Modelling the dynamics of turbulent floods

Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre manifold theory to derive dynamical models for the evolution of the water depth and of vertically averaged flow velocity and turbulent parameters. This new model for the shallow water dynamics of turbulent flow: resolves the vertical structure of the flow and the turbulence; includes interaction between turbulence and long waves; and gives a rational alternative to classical models for turbulent environmental flows

Anisotropic eddy-viscosity concept for strongly detached unsteady flows

The accurate prediction of the flow physics around bodies at high Reynolds number is a challenge in aerodynamics nowadays. In the context of turbulent flow modeling, recent advances like large eddy simulation (LES) and hybrid methods [detached eddy simulation (DES)] have considerably improved the physical relevance of the numerical simulation. However, the LES approach is still limited to the low-Reynolds-number range concerning wall flows. The unsteady Reynolds-averaged Navier–Stokes (URANS) approach remains a widespread and robust methodology for complex flow computation, especially in the near-wall region. Complex statistical models like second-order closure schemes [differential Reynolds stress modeling (DRSM)] improve the prediction of these properties and can provide an efficient simulationofturbulent stresses. Fromacomputational pointofview, the main drawbacks of such approaches are a higher cost, especially in unsteady 3-D flows and above all, numerical instabilities

An analytical treatment of the Clock Paradox in the framework of the Special and General Theories of Relativity

In this paper we treat the so called clock paradox in an analytical way by assuming that a constant and uniform force F of finite magnitude acts continuously on the moving clock along the direction of its motion assumed to be rectilinear. No inertial motion steps are considered. The rest clock is denoted as (1), the to-and-fro moving clock is (2), the inertial frame in which (1) is at rest in its origin and (2) is seen moving is I and, finally, the accelerated frame in which (2) is at rest in its origin and (1) moves forward and backward is A. We deal with the following questions: I) What is the effect of the finite force acting on (2) on the proper time intervals measured by the two clocks when they reunite? Does a differential aging between the two clocks occur, as it happens when inertial motion and infinite values of the accelerating force is considered? The Special Theory of Relativity is used in order to describe the hyperbolic motion of (2) in the frame I II) Is this effect an absolute one, i.e. does the accelerated observer A comoving with (2) obtain the same results as that in I, both qualitatively and quantitatively, as it is expected? We use the General Theory of Relativity in order to answer this question.Comment: LaTex2e, 19 pages, no tables, no figures. Rewritten version, it amends the previous one whose results about the treatment with General Relativity were wrong. References added. Eq. (55) corrected. More refined version. Comments and suggestions are warmly welcom

Maximum Coronal Mass Ejection Speed as an Indicator of Solar and Geomagnetic Activities

We investigate the relationship between the monthly averaged maximal speeds of coronal mass ejections (CMEs), international sunspot number (ISSN), and the geomagnetic Dst and Ap indices covering the 1996-2008 time interval (solar cycle 23). Our new findings are as follows. (1) There is a noteworthy relationship between monthly averaged maximum CME speeds and sunspot numbers, Ap and Dst indices. Various peculiarities in the monthly Dst index are correlated better with the fine structures in the CME speed profile than that in the ISSN data. (2) Unlike the sunspot numbers, the CME speed index does not exhibit a double peak maximum. Instead, the CME speed profile peaks during the declining phase of solar cycle 23. Similar to the Ap index, both CME speed and the Dst indices lag behind the sunspot numbers by several months. (3) The CME number shows a double peak similar to that seen in the sunspot numbers. The CME occurrence rate remained very high even near the minimum of the solar cycle 23, when both the sunspot number and the CME average maximum speed were reaching their minimum values. (4) A well-defined peak of the Ap index between 2002 May and 2004 August was co-temporal with the excess of the mid-latitude coronal holes during solar cycle 23. The above findings suggest that the CME speed index may be a useful indicator of both solar and geomagnetic activities. It may have advantages over the sunspot numbers, because it better reflects the intensity of Earth-directed solar eruptions

Applicability of frozen-viscosity models of unsteady wall shear stress

The validity of assumed frozen-viscosity conditions underpinning an important class of theoretical models of unsteady wall shear stress in transient flows in pipes and channels is assessed using detailed computational fluid dynamics (CFD) simulations. The need for approximate one-dimensional ð1DÞfx; tg models of the wall stress is unavoidable in analyses of transient flows in extensive pipe networks because it would be economically impracticable to use higher order methods of analysis. However, the bases of the various models have never been established rigorously. It is shown herein that a commonly used approach developed by the first authors is flawed in the case of smoothwall flows although it is more plausible for rough-wall flows. The assessment process is undertaken for a particular, but important, unsteady flow case, namely, a uniform acceleration from an initially steady turbulent flow. First, detailed predictions from a validated CFD method are used to derive baseline solutions with which predictions based on approximate models can be compared. Then, alternative solutions are obtained using various prescribed frozen-viscosity distributions. Differences between these solutions and the baseline solutions are used to determine which frozen-viscosity distributions are the most promising starting points for developing 1Dfx; tg models of unsteady components of wall shear stress. It is shown that no frozen-viscosity distribution performs well for large times after the commencement of an acceleration. However, even the simplest approximation (laminar) performs well for short durations—which is when the greatest amplitudes of the unsteady components occu

Anomalities in the Analysis of Calibrated Data

This study examines effects of calibration errors on model assumptions and data--analytic tools in direct calibration assays. These effects encompass induced dependencies, inflated variances, and heteroscedasticity among the calibrated measurements, whose distributions arise as mixtures. These anomalies adversely affect conventional inferences, to include the inconsistency of sample means; the underestimation of measurement variance; and the distributions of sample means, sample variances, and Student's t as mixtures. Inferences in comparative experiments remain largely intact, although error mean squares continue to underestimate the measurement variances. These anomalies are masked in practice, as conventional diagnostics cannot discern irregularities induced through calibration. Case studies illustrate the principal issues

Boundary-crossing identities for diffusions having the time-inversion property

We review and study a one-parameter family of functional transformations, denoted by (S (β)) β∈ℝ, which, in the case β<0, provides a path realization of bridges associated to the family of diffusion processes enjoying the time-inversion property. This family includes Brownian motions, Bessel processes with a positive dimension and their conservative h-transforms. By means of these transformations, we derive an explicit and simple expression which relates the law of the boundary-crossing times for these diffusions over a given function f to those over the image of f by the mapping S (β), for some fixed β∈ℝ. We give some new examples of boundary-crossing problems for the Brownian motion and the family of Bessel processes. We also provide, in the Brownian case, an interpretation of the results obtained by the standard method of images and establish connections between the exact asymptotics for large time of the densities corresponding to various curves of each family

Flory-Huggins theory for athermal mixtures of hard spheres and larger flexible polymers

A simple analytic theory for mixtures of hard spheres and larger polymers with excluded volume interactions is developed. The mixture is shown to exhibit extensive immiscibility. For large polymers with strong excluded volume interactions, the density of monomers at the critical point for demixing decreases as one over the square root of the length of the polymer, while the density of spheres tends to a constant. This is very different to the behaviour of mixtures of hard spheres and ideal polymers, these mixtures although even less miscible than those with polymers with excluded volume interactions, have a much higher polymer density at the critical point of demixing. The theory applies to the complete range of mixtures of spheres with flexible polymers, from those with strong excluded volume interactions to ideal polymers.Comment: 9 pages, 4 figure

Modeling long-range memory with stationary Markovian processes

In this paper we give explicit examples of power-law correlated stationary Markovian processes y(t) where the stationary pdf shows tails which are gaussian or exponential. These processes are obtained by simply performing a coordinate transformation of a specific power-law correlated additive process x(t), already known in the literature, whose pdf shows power-law tails 1/x^a. We give analytical and numerical evidence that although the new processes (i) are Markovian and (ii) have gaussian or exponential tails their autocorrelation function still shows a power-law decay =1/T^b where b grows with a with a law which is compatible with b=a/2-c, where c is a numerical constant. When a<2(1+c) the process y(t), although Markovian, is long-range correlated. Our results help in clarifying that even in the context of Markovian processes long-range dependencies are not necessarily associated to the occurrence of extreme events. Moreover, our results can be relevant in the modeling of complex systems with long memory. In fact, we provide simple processes associated to Langevin equations thus showing that long-memory effects can be modeled in the context of continuous time stationary Markovian processes.Comment: 5 figure