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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.

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]

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 locking section. A driving-locking 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 deformation velocity of Shuping landslide depends strongly on the reservoir level but only slightly on rainfall. Seepage modelling 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 locking 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 deformation velocity. Corrective transfer of earth mass from the driving section to the locking section successfully reduced the deformation of Shuping landslide, and is a feasible treatment for huge reservoir landslides in similar geological settings. [ABSTRACT FROM AUTHOR]

Abstract: The rainfall–run‐off convolution integral is analytically solved for several models for the elementary hydrograph. These solutions can be combined with available rainfall frequency analyses to predict flood flows along streams for different recurrence intervals, using no free parameters for gauged streams and one estimable parameter for ungauged streams. Extreme discharge magnitudes at gauged sites can be typically estimated within a factor of two of actual records, using no historical data on extreme flows. The flow predictions reproduce several important characteristics of the flood phenomenon, such as the slope of the regression line between observed extreme flows and basin area on the conventional logQ versus logA plot. Importantly, for the models and data sets investigated, the storm duration of greatest significance to flooding was found to approximate the intrinsic transport timescale of the particular watershed, which increases with basin size. Thus, storms that deliver extraordinary amounts of rainfall over a particular time interval will most greatly activate basins whose time constants approximately equal that interval. This theoretical finding is supported by examination of the regional hydrological response to the massive storms of September 14, 2008, and April 28–30, 2017, which caused extraordinary record flooding of basins of about 5–100 km2 and 500–4,000 km2, respectively, but produced few records in basins that were larger or smaller than those ranges. [ABSTRACT FROM AUTHOR]

Forces external to the oblate spheroid shape, observed from planetary to galactic scales, are demonstrably non-central, which has important ramifications for planetary science. We simplify historic formulae and derive new analytical solutions for the gravitational potential and force outside a constant density oblate. Numerical calculations that sum point mass contributions in a >10 9 element mesh confirm our equations. We show that contours of constant force and potential about oblate bodies are closely approximated by two confocal families whose foci ( f ) respectively are (9/10) ½ ae and (3/5) ½ ae for a body with f  =  ae . This leads to useful approximations that address internal density variations. We demonstrate that the force on a general point is not directed towards the oblate's center, nor are forces simply proportional to the inverse square of that distance, despite forces in the equatorial and axial directions pointing towards the center. Our results explain complex dynamics of galactic systems. Because most planets and stars have an aspect ratio >0.9, the spherical approximation is reasonable except for orbits within ∼2 body radii. We show that applying the “generalized” potential, which assumes central forces, yields J 2 values half those expected for oblate bodies, and probably underestimates masses of Uranus and Neptune by ∼0.2%. We show that the inner Saturnian moons are subject to non-central forces, which may affect calculations of their orbital precession. Our new series should improve interpretation of flyby data. [ABSTRACT FROM AUTHOR]

Galactic mass consistent with luminous mass is obtained by fitting rotation curves (RC = tangential velocities vs. equatorial radius r) using Newtonian force models, or can be unambiguously calculated from RC data using a model based on spin. In contrast, mass exceeding luminous mass is obtained from multi-parameter fits using potentials associated with test particles orbiting in a disk around a central mass. To understand this disparity, we explore the premises of these mainstream disk potential models utilizing the theorem of Gauss, thermodynamic concepts of Gibbs, the findings of Newton and Maclaurin, and well-established techniques and results from analytical mathematics. Mainstream models assume that galactic density in the axial (z) and r directions varies independently: we show that this is untrue for self-gravitating objects. Mathematics and thermodynamic principles each show that modifying Poisson’s equation by summing densities is in error. Neither do mainstream models differentiate between interior and exterior potentials, which is required by potential theory and has been recognized in seminal astronomical literature. The theorem of Gauss shows that: (1) density in Poisson’s equation must be averaged over the interior volume; (2) logarithmic gravitational potentials implicitly assume that mass forms a long, line source along the z axis, unlike any astronomical object; and (3) gravitational stability for three-dimensional shapes is limited to oblate spheroids or extremely tall cylinders, whereas other shapes are prone to collapse. Our findings suggest a mechanism for the formation of the flattened Solar System and of spiral galaxies from gas clouds. The theorem of Gauss offers many advantages over Poisson’s equation in analyzing astronomical problems because mass, not density, is the key parameter. [ABSTRACT FROM AUTHOR]

High frequency monitoring of water quality and stable isotopes quantify large hydrological and geochemical differences across a rural to urban land use gradient that includes three watersheds and two of their subbasins. Following precipitation events, floods on a rural stream feature hydrographs with low peak discharges and long lag times, high baseflow contributions, and small geochemical variations. In contrast, the flows of an urban stream and its tributary respond in a flashy manner, with average lag times decreasing by at least 55% compared to the rural stream. We also observed that baseflow contributions during floods decreased by an average of 40% in the urban streams. Importantly, we find that reduced baseflow as a function of increasing impervious surface area is not a linear trend among the streams, and suburban streams are less impacted than would be predicted by impervious surface area alone. The urban streams also exhibit large variations in water quality parameters during flooding events, often with five times the variability of the rural end-member. These differences are observed among all physical and geochemical characteristics that were monitored, including flow magnitude, stable isotope ratios, temperature, dissolved oxygen (DO), pH, turbidity, specific conductivity, concentrations of Cl − and nutrients, and bacterial loads. The great variability of urban streams following storms is paralleled by their larger diurnal and seasonal oscillations. Collectively, the extreme variations in the physical and geochemical character of urban streams have negative consequences to environmental quality and aquatic life. [ABSTRACT FROM AUTHOR]

Flooding in the Mississippi basin has become increasingly uncertain, and a succession of progressively higher, peak annual water levels is observed at many sites. Many record levels set in the central USA by the huge 1993 flood have already been superseded. Methodology developed elsewhere that recognizes trends of river stages is used to estimate present-day flood risk at 27 sites in the Mississippi basin that have >100 years of continuous stage record. Unlike official estimates that are fundamentally based on discharge, this methodology requires only data on river stage. A novel plot linearizes the official flood levels that are indirectly derived from the complex, discharge-based calculations and demonstrates that the neglect of trends has resulted in the effective use of undersized means and standard deviations in flood risk analysis. A severe consequence is that official 'base flood' levels are underestimated by 0.4 to 2 m at many sites in the central USA. [ABSTRACT FROM AUTHOR]

A theoretical, dimensionless rainfall-runoff model was used to simulate the discharge of Wulongdong spring in western Hubei province, South China. The single parameter (time constant τ) in the model is easy to obtain by fitting the recession rate of the observed hydrographs. The model was scaled by simply matching the total annual flow volume of the model to the observed value. Annual distribution of actual evapotranspiration was embedded in the model input to calculate the accumulated deficit of soil moisture before each rain event. Hourly precipitation input data performed better than daily data, defining τ of 0.85 days and returning a Nash-Sutcliffe efficiency of 0.89 and the root mean square error of 0.07. This model offers an effective way to simulate the discharge of karst springs that respond sensitively to rainfall events. The model parameters of a successful simulation can be used to estimate the recharge area and indicate the intrinsic response time of the basin. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

To explore planetary evolution, we provide conductive cooling profiles that account for planet size, phonon diffusivity and various internal heating scenarios. Our new analytical solution for simple cooling of spheres reveals that heat is removed from only Earth's outermost ~1000 km over geological time. Numerical models with decaying heat production show that any upward concentration of radionuclides causes high temperatures at shallow depths, forcing interior temperatures to increase with time while producing a thermal gradient that forbids lower mantle convection. Hence, differentiation drives upper mantle magmatism and tectonics, leaving a quiescent but hot deep interior, while slowly melting the core. [ABSTRACT FROM AUTHOR]

Fertilizer use has increased 10-fold since World War II. Current application rates are staggering and greatly exceed the amounts absorbed by plants. For example, the average amount of nitrogen applied [...]