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The dynamic behavior of flood waves on rivers is essential to flood prediction. Natural flood waves are complex due to tributary inputs, rainfall variations, and overbank flows, so this study examines hydropower dam releases, which are simpler to analyze because channel effects are isolated. Successive arrival times and heights of peaks along 9 rivers with multiple stream gauges downstream of hydroelectric dams show that flow peaks typically become exponentially lower and wider with distance. The propagation velocity of peaks increases with water depth and channel slope but decreases with downstream distance and greater channel tortuosity. A rich hierarchy of velocities was found. Hydropower pulses progress at or in slight excess of the theoretical celerity, which is faster than the propagation rate of average natural floods, which in turn exceeds the mean velocity of water in the channel, yet the water moves faster than the peaks of record floods. The progressive changes to the height, shape, and velocity of hydropower flow peaks are simulated by the first analytical solution to the convolution integral for a rectangular source pulse that is based on diffusion-advection theory. Available data support some widely held expectations while refuting others. An expanded definition of "water mining" is proposed. [ABSTRACT FROM AUTHOR]

The historic, classical thermodynamic model of star interiors neglects luminosity (L), and consequently predicts ultrahigh central solar temperatures (T - 15 x 106 K). Modern models yield similar T profiles mostly because local thermal equilibrium and multiple free parameters are used. Instead, long-term stability of stars signifies disequilibrium where energy generated equals energy emitted. We assume that heat is generated in a shell defining the core and use Fourier's model, which describes diffusion of heat, including via radiation. to predict the T profile. Under steadystate, power L transmitted through each shell is constant above the zone of energy generation. Hence, L is independent of spherical radius (s), so the Stefan-Boltzmann law dictates T(s), and material properties are irrelevant. Temperature is constant in the core and proportional to Dtr-1/2 above. A point source core sets the upper limit on T(s). giving Taverage = (6/5) 1 451 r| ace• Core size or convecting regions little affect our results. We also construct a parameter-free model for interior pressure (P) and density (p) by inserting our T(s) formula into an ideal gas law (P/poLT) while using the equation for hydrostatic gravitational compression. We find P oc s-·1, p (X s-.5~, and paverage =6x p,uN-ace· Another result, Ln< mass·3·3, agrees with accepted empirical rules for main sequence stars, and validates our model. The total solar mass already "burned" suggests that fusion occurs near L„4400 where P - 0.5 x 1012 Pa, in agreement with H-bomb pressure estimates. Implications are discussed. [ABSTRACT FROM AUTHOR]

Available inventories of baryonic mass in the universe are based largely on galactic data and empirical calculations made >20 years ago. Values falling below cosmological estimates underlie proposals that certain rarified gassy regions could have extremely high T, which motivated absorption measurements and hydrodynamic models. Yet, the shortfall remains. We inventory the total baryonic mass, focusing on gravitational interactions and updated measurements. A recent analytical inverse method for analyzing galactic rotation curves quantified how baryon mass and associated volumetric density (ρ) depend on distance (r) from galactic centers. The model is based on the dynamical consequences of the observed oblate shape of galaxies and the Virial Theorem. The parameter-free solution provides ρ(r) ∝ 1/r2 which describes star-rich galactic interiors, gas-rich outer discoids, circumgalactic media, and gradation into intergalactic media. Independent observational determinations of baryonic ρ validate that our 1/r2 result describes baryons alone. This solution shows that total baryonic mass associated with any galaxy is 2.4 to 40 times detectable luminosity, depending on galaxy size and spacing. Luminosity data within 50 Mpc show that Andromeda equivalents separated by ~1 Mpc represent the local universe. Combining the above yields (6 ± 2) × 10−25 kg m−3 for the present-day universe. Three other approaches support this high density: (1) evaluating trends and luminosity data near 1000 Mpc; (2) using a recent estimate for the number of galaxies in the universe; (3) calculating an energy balance. We discuss uncertainties in the critical density. Implications of large baryonic ρ are briefly discussed. [ABSTRACT FROM AUTHOR]

Spiral galaxies are discrete spheroidal objects with highly organized, circular internal motions about a special axis. Available models do not describe these key features or explain why the central regions rotate like a solid body. Practically all previous models describe galaxies as a collection of orbiting test particles, utilize numerous fitting parameters, and require either copious amounts of surrounding dark matter that have not been detected, or modifications to Newton's law, to fit the observed dependence of equatorial velocity on radius. Our paper probes the reasonable alternative that galaxies are discrete, spinning objects. Our analytical forward models, constructed by applying the virial theorem and Newton's law to Maclaurin's spinning spheroids with varying internal density, explain why galactic rotation is organized into this three-dimensional shape. Without invoking dark matter, our spin model explains why the outermost rotational velocities are nearly constant, yet depend on galaxy size, and, with no free parameters, provides masses of 14 important galaxies consistent with their luminosities. We show that proposed modifications to Newton's law compensate for the dynamical differences between a flattened, spinning, Newtonian spheroid, and a collection of orbits. Key words: virial theorem, galactic rotation, dark matter, non-Newtonian forces, spin. Les galaxies spirales sont des objets discrets avec des mouvements circulaires internes hautement organises autour d'un axe special. Les modeles disponibles ne decrivent pas ces caracteristiques centrales ni n'expliquent pourquoi la region centrale tourne comme un corps rigide. Pratiquement tous les modeles anterieurs decrivent les galaxies comme une collection de particules tests en orbite, utilisent de nombreux parametres d'ajustement et requierent des quantites genereuses de matiere noire qui n'ont pas ete detectees, ou encore des modifications a la loi de Newton, afin de s'ajuster aux resultats observes de la dependance de la vitesse equatoriale sur le rayon. Nous sondons ici une alternative raisonnable ou les galaxies sont des objets discrets en rotation. Notre modele analytique, construit en appliquant le theoreme du viriel et la loi de Newton a des spheroides en rotation de Mclaurin avec une densite interne variable, explique pourquoi la rotation galactique est organisee sous cette forme trois-dimensionnelle. Sans besoin de matiere noire, notre modele explique pourquoi les vitesses de rotation externes sont pratiquement constantes, tout en dependant de la grandeur de la galaxie et, sans parametre libre, fournit les masses de 14 galaxies importantes coherentes avec leur luminosite. Nous montrons que les modifications apportees a la loi de Newton compensent pour la difference dynamique entre le spin d'un spheroide newtonien aplati et une collection d'orbites. [Traduit par la Redaction] Mots-cles: theoreme du viriel, rotation galactique, matiere noire, forces non newtoniennes, spin., 1. Introduction Despite decades of intensive searches, non-baryonic particles have not been directly detected [1, 2]. Observational evidence for dark matter is thus limited to forward (fitting) models of galactic [...]

By exploring diverse simple cases, we show that the virial theorem (VT) of Clausius rests on limits of integration in temporal averages being specified by spatial symmetry, rather than on long durations as heretofore claimed. We show the VT results from linear momentum cancelling in all directions over the restricted space that defines any given bound state, via a balance that involves canonical conjugate pairs of position and momentum; this constraint differs from conservation of energy or momentum. The importance of space is underscored by considering behavior of the ideal gas, which is time- independent. Because each distinct force induces a specific type of motion, which in turn has a characteristic length scale, separate VTs are required for each process, which we confirm by example. Combining unrelated potentials in the VT or in its underlying mathematical identity is invalid because this procedure, used in astrophysics, permits energy exchanges that violate selection rules, symmetry constraints, or thermodynamic law. Our analysis unearths an erroneous numerical factor concerning rotation, helps explain the origin of axial spin in our Solar System, and casts doubt on the historical link of gravitation with temperature. Key words: virial theorem, Lagrange-Jacobi identity, ideal gas, canonical conjugates. En examinant plusieurs cas simples, nous montrons que le theoreme du viriel (VT) de Clausius repose sur des limites finies d'integration de moyennes dans le temps basees sur des symetries spatiales, plutot que sur de longues durees comme generalement presente. Nous montrons que le moment lineaire s'annule dans toutes les directions sur un espace borne qui definit tout etat lie, en utilisant un equilibre qui implique la paire canonique conjuguee d'impulsion-position; cette contrainte est differente de celles basees sur la conservation de l'energie ou de l'impulsion. L'importance de l'aspect spatial est soulignee en considerant le comportement du gaz parfait, qui est independant du temps. Parce que chaque force distincte induit un mouvement different, qui a sa propre echelle de longueur caracteristique, differents VT sont requis pour chaque processus, ce que nous confirmons par un exemple. La combinaison de potentiels non relies dans le meme VT ou dans sa formulation mathematique est invalide, parce que cette procedure, utilisee en astrophysique, permet des echanges d'energie qui violent les regles de selection, les contraintes de symetrie ou les lois de la thermodynamique. Notre analyse fait ressortir des facteurs numeriques errones concernant la rotation, aide a expliquer l'origine du spin axial dans notre systeme solaire et jette un doute sur le lien historiquement fait entre la gravite et la temperature. [Traduit par la Redaction] Mots-cles: theoreme du viriel, formulation Lagrange-Jacobi, gaz parfait, canonique conjuguee. PACS Nos.: 11.27.+d, 05.70.-a., 1. Introduction The virial theorem (VT) of Clausius [1] describes diverse phenomena in bound, conservative systems whose scales range from quantum to astronomical [2-4]. Because Clausius was concerned with temperature [...]

Kepler's discoveries were permitted by his remarkable insight to place the Sun at the focus of an elliptical planetary orbit. This coordinate system reduces a 2-dimensional orbit to a single spatial dimension. We consider an alternative coordinate system centered on the "image focus," which is the symmetrical (mirror) counterpart of the "real focus" occupied by the Sun. Our analytical approach provides new purely geometric formulae and an exact relationship for the dynamic property of orbital time. In addition, considering the mirror symmetry of the ellipse leads to a simple approximation: the radial hand of an orbital clock rotates counterclockwise at a nearly steady angular velocity 2π/T about the "image focus," where T is the orbital period. This approximation is a useful pedagogic tool and has good accuracy for orbits with low to moderate eccentricities, since the deviation from the exact result goes as eccentricity squared. Planetary comparisons are made. In particular, the angular speeds of Mercury and Jupiter are highly variable in the geocentric and heliocentric reference frames, but are nearly constant in the image focus reference frame. Our findings resolve whether the image focus is the location for observing uniform motion of an elliptical orbit, and pertain to their stability. [ABSTRACT FROM AUTHOR]

Extremely slow recession of the Moon from the Earth has been recently proposed and attributed to conversion of Earth's axial spin to lunar orbital momentum. This hypothesis is inconsistent with long-standing recognition that the Moon's orbit involves three-body interactions. This and other short-comings, such as Earth's spin loss being internal, are summarized here. Considering point-masses is justified by theory and observational data on other moons. We deduce that torque in the Earth-Moon-Sun system increases eccentricity of the lunar orbit but decreases its inclination over time. Consequently, the average lunar orbital radius is decreasing. We also show that lunar drift is too small to be constrained through lunar laser ranging measurements, mainly because atmospheric refraction corrections are comparatively large and variations in lunar cycles are under-sampled. Our findings support co-accretion and explain how orbits evolve in many-body point-mass systems. [ABSTRACT FROM AUTHOR]

Available data on insulating, semiconducting, and metallic solids verify our new model that incorporates steady-state heat flow into a macroscopic, thermodynamic description of solids, with agreement being best for isotropic examples. Our model is based on: (1) mass and energy conservation; (2) Fourier's law; (3) Stefan–Boltzmann's law; and (4) rigidity, which is a large, yet heretofore neglected, energy reservoir with no counterpart in gases. To account for rigidity while neglecting dissipation, we consider the ideal, limiting case of a perfectly frictionless elastic solid (PFES) which does not generate heat from stress. Its equation-of-state is independent of the energetics, as in the historic model. We show that pressure-volume work (PdV) in a PFES arises from internal interatomic forces, which are linked to Young's modulus (Ξ) and a constant (n) accounting for cation coordination. Steady-state conditions are adiabatic since heat content (Q) is constant. Because average temperature is also constant and the thermal gradient is fixed in space, conditions are simultaneously isothermal: Under these dual restrictions, thermal transport properties do not enter into our analysis. We find that adiabatic and isothermal bulk moduli (B) are equal. Moreover, Q/V depends on temperature only. Distinguishing deformation from volume changes elucidates how solids thermally expand. These findings lead to simple descriptions of the two specific heats in solids: ∂ln(cP)/∂P = −1/B; cP = nΞ times thermal expansivity divided by density; cP = cVnΞ/B. Implications of our validated formulae are briefly covered. [ABSTRACT FROM AUTHOR]

Data from the 1803-1806 Lewis and Clark expedition and nineteenth century stage records are used to quantitatively benchmark natural, premanagement hydrology of the lower Missouri River and assess the magnitude and timing of hydrologic change over nearly two centuries. Data show doubling in daily stage variability from the nineteenth century to 2005. Annual maximum stages have, at some sites, become more extreme, and their seasonality is less regular. Observed changes adversely affect riverine habitat and flood levels; their timing, beginning as early as 1900, suggests that channelization is the major driver. Keywords: basin management, Missouri River, hydrology, channelization, Lewis and Clark.

Abstract: Analysis of hydrologic, meteorologic, and isotopic data collected over 3 yr quantifies and explains the enormous variability and isotopic enrichment ([δ.sup.18]O = +16.9, δD = +50.0) of alpine Lake [...]

Landslides whose slide surface is gentle near the toe and relatively steep in the middle and rear part are common in the Three Gorges Reservoir area, China. The mass that overlies the steep part of the slide surface is termed the "driving section", and that which overlies the gentle part of the slide surface is termed the "resisting section". A driving–resisting model is presented to elucidate the deformation mechanism of reservoir landslides of this type, as exemplified by Shuping landslide. More than 13 years of field observations that include rainfall, reservoir level, and deformation show that the displacement velocity of Shuping landslide depends strongly on the reservoir level but only slightly on rainfall. Seepage modeling shows that the landslide was destabilized shortly after the reservoir was first impounded to 135 m, which initiated a period of steady deformation from 2003 to 2006 that was driven by buoyancy forces on the resisting section. Cyclical water level fluctuations in subsequent years also affected slope stability, with annual "jumps" in displacement coinciding with drawdown periods that produce outward seepage forces. In contrast, the inward seepage force that results from rising reservoir levels stabilizes the slope, as indicated by decreased displacement velocity. Corrective transfer of earth mass from the driving section to the resisting section successfully reduced the deformation of Shuping landslide and is a feasible treatment for huge reservoir landslides in similar geological settings. [ABSTRACT FROM AUTHOR]