Appearance Of Caustics Research Articles

Interactions between Mesoscale and Submesoscale Gravity Waves and Their Efficient Representation in Mesoscale-Resolving Models

AbstractAs present weather forecast codes and increasingly many atmospheric climate models resolve at least part of the mesoscale flow, and hence also internal gravity waves (GWs), it is natural to ask whether even in such configurations subgrid-scale GWs might impact the resolved flow and how their effect could be taken into account. This motivates a theoretical and numerical investigation of the interactions between unresolved submesoscale and resolved mesoscale GWs, using Boussinesq dynamics for simplicity. By scaling arguments, first a subset of submesoscale GWs that can indeed influence the dynamics of mesoscale GWs is identified. Therein, hydrostatic GWs with wavelengths corresponding to the largest unresolved scales of present-day limited-area weather forecast models are an interesting example. A large-amplitude WKB theory, allowing for a mesoscale unbalanced flow, is then formulated, based on multiscale asymptotic analysis utilizing a proper scale-separation parameter. Purely vertical propagation of submesoscale GWs is found to be most important, implying inter alia that the resolved flow is only affected by the vertical flux convergence of submesoscale horizontal momentum at leading order. In turn, submesoscale GWs are refracted by mesoscale vertical wind shear while conserving their wave-action density. An efficient numerical implementation of the theory uses a phase-space ray tracer, thus handling the frequent appearance of caustics. The WKB approach and its numerical implementation are validated successfully against submesoscale-resolving simulations of the resonant radiation of mesoscale inertia GWs by a horizontally as well as vertically confined submesoscale GW packet.

Formation of caustics in k-essence and Horndeski theory

We study propagation of waves and appearance of caustics in k-essence and galileon theories. First we show that previously known solutions for travelling waves in k-essence and galileon models correspond to very specific fine-tuned initial conditions. On the contrary, as we demonstrate by the method of characteristics, generic initial conditions leads to a wave in k-essence which ends up with formation of caustics. Finally, we find that any wave solution in pure k-essence is also a solution for a galileon theory with the same k-essence term. Thus in the Horndeski theory with a k-essence term formation of caustics is generic. We discuss physical consequences of the caustics formation and possible ways to cure the problem.

Depth migration by the Gaussian beam summation method

Seismic depth migration aims to produce an image of seismic reflection interfaces. Ray methods are suitable for subsurface target-oriented imaging and are less costly compared to two-way wave-equation-based migration, but break down in cases when a complex velocity structure gives rise to the appearance of caustics. Ray methods also have difficulties in correctly handling the different branches of the wavefront that result from wave propagation through a caustic. On the other hand, migration methods based on the two-way wave equation, referred to as reverse-time migration, are known to be capable of dealing with these problems. However, they are very expensive, especially in the 3D case. It can be prohibitive if many iterations are needed, such as for velocity-model building. Our method relies on the calculation of the Green functions for the classical wave equation by per-forming a summation of Gaussian beams for the direct and back-propagated wavefields. The subsurface image is obtained by cal-culating the coherence between the direct and backpropagated wavefields. To a large extent, our method combines the advantages of the high computational speed of ray-based migration with the high accuracy of reverse-time wave-equation migration because it can overcome problems with caustics, handle all arrivals, yield good images of steep flanks, and is readily extendible to target-oriented implementation. We have demonstrated the quality of our method with several state-of-the-art benchmark subsurface models, which have velocity variations up to a high degree of complexity. Our algorithm is especially suited for efficient imaging of selected subsurface subdomains, which is a large advantage particularly for 3D imaging and velocity-model refinement applications such as subsalt velocity-model improvement. Because our method is also capable of providing highly accurate migration results in structurally complex subsurface settings, we have also included the concept of true-amplitude imaging in our migration technique.

Search for exotic matter from gravitational microlensing observations of stars

We consider small-scale spheroidal clusters of weakly interacting massive particles in our Galaxy as non-compact gravitational microlenses and predict the appearance of caustics in the plane of a lensed source. The crossing of these caustics by a lensed star can produce a large variety of light curves, including some observed in actual microlensing events that have been interpreted as manifestations of binary gravitational lenses. We consider also observable effects during the gravitational microlensing of stars of non-zero angular size with a given brightness distribution across their disks by such an exotic objects as natural wormholes and objects whose space-time environment is described with the NUT metric. We demonstrate that, under certain conditions, the microlensing light curves, chromatic and polarizational effects due to the properties of the lens and the star disk brightness distributions can differ considerably from those observed for a Schwarzschild gravitational lens, so that their analysis can facilitate the identification of such objects.

Lagrangian and Eulerian descriptions of inertial particles in random flows

We study how the spatial distribution of inertial particles evolves with time in a random flow. We describe an explosive appearance of caustics and show how they influence an exponential growth of clusters due to smooth parts of the flow, leading in particular to an exponential growth of the average distance between particles. We demonstrate how caustics restrict applicability of Lagrangian description to inertial particles.

Experimental investigation of the travel-time variance of an acoustic wave propagating through the grid-generated turbulence

An experimental technique for the investigation of the behaviour of acoustic wave propagation through a turbulent medium is discussed. The present study utilizes the ultrasonic travel-time technique to diagnose a grid-generated turbulence. Travel-time variance is studied versus mean flow velocity, travel distance and outer turbulence scale. The effect of thermal fluctuations, which result in fluctuations of sound speed, is studied using a heated-grid experiment. Experimental data obtained using ultrasonic technique confirm numerical and theoretical predictions of nonlinear increase of the travel-time variance with propagation distance, which could be connected to the occurrence of caustics. The effect of turbulent intensity on the travel-time variance and appearance of caustics is studied. It is demonstrated experimentally that the higher turbulence intensity leads to the shorter distance, at which the first caustic occurs. The probability density for caustics appearance is analysed against the measured wave amplitude fluctuations. The analysis reveals that the region of high-amplitude fluctuations corresponds to the region where the probability of formation of random caustics differs from zero. Experimental results are in very good agreement with theoretical and numerical predictions.

Universality in the Distribution of Caustics in the Expanding Universe

We numerically investigate the long--time evolution of density perturbations after the first appearance of caustics in an expanding cosmological model with one--dimensional `single--wave' initial conditions. Focussing on the time--intervals of caustic appearances and the spatial distribution of caustics at subsequent times, we find that the time--intervals of caustic appearances approach a constant, i.e., their time--subsequent ratio converges to 1; it is also found that the spatial distribution of caustics at a given time features some universality rules, e.g., the ratio between the position of the nearest caustic from the center and that of the second nearest caustic from the center approaches a constant. Furthermore we find some rules for the mass distribution for each caustic. Using these universality constants we are in the position to predict the spatial distribution of caustics at an arbitrary time in order to give an estimate for the power spectral index in the fully--developed non--dissipative turbulent (`virialized') regime.

Microlensing by a noncompact spheroidal gravitational lens

In the process of their evolution, small-scale clusters of weakly interacting massive particles (WIMPs) that formed in the early Universe can acquire rotational momentum and spheroidal shape. Even small oblateness of a cluster similar to that of the critical Roche surface can lead to the appearance of caustics in the plane of a source lensed by the object. The multiple source images that form in this case cannot be resolved in modern observations, and the cluster behaves like a noncompact spheroidal lens. The caustic crossing that occurs in the case of relative motion of the observer, the cluster of particles, and the lensed star can produce a large variety of flux curves, including those such as have been observed during microlensing events and interpreted as manifestations of binary gravitational lenses. Therefore, we cannot rule out the possibility that at least some of these events might actually be associated with clusters of WIMPs.

Evolution of the Power Spectrum and Self‐Similarity in the Expanding One‐dimensional Universe

We have investigated time evolutions of power spectra of density fluctuations for a long time after the first appearance of caustics in the expanding one-dimensional universe. It is found that when an initial power spectrum is scale-free with a power index n, self-similarity of the time evolution of the power spectrum is achieved. We find that the power spectrum can be separated roughly into three regimes according to the shape of the power spectrum: the linear regime (k ksnl: regime 3). The power index of the power spectrum in each regime has values of n, -1, and μ, respectively, which depend on n. Even in the case of an initial power-law spectrum with a cutoff scale, there might be the possibility of self-similar evolution of the power spectrum after the appearance of the caustics. It is found, however, that self-similarity is not achieved in this case. The shape of the power spectrum on scales smaller than the cutoff scale can be separated roughly into two regimes: the virialized regime (kcut kcs: regime 5). The power index of the power spectrum is ν, which may be determined by the distribution of singular points in regime 4. In regime 5, the value of the power index is -1. Moreover, we show the general property of the shape of a power spectrum with a general initial condition.

Nonlinear Growth of Two-dimensional Cosmological Density Fluctuations and Type of Singularity in Accord with the Catastrophe Theory

view Abstract Citations (3) References (21) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Nonlinear Growth of Two-dimensional Cosmological Density Fluctuations and Type of Singularity in Accord with the Catastrophe Theory Gouda, Naoteru Abstract Nonlinear growth of cosmological density fluctuations from the initial small fluctuations with a non- scale-free or scale-free power spectrum is analyzed in the two-dimensional system by the N-body simulations. It is found that after the first appearance of singularities of density (caustics), the power spectrum of the density fields obeys the power law even on small scales below the cutoff scale of the initial power spectrum. The value of the power index on these scales is almost -2 irrespective of the detailed initial conditions in the case that the initial power index n of the power spectrum on large scales is small and/or the cutoff scale is large. In these cases, the filament structures of the particle distribution (the "filament" shape of caustics of particle trajectories) clearly appear everywhere. It is shown that the power index on the small scales below the typical size of the thickness of filaments is determined only by the type of the singularity (caustics) irrespective of the detailed initial conditions. The type of the singularity is classified in accord with the catastrophe theory. In the above case, singularities of A2 type stably appear isotropically everywhere after the first appearance of caustics, and this is the reason why the value of the power index is almost -2. Publication: The Astrophysical Journal Pub Date: October 1996 DOI: 10.1086/177795 Bibcode: 1996ApJ...469..455G Keywords: COSMOLOGY: THEORY; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE full text sources ADS |

On the appearance of caustics for plane sound-wave propagation in moving random media

Abstract In this paper we derive expressions for the probability densities of the appearance of the first caustic for a plane sound wave propagating in moving random media. Our approach generalizes the previous work by White et al. and Klyatskin in the case of motionless media. It allows us to calculate analytically the probability density functions for two- and three-dimensional media and to express these functions in terms of the diffusion coefficient. Explicit equations are given for Gaussian and von Karman spectra of velocity fluctuations. If the random scalar or vectorial fluctuations of the medium have the same contribution to the refractive-index fluctuations, we demonstrate that in a moving medium caustics appear at shorter distances than in a non-moving one. The two-dimensional version of the theory is tested by numerical simulations in the case of velocity fluctuations with Gaussian spectra. Numerical results are in very good agreement with the theoretical predictions.