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Aerothermodynamics, Nonlinear Acoustics and the Meteorological Equations
The study of low-Mach-number flows occurs in the general context of asymptotic modelling of fluid flows, and in a recent book (Zeytounian 2004, Chap....
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Applications of the Correlation Length
The correlation length is the system–dependent parameter, which defines the structure of the dominant current–carrying (electric or fluid) paths....
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Pressure Saturation Curves and the Critical Volume Fraction for Percolation
The pressure-saturation curves of porous media give fundamental information about the pore space. In equilibrium, ignoring effects due to hysteresis,...
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Effects of Multi-Scale Heterogeneity
It is generally agreed that problems with multi-scale heterogeneity present the biggest challenge to computation and understanding. A few such...
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Some Aspects of Low-Mach-Number External Flows
In this chapter, we consider first, in Sect. 4.1, a detailed derivation of the Navier–Fourier initial–boundary–value problem for the Navier velocity...
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Comparison of Single and Two‐Fluid Approaches
The results of the “0D„ analyses gathered in Tables 5.1 and 6.1 and discussed in Sects. 5.3 and 6.2 provide the basis for comparing Dam's к–ε and...
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Conclusion, Future Modeling Trends
The relevance of this study stands not in the topics that have been discussed, since most of them have already been explored for many years now, but...
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Single‐Fluid Approach: Example of Dam's к–ε Model
The statistical equations for the turbulent flow of an incompressible fluid are found in the literature [58], but they are adapted here to the...
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Specific Treatment of Shocks: Constraints on Models1
Before examining the phenomenology of the interaction between a shock and turbulent or material heterogeneities, it is useful to recall that the...
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Two‐Fluid Approach: Example of Awe's Model
Two‐fluid descriptions often use explicitly separate treatments for the conservation equations in each fluid, along with expressions for exchange...
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Some Aspects of Low-Mach-Number Internal Flows
In the present chapter, the main problem concerns low-Mach-number flow affected by acoustic effects in a confined gas over a long time.
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Slow Atmospheric Motion as a Low-Mach-Number Flow
First, in Sect. 6.1, we discuss in detail various facets of the applicability of the Boussinesq approximation to slow atmospheric motion. In Sect....
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The Many Faces of the Asymptotics of Low-Mach-Number Flows
It has long been known (Janzen 1913 and Rayleigh 1916) that asymptotic methods provide a sound way of describing incompressible aerodynamics...
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A First Approach to the Asymptotics of Low-Mach-Number Flows
In this chapter, we describe an initial (rather ‘naive’) approach to the asymptotics of low-Mach-number flows, based mainly on consideration of the...
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Specific Examples of Critical Path Analysis
At the end of Chap. 1 the general technique of critical path analysis was introduced. This technique will actually form the basis of most of the...
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Basic Constitutive Relations for Unsaturated Media
The following sections describe how to find the hydraulic conductivity, air permeability, electrical conductivity, as well as solute and gas...
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Review of Different Instability Types and Regimes
The three major types of “ideal„ instabilities studied here are [92]:
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Applications of the Cluster Statistics
This chapter presents a conceptually straightforward treatment of spatial correlations of “random” heterogeneous media, but does not intend to...
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Porous Media Primer for Physicists
During the 1980's physicists (and some geophysicists) devoted considerable efforts to understanding the physical (meaning here not hydraulic)...