and RMSE (Root Mean Square Error). In general, the schemes showed improvement relative to each type of application. In particular, the numerical scheme here called Prog Q(k+1)xQ(k+1) stood out presenting advantages with greater numerical stability in relation to the original scheme. However, this scheme was not successful in the tide simulation situation. In addition, it was observed that the inclusion of the hydraulic radius calculation without simplification in the numerical schemes improved the results without increasing the computational time.

Analytical linear perturbation theory for highly eccentric satellite orbits

1995 ◽  
Vol 61 (4) ◽  
pp. 369-387 ◽  
Author(s):  
Eugene Brumberg ◽  
Victor A. Brumberg ◽  
Thomas Konrad ◽  
Michael Soffel
Keyword(s):  
Perturbation Theory ◽  
Linear Perturbation ◽  
Satellite Orbits ◽  
Linear Perturbation Theory

A Dynamical Model for Studying the Stability of Thermo-Solutal Convection Under the Effect of Vertical Vibration

2005 ◽  
Author(s):  
Y. P. Razi ◽  
M. Mojtabi ◽  
K. Maliwan ◽  
M. C. Charrier-Mojtabi ◽  
A. Mojtabi
Keyword(s):  
Stability Analysis ◽  
Mechanical Vibration ◽  
Stability Limit ◽  
Lewis Number ◽  
Vertical Vibration ◽  
Wave Number ◽  
Dimensionless Wave Number ◽  
Non Linear ◽  
Linear Differential ◽  
The Stability

This paper concerns the thermal stability analysis of porous layer saturated by a binary fluid under the influence of mechanical vibration. The linear stability analysis of this thermal system leads us to study the following damped coupled Mathieu equations: BH¨+B(π2+k2)+1H˙+(π2+k2)−k2k2+π2RaT(1+Rsinω*t*)H=k2k2+π2(NRaT)(1+Rsinω*t*)Fε*BF¨+Bπ2+k2Le+ε*F˙+π2+k2Le−k2k2+π2NRaT(1+Rsinω*t*)F=k2k2+π2RaT(1+Rsinω*t*)H where RaT is thermal Rayleigh number, R is acceleration ratio (bω2/g), Le is the Lewis number, k is the dimensionless wave-number, ε* is normalized porosity and N is the buoyancy ratio (H and F are perturbations of temperature and concentration fields). In the follow up, the non-linear behavior of the problem is studied via a generalization of the Lorenz model (five coupled non-linear differential equations with periodic coefficients). In the presence or absence of gravity, the stability limit for the onset of stationary as well as Hopf bifurcations is determined.

Stability Features of the Saucer-Shaped Blend-Wing-Body Aircraft

2013 ◽  
Vol 712-715 ◽  
pp. 1307-1311
Author(s):  
Lin Lin Wang ◽  
Ge Gao
Keyword(s):  
Perturbation Theory ◽  
Longitudinal Mode ◽  
Flight Dynamics ◽  
Aerodynamic Characteristics ◽  
Linear Perturbation ◽  
Low Speed ◽  
Similarities And Differences ◽  
Linear Perturbation Theory ◽  
Dutch Roll ◽  
Directional Flight

The saucer-shaped aircraft is a novel aircraft adopting blend-wing-body configuration. The linear perturbation theory based on the classic flight dynamics was used to analyze the longitudinal, lateral and directional flight qualities of the saucer-shaped aircraft under low speed conditions. The flight qualities were given. Meanwhile the aerodynamic characteristics of the saucer-shaped aircraft, the conventional aircraft and the flying wing aircraft were also contrasted to discuss their similarities and differences. The results show that the saucer-shaped aircraft has stable longitudinal mode, rollover mode and Dutch roll mode. The spiral mode is unstable. The saucer-shaped aircraft exhibits superior flight qualities and excellent comprehensive performances.

scholarly journals Contributions to the Local Gravitational Field from beyond the Local Supercluster

1987 ◽  
Vol 117 ◽  
pp. 435-443
Author(s):  
A. Yahil
Keyword(s):  
Gravitational Field ◽  
Background Radiation ◽  
Nonlinear Effects ◽  
Linear Perturbation ◽  
Density Parameter ◽  
Microwave Background ◽  
Dipole Component ◽  
Local Supercluster ◽  
Microwave Background Radiation ◽  
Linear Perturbation Theory

IRAS 60μ sources are used to map the local (≲200h−1 Mpc, Ho =100h km s−1 Mpc−1) gravitational field, and to determine its dipole component, on the assumption that the infrared radiation traces the matter. The dipole moment is found to point in the direction of the anisotropy of the microwave background radiation. Comparison of the two anisotropies, using linear perturbation theory, yields an estimate of the cosmological density parameter, Ω =0.85±0.16, with nonlinear effects increasing Ωo by ∼15%. The quadrupolar tidal field within the Local Supercluster, due presumably to the same density inhomogeneities, is detected in a kinematical study of the velocity field.

scholarly journals Spiral-arm instability – III. Fragmentation of primordial protostellar discs

2019 ◽  
Vol 491 (1) ◽  
pp. L24-L28 ◽  
Author(s):  
Shigeki Inoue ◽  
Naoki Yoshida
Keyword(s):  
Gravitational Instability ◽  
Finite Thickness ◽  
Linear Perturbation ◽  
Gas Cooling ◽  
Formation And Evolution ◽  
Linear Perturbation Theory ◽  
The Stability ◽  
Protostellar Discs ◽  
Self Gravity ◽  
Spiral Arm

ABSTRACT We study the gravitational instability and fragmentation of primordial protostellar discs by using high-resolution cosmological hydrodynamics simulations. We follow the formation and evolution of spiral arms in protostellar discs, examine the dynamical stability, and identify a physical mechanism of secondary protostar formation. We use linear perturbation theory based on the spiral-arm instability (SAI) analysis in our previous studies. We improve the analysis by incorporating the effects of finite thickness and shearing motion of arms, and derive the physical conditions for SAI in protostellar discs. Our analysis predicts accurately the stability and the onset of arm fragmentation that is determined by the balance between self-gravity and gas pressure plus the Coriolis force. Formation of secondary and multiple protostars in the discs is explained by the SAI, which is driven by self-gravity and thus can operate without rapid gas cooling. We can also predict the typical mass of the fragments, which is found to be in good agreement with the actual masses of secondary protostars formed in the simulation.

Der Einfluß des Entladungsgefäßes auf die Bestimmung der Plasmaelektronendichte mit Hohlraumresonatoren / The Influence of the Discharge Tube on the Determination of the Plasma Electron Density by Means of Cavity Resonators

1972 ◽  
Vol 27 (3) ◽  
pp. 491-499 ◽  
Author(s):  
G Janzen
Keyword(s):  
Electron Density ◽  
Discharge Tube ◽  
Plasma Electron ◽  
Microwave Cavity ◽  
Linear Perturbation ◽  
Density Profiles ◽  
Cavity Resonators ◽  
Resonance Modes ◽  
Linear Perturbation Theory ◽  
Electron Density Profiles

AbstractThe eigenvalue equation of a plasma-discharge tube configuration in a cylindrical microwave cavity is derived and solved numerically by an exact theory for TMlm0 , TM0mn, and TE0mn resonance modes. The radial and axial electron density profiles are assumed to be homogeneous. The factors of proportionality between electron density and shift of the resonance frequency derived from the linear perturbation theory are compared with the exactly computed eigenvalues. Hence the range of validity of the linearly computed factors of proportionality (geometry factors) can be established. By considering the influence of the discharge tube the geometry factors are altered and consequently the sensitivity of the measurement. The influence of the discharge tube can be taken into account by means of suitable correction factors.

scholarly journals Re-examination of Large Scale Structure & Cosmic Flows

2014 ◽  
Vol 11 (S308) ◽  
pp. 310-317
Author(s):  
Marc Davis ◽  
Adi Nusser
Keyword(s):  
Perturbation Theory ◽  
Velocity Field ◽  
Gravity Field ◽  
Inverse Method ◽  
Large Scale ◽  
Linear Perturbation ◽  
Data Set ◽  
Galaxy Distribution ◽  
Standard Values ◽  
Linear Perturbation Theory

AbstractComparison of galaxy flows with those predicted from the local galaxy distribution ended as an active field after two analyses came to vastly different conclusions 25 years ago, but that was due to faulty data. All the old results are therefore suspect. With new data collected in the last several years, the problem deserves another look. The goal is to explain the 640 km/s dipole anisotropy of the CMBR. For this we analyze the gravity field inferred from the enormous data set derived from the 2MASS collection of galaxies (Huchra et al. 2005), and compare it to the velocity field derived from the well calibrated SFI++ Tully-Fisher catalog (Springob et al. 2007). Using the “Inverse Method” to minimize Malmquist biases, within 10,000 km/s the gravity field is seen to predict the velocity field (Davis et al. 2011) to remarkable consistency. This is a beautiful demonstration of linear perturbation theory and is fully consistent with standard values of the cosmological variables.

scholarly journals NEW HOLOGRAPHIC CHAPLYGIN GAS MODEL OF DARK ENERGY

2011 ◽  
Vol 20 (03) ◽  
pp. 281-297 ◽  
Author(s):  
M. MALEKJANI ◽  
A. KHODAM-MOHAMMADI
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
Chaplygin Gas ◽  
Accelerated Expansion ◽  
Linear Perturbation ◽  
Generalized Chaplygin Gas ◽  
Infrared Cutoff ◽  
Scalar Field Models ◽  
Linear Perturbation Theory ◽  
Limiting Case

In this work, we investigate the holographic dark energy model with a new infrared cutoff (new HDE model), proposed by Granda and Oliveros. Using this new definition for the infrared cutoff, we establish the correspondence between the new HDE model and the standard Chaplygin gas (SCG), generalized Chaplygin gas (GCG) and modified Chaplygin gas (MCG) scalar field models in a nonflat universe. The potential and dynamics for these scalar field models, which describe the accelerated expansion of the universe, are reconstructed. According to the evolutionary behavior of the new HDE model, we derive the same form of dynamics and potential for the different SCG, GCG and MCG models. We also calculate the squared sound speed of the new HDE model as well as the SCG, GCG and MCG models, and investigate the new HDE Chaplygin gas models from the viewpoint of linear perturbation theory. In addition, all results in the nonflat universe are discussed in the limiting case of the flat universe, i.e. k = 0.

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