Scalar resonances in a unitary pi pi S-wave model for D(+)->pi(+)pi(-)pi(+)

We propose a model for D(+)->pi(+)pi(-)pi(+) decays following experimental results which indicate that the two-pion interaction in the S wave is dominated by the scalar resonances f(0)(600)/sigma and f(0)(980). The weak decay amplitude for D(+)-> R pi(+), where R is a resonance that subsequently decays into pi(+)pi(-), is constructed in a factorization approach. In the S wave, we implement the strong decay R ->pi(+)pi(-) by means of a scalar form factor. This provides a unitary description of the pion-pion interaction in the entire kinematically allowed mass range m(pi pi)(2) from threshold to about 3 GeV(2). In order to reproduce the experimental Dalitz plot for D(+)->pi(+)pi(-)pi(+), we include contributions beyond the S wave. For the P wave, dominated by the rho(770)(0), we use a Breit-Wigner description. Higher waves are accounted for by using the usual isobar prescription for the f(2)(1270) and rho(1450)(0). The major achievement is a good reproduction of the experimental m(pi pi)(2) distribution, and of the partial as well as the total D(+)->pi(+)pi(-)pi(+) branching ratios. Our values are generally smaller than the experimental ones. We discuss this shortcoming and, as a by-product, we predict a value for the poorly known D ->sigma transition form factor at q(2)=m pi(2).

Water wave-driven seepage in marine sediments

The action of water waves moving over a porous seabed drives a seepage flux into and out of the marine sediments. The volume of fluid exchange per wave cycle may affect the rate of contaminant transport in the sediments. In this paper, the dynamic response of the seabed to ocean waves is treated analytically on the basis of pore-elastic theory applied to a porous seabed. The seabed is modelled as a semi-infinite, isotropic, homogeneous material. Most previous investigations on the wave-seabed interaction problem have assumed quasi-static conditions within the seabed, although dynamic behaviour often occurs in natural environments. Furthermore, wave pressures used in the previous approaches were obtained from conventional ocean wave theories: which are based on the assumption of an impermeable rigid seabed. By introducing a complex wave number, we derive a new wave dispersion equation, which includes the seabed characteristics (such as soil permeability, shear modulus, etc.). Based on the new closed-form analytical solution, the relative differences of the wave-induced seabed response under dynamic and quasi-static conditions are examined. The effects of wave and soil parameters on the seepage flux per wave cycle are also discussed in detail. (C) 2000 Elsevier Science Ltd. All rights reserved.

Beach water table fluctuations due to wave run-up: Capillarity effects

High-frequency beach water table fluctuations due to wave run-up and rundown have been observed in the field [Waddell, 1976]. Such fluctuations affect the infiltration/exfiltration process across the beach face and the interstitial oxygenation process in the beach ecosystem. Accurate representation of high-frequency water table fluctuations is of importance in the modeling of (1) the interaction between seawater and groundwater, more important, the effects on swash sediment transport and (2) the biological activities in the beach ecosystem. Capillarity effects provide a mechanism for high-frequency water table fluctuations. Previous modeling approaches adopted the assumption of saturated flow only and failed to predict the propagation of high-frequency fluctuations in the aquifer. In this paper we develop a modified kinematic boundary condition (kbc) for the water table which incorporates capillarity effects. The application of this kbc in a boundary element model enables the simulation of high-frequency water table fluctuations due to wave run-up. Numerical tests were carried out for a rectangular domain with small-amplitude oscillations; the behavior of water table responses was found to be similar to that predicted by an analytical solution based on the one-dimensional Boussinesq equation. The model was also applied to simulate the water table response to wave run-up on a doping beach. The results showed similar features of water table fluctuations observed in the field. In particular, these fluctuations are standing wave-like with the amplitude becoming increasingly damped inland. We conclude that the modified kbc presented here is a reasonable approximation of capillarity effects on beach water table fluctuations. However, further model validation is necessary before the model can confidently be used to simulate high-frequency water table fluctuations due to wave run-up.

Simulation of wave action on a moored container carrier inside Sines’ Harbour

The integrated numerical tool SWAMS (Simulation of Wave Action on Moored Ships) is used to simulate the behavior of a moored container carrier inside Sines’ Harbour. Wave, wind, currents, floating ship and moorings interaction is discussed. Several case scenarios are compared differing in the layout of the harbour and wind and wave conditions. The several harbour layouts correspond to proposed alternatives for the future expansion of Sines’ terminal XXI that include the extension of the East breakwater and of the quay. Additionally, the influence of wind on the behavior of the ship moored and the introduction of pre tensioning the mooring lines was analyzed. Hydrodynamic forces acting on the ship are determined using a modified version of the WAMIT model. This modified model utilizes the Haskind relations and the non-linear wave field inside the harbour obtained with finite element numerical model, BOUSS-WMH (Boussinesq Wave Model for Harbors) to get the wave forces on the ship. The time series of the moored ship motions and forces on moorings are obtained using BAS solver. © 2015 Taylor & Francis Group, London.

Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

Distorted-wave calculation of cross sections for inner-shell ionization by electron and positron impact

The relativistic distorted-wave Born approximation is used to calculate differential and total cross sections for inner shell ionization of neutral atoms by electron and positron impact. The target atom is described within the independent-electron approximation using the self-consistent Dirac-Fock-Slater potential. The distorting potential for the projectile is also set equal to the Dirac-Fock-Slater potential. For electrons, this guarantees orthogonality of all the orbitals involved and simplifies the calculation of exchange T-matrix elements. The interaction between the projectile and the target electrons is assumed to reduce to the instantaneous Coulomb interaction. The adopted numerical algorithm allows the calculation of differential and total cross sections for projectiles with kinetic energies ranging from the ionization threshold up to about ten times this value. Algorithm accuracy and stability are demonstrated by comparing differential cross sections calculated by our code with the distorting potential set to zero with equivalent results generated by a more robust code that uses the conventional plane-wave Born approximation. Sample calculation results are presented for ionization of K- and L-shells of various elements and compared with the available experimental data.

What can we learn about gravitational wave physics with an elastic spherial antenna?

A general formalism is set up to analyze the response of an arbitrary solid elastic body to an arbitrary metric gravitational wave (GW) perturbation, which fully displays the details of the interaction antenna wave. The formalism is applied to the spherical detector, whose sensitivity parameters are thereby scrutinized. A multimode transfer function is defined to study the amplitude sensitivity, and absorption cross sections are calculated for a general metric theory of GW physics. Their scaling properties are shown to be independent of the underlying theory, with interesting consequences for future detector design. The GW incidence direction deconvolution problem is also discussed, always within the context of a general metric theory of the gravitational field.

Measures of ionicity of alkaline-earth oxides from the analysis of ab initio cluster wave functions

We present an analysis of the M-O chemical bonding in the binary oxides MgO, CaO, SrO, BaO, and Al2O3 based on ab initio wave functions. The model used to represent the local environment of a metal cation in the bulk oxide is an MO6 cluster which also includes the effect of the lattice Madelung potential. The analysis of the wave functions for these clusters leads to the conclusion that all the alkaline-earth oxides must be regarded as highly ionic oxides; however, the ionic character of the oxides decreases as one goes from MgO, almost perfectly ionic, to BaO. In Al2O3 the ionic character is further reduced; however, even in this case, the departure from the ideal, fully ionic, model of Al3+ is not exceptionally large. These conclusions are based on three measures, a decomposition of the Mq+-Oq- interaction energy, the number of electrons associated to the oxygen ions as obtained from a projection operator technique, and the analysis of the cation core-level binding energies. The increasing covalent character along the series MgO, CaO, SrO, and BaO is discussed in view of the existing theoretical models and experimental data.

A subcritical instability of wave-driven alongshore currents

The development of shear instabilities of a wave-driven alongshore current is investigated. In particular, we use weakly nonlinear theory to investigate the possibility that such instabilities, which have been observed at various sites on the U.S. coast and in the laboratory, can grow in linearly stable flows as a subcritical bifurcation by resonant triad interaction, as first suggested by Shrira eta/. [1997]. We examine a realistic longshore current profile and include the effects of eddy viscosity and bottom friction. We show that according to the weakly nonlinear theory, resonance is possible and that these linearly stable flows may exhibit explosive instabilities. We show that this phenomenon may occur also when there is only approximate resonance, which is more likely in nature. Furthermore, the size of the perturbation that is required to trigger the instability is shown in some circumstances to be consistent with the size of naturally occurring perturbations. Finally, we consider the differences between the present case examined and the more idealized case of Shrira et a/. [ 1997]. It is shown that there is a possibility of coupling between triads, due to the richer modal structure in more realistic flows, which may act to stabilize the flow and act against the development of subcritical bifurcations. Extensive numerical tests are called for.

The counter-propagating Rossby-wave perspective on baroclinic instability. I: Mathematical basis

It is shown that Bretherton's view of baroclinic instability as the interaction of two counter-propagating Rossby waves (CRWs) can be extended to a general zonal flow and to a general dynamical system based on material conservation of potential vorticity (PV). The two CRWs have zero tilt with both altitude and latitude and are constructed from a pair of growing and decaying normal modes. One CRW has generally large amplitude in regions of positive meridional PV gradient and propagates westwards relative to the flow in such regions. Conversely, the other CRW has large amplitude in regions of negative PV gradient and propagates eastward relative to the zonal flow there. Two methods of construction are described. In the first, more heuristic, method a ‘home-base’ is chosen for each CRW and the other CRW is defined to have zero PV there. Consideration of the PV equation at the two home-bases gives ‘CRW equations’ quantifying the evolution of the amplitudes and phases of both CRWs. They involve only three coefficients describing the mutual interaction of the waves and their self-propagation speeds. These coefficients relate to PV anomalies formed by meridional fluid displacements and the wind induced by these anomalies at the home-bases. In the second method, the CRWs are defined by orthogonality constraints with respect to wave activity and energy growth, avoiding the subjective choice of home-bases. Using these constraints, the same form of CRW equations are obtained from global integrals of the PV equation, but the three coefficients are global integrals that are not so readily described by ‘PV-thinking’ arguments. Each CRW could not continue to exist alone, but together they can describe the time development of any flow whose initial conditions can be described by the pair of growing and decaying normal modes, including the possibility of a super-modal growth rate for a short period. A phase-locking configuration (and normal-mode growth) is possible only if the PV gradient takes opposite signs and the mean zonal wind and the PV gradient are positively correlated in the two distinct regions where the wave activity of each CRW is concentrated. These are easily interpreted local versions of the integral conditions for instability given by Charney and Stern and by Fjørtoft.

The counter-propagating Rossby-wave perspective on baroclinic instability. II: Application to the Charney model

The constant-density Charney model describes the simplest unstable basic state with a planetary-vorticity gradient, which is uniform and positive, and baroclinicity that is manifest as a negative contribution to the potential-vorticity (PV) gradient at the ground and positive vertical wind shear. Together, these ingredients satisfy the necessary conditions for baroclinic instability. In Part I it was shown how baroclinic growth on a general zonal basic state can be viewed as the interaction of pairs of ‘counter-propagating Rossby waves’ (CRWs) that can be constructed from a growing normal mode and its decaying complex conjugate. In this paper the normal-mode solutions for the Charney model are studied from the CRW perspective. Clear parallels can be drawn between the most unstable modes of the Charney model and the Eady model, in which the CRWs can be derived independently of the normal modes. However, the dispersion curves for the two models are very different; the Eady model has a short-wave cut-off, while the Charney model is unstable at short wavelengths. Beyond its maximum growth rate the Charney model has a neutral point at finite wavelength (r=1). Thereafter follows a succession of unstable branches, each with weaker growth than the last, separated by neutral points at integer r—the so-called ‘Green branches’. A separate branch of westward-propagating neutral modes also originates from each neutral point. By approximating the lower CRW as a Rossby edge wave and the upper CRW structure as a single PV peak with a spread proportional to the Rossby scale height, the main features of the ‘Charney branch’ (0interaction of the CRWs. The underlying dynamics determining the nature of all the solutions is the difference in the scale-dependence of PV inversion for boundary and interior PV anomalies, the Rossby-wave propagation mechanism and the CRW interaction. The behaviour of the Charney modes and the first neutral branch, which rely on tropospheric PV gradients, are arguably more applicable to the atmosphere than modes of the Eady model where the positive PV gradient exists only at the tropopause

The counter-propagating Rossby-wave perspective on baroclinic instability. Part III: Primitive-equation disturbances on the sphere

Baroclinic instability of perturbations described by the linearized primitive quations, growing on steady zonal jets on the sphere, can be understood in terms of the interaction of pairs of counter-propagating Rossby waves (CRWs). The CRWs can be viewed as the basic components of the dynamical system where the Hamiltonian is the pseudoenergy and each CRW has a zonal coordinate and pseudomomentum. The theory holds for adiabatic frictionless flow to the extent that truncated forms of pseudomomentum and pseudoenergy are globally conserved. These forms focus attention on Rossby wave activity. Normal mode (NM) dispersion relations for realistic jets are explained in terms of the two CRWs associated with each unstable NM pair. Although derived from the NMs, CRWs have the conceptual advantage that their structure is zonally untilted, and can be anticipated given only the basic state. Moreover, their zonal propagation, phase-locking and mutual interaction can all be understood by ‘PV-thinking’ applied at only two ‘home-bases’—potential vorticity (PV) anomalies at one home-base induce circulation anomalies, both locally and at the other home-base, which in turn can advect the PV gradient and modify PV anomalies there. At short wavelengths the upper CRW is focused in the mid-troposphere just above the steering level of the NM, but at longer wavelengths the upper CRW has a second wave-activity maximum at the tropopause. In the absence of meridional shear, CRW behaviour is very similar to that of Charney modes, while shear results in a meridional slant with height of the air-parcel displacement-structures of CRWs in sympathy with basic-state zonal angular-velocity surfaces. A consequence of this slant is that baroclinically growing eddies (on jets broader than the Rossby radius) must tilt downshear in the horizontal, giving rise to up-gradient momentum fluxes that tend to accelerate the barotropic component of the jet.

The counter-propagating Rossby-wave perspective on baroclinic instability. Part IV: Nonlinear life cycles

Pairs of counter-propagating Rossby waves (CRWs) can be used to describe baroclinic instability in linearized primitive-equation dynamics, employing simple propagation and interaction mechanisms at only two locations in the meridional plane—the CRW ‘home-bases’. Here, it is shown how some CRW properties are remarkably robust as a growing baroclinic wave develops nonlinearly. For example, the phase difference between upper-level and lower-level waves in potential-vorticity contours, defined initially at the home-bases of the CRWs, remains almost constant throughout baroclinic wave life cycles, despite the occurrence of frontogenesis and Rossby-wave breaking. As the lower wave saturates nonlinearly the whole baroclinic wave changes phase speed from that of the normal mode to that of the self-induced phase speed of the upper CRW. On zonal jets without surface meridional shear, this must always act to slow the baroclinic wave. The direction of wave breaking when a basic state has surface meridional shear can be anticipated because the displacement structures of CRWs tend to be coherent along surfaces of constant basic-state angular velocity, U. This results in up-gradient horizontal momentum fluxes for baroclinically growing disturbances. The momentum flux acts to shift the jet meridionally in the direction of the increasing surface U, so that the upper CRW breaks in the same direction as occurred at low levels

Convectively coupled equatorial waves: A new methodology for identifying wave structures in observational data

Convectively coupled equatorial waves are fundamental components of the interaction between the physics and dynamics of the tropical atmosphere. A new methodology, which isolates individual equatorial wave modes, has been developed and applied to observational data. The methodology assumes that the horizontal structures given by equatorial wave theory can be used to project upper- and lower-tropospheric data onto equatorial wave modes. The dynamical fields are first separated into eastward- and westward-moving components with a specified domain of frequency–zonal wavenumber. Each of the components for each field is then projected onto the different equatorial modes using the y structures of these modes given by the theory. The latitudinal scale yo of the modes is predetermined by data to fit the equatorial trapping in a suitable latitude belt y = ±Y. The extent to which the different dynamical fields are consistent with one another in their depiction of each equatorial wave structure determines the confidence in the reality of that structure. Comparison of the analyzed modes with the eastward- and westward-moving components in the convection field enables the identification of the dynamical structure and nature of convectively coupled equatorial waves. In a case study, the methodology is applied to two independent data sources, ECMWF Reanalysis and satellite-observed window brightness temperature (Tb) data for the summer of 1992. Various convectively coupled equatorial Kelvin, mixed Rossby–gravity, and Rossby waves have been detected. The results indicate a robust consistency between the two independent data sources. Different vertical structures for different wave modes and a significant Doppler shifting effect of the background zonal winds on wave structures are found and discussed. It is found that in addition to low-level convergence, anomalous fluxes induced by strong equatorial zonal winds associated with equatorial waves are important for inducing equatorial convection. There is evidence that equatorial convection associated with Rossby waves leads to a change in structure involving a horizontal structure similar to that of a Kelvin wave moving westward with it. The vertical structure may also be radically changed. The analysis method should make a very powerful diagnostic tool for investigating convectively coupled equatorial waves and the interaction of equatorial dynamics and physics in the real atmosphere. The results from application of the analysis method for a reanalysis dataset should provide a benchmark against which model studies can be compared.