Dispersion relation

About: Dispersion relation is a research topic. Over the lifetime, 21482 publications have been published within this topic receiving 383295 citations.

A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution

Abstract: A broad class of astronomical accretion disks is presently shown to be dynamically unstable to axisymmetric disturbances in the presence of a weak magnetic field, an insight with consequently broad applicability to gaseous, differentially-rotating systems. In the first part of this work, a linear analysis is presented of the instability, which is local and extremely powerful; the maximum growth rate, which is of the order of the angular rotation velocity, is independent of the strength of the magnetic field. Fluid motions associated with the instability directly generate both poloidal and toroidal field components. In the second part of this investigation, the scaling relation between the instability's wavenumber and the Alfven velocity is demonstrated, and the independence of the maximum growth rate from magnetic field strength is confirmed.

P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method

Abstract: I present a finite-difference method for modeling P-SV wave propagation in heterogeneous media This is an extension of the method I previously proposed for modeling SH-wave propagation by using velocity and stress in a discrete grid The two components of the velocity cannot be defined at the same node for a complete staggered grid: the stability condition and the P-wave phase velocity dispersion curve do not depend on the Poisson's ratio, while the S-wave phase velocity dispersion curve behavior is rather insensitive to the Poisson's ratio Therefore, the same code used for elastic media can be used for liquid media, where S-wave velocity goes to zero, and no special treatment is needed for a liquid-solid interface Typical physical phenomena arising with P-SV modeling, such as surface waves, are in agreement with analytical results The weathered-layer and corner-edge models show in seismograms the same converted phases obtained by previous authors This method gives stable results for step discontinuities, as shown for a liquid layer above an elastic half-space The head wave preserves the correct amplitude Finally, the corner-edge model illustrates a more complex geometry for the liquid-solid interface As the Poisson's ratio v increases from 025 to 05, the shear converted phases are removed from seismograms and from the time section of the wave field

Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability

Abstract: The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.

Convectively Coupled Equatorial Waves: Analysis of Clouds and Temperature in the Wavenumber–Frequency Domain

Abstract: A wavenumber-frequency spectrum analysis is performed for all longitudes in the domain 158S‐158N using a long (;18 years) twice-daily record of satellite-observed outgoing longwave radiation (OLR), a good proxy for deep tropical convection. The broad nature of the spectrum is red in both zonal wavenumber and frequency. By removing an estimated background spectrum, numerous statistically significant spectral peaks are isolated. Some of the peaks correspond quite well to the dispersion relations of the equatorially trapped wave modes of shallow water theory with implied equivalent depths in the range of 12‐50 m. Cross-spectrum analysis with the satellite-based microwave sounding unit deep-layer temperature data shows that these spectral peaks in the OLR are ‘‘coupled’’ with this dynamical field. The equivalent depths of the convectively coupled waves are shallower than those typical of equatorial waves uncoupled with convection. Such a small equivalent depth is thought to be a result of the interaction between convection and the dynamics. The convectively coupled equatorial waves identified correspond to the Kelvin, n 5 1 equatorial Rossby, mixed Rossby-gravity, n 5 0 eastward inertiogravity, n 5 1 westward inertio-gravity (WIG), and n 5 2 WIG waves. Additionally, the Madden‐Julian oscillation and tropical depression-type disturbances are present in the OLR spectra. These latter two features are unlike the convectively coupled equatorial waves due to their location away from the equatorial wave dispersion curves in the wavenumber-frequency domain. Extraction of the different convectively coupled disturbances in the time‐longitude domain is performed by filtering the OLR dataset for very specific zonal wavenumbers and frequencies. The geographical distribution of the variance of these filtered data gives further evidence that some of the spectral peaks correspond to particular equatorial wave modes. The results have implications for the cumulus parameterization problem, for the excitation of equatorial waves in the lower stratosphere, and for extended-range forecasting in the Tropics.