Choice Of Wavenumber Research Articles

Modeling ocean eddies using exact solutions of the Charney–Obukhov equation

New exact solutions of the Charney–Obukhov equation for the ocean are obtained in the form of a partial superposition of elementary solutions with different wave numbers. The boundary conditions for the ocean are satisfied due to the presence of a carrier zonal flow in the solution. The existing arbitrariness in the choice of wave numbers and other solution parameters makes it possible to simulate an arbitrary stream function profile at a fixed ocean depth on an interval of a fixed length using a Fourier series or in a circle of a fixed radius using a Fourier–Bessel series. An example of modeling a Gaussian stream function profile on the ocean surface in the presence of circular symmetry is considered.

Bright soliton propagation with loss and gain phenomena in transversely connected nonlinear pendulum pairs

In this work, we seek to investigate the dynamics of bright soliton in a chain of coupled pendulum pairs. After deriving the linear dispersion relation from the equation of the model, we find that among the obtained modes, the fast mode is the one on which we are going to be focused. Since the discrete simultaneous equation describing the dynamics of the model has not been extensively studied in the literature, we assume that the two lines of the model are proportional to each other. We use the rotating wave approximation method to derive a NLS equation governing the propagation of waves in the network. Depending on the choice of wave number, we deduce that the system supports bright and hole-soliton solutions. We use the obtained bright soliton as the initial condition for numerical computation, which demonstrates the significant role of the transverse coupling parameter in the system. That is, it affects the behavior of the forward-bright soliton generated in the system. The lattice allows gain and loss phenomena during the propagation of the waves.

Zero Flux Eigenvalues (ZFE’s) of Tight Aspect Ratio Tokamaks

Compact toroidal magnetized plasmas are an important part of the world’s magnetic fusion and plasma science efforts. These devices can play an integral role in the development of magnetic fusion as a viable commercial energy source, and in our understanding of plasma instabilities, particle and energy transport, and magnetic field transport. In this paper, we are developing a numerical program to study the magnetic dynamo or relaxation of CT’s characterized by arbitrary tight aspect ratio (major to minor radii of tokamak) and arbitrary cross-sections (Multi-pinch and D-Shaped). The lowest ZFE’s has been calculated through the Taylor’s relaxed state (force-free) toroidal plasmas equation. For ZFE’s, we use the toroidal flux vanishing boundary condition along the whole boundary of tokamaks. Several runs of the program for various wave numbers showed that ZFE was very insensitive to the choice of wave numbers. Besides, the CT’s poloidal magnetic field topologies are well represented. It was very interesting to check our methods for the cases when aspect ratio tends to unity (zero tokamak whole). A good fulfillment of the boundary condition is achieved.

Differences between downscaling with spectral and grid nudging using WRF

Abstract. Dynamical downscaling has been extensively used to study regional climate forced by large-scale global climate models. During the downscaling process, however, the simulation of regional climate models (RCMs) tends to drift away from the driving fields. Developing a solution that addresses this issue, by retaining the large scale features (from the large-scale fields) and the small-scale features (from the RCMs) has led to the development of "nudging" techniques. Here, we examine the performance of two nudging techniques, grid and spectral nudging, in the downscaling of NCEP/NCAR data with the Weather Research and Forecasting (WRF) Model. The simulations are compared against the results with North America Regional Reanalysis (NARR) data set at different scales of interest using the concept of similarity. We show that with the appropriate choice of wave numbers, spectral nudging outperforms grid nudging in the capacity of balancing the performance of simulation at the large and small scales.

Long-Wave Instabilities in a Non-Newtonian Film on a Nonuniformly Heated Inclined Plane

A thin liquid layer of a non-Newtonian film falling down an inclined plane that is subjected to nonuniform heating has been considered. The temperature of the inclined plane is assumed to be linearly distributed and the case when the temperature gradient is positive or negative is investigated. The film flow is influenced by gravity, mean surface tension, and thermocapillary forces acting along the free surface. The coupling of thermocapillary instability and surface-wave instabilities is studied for two-dimensional disturbances. A nonlinear evolution equation is derived by applying the long-wave theory, and the equation governs the evolution of a power-law film flowing down a nonuniformly heated inclined plane. The linear stability analysis shows that the film flow system is stable when the plate temperature decreases in the downstream direction while it is less stable for increasing temperature along the plate. Weakly nonlinear stability analysis using the method of multiple scales has been investigated and this leads to a secular equation of the Ginzburg–Landau type. The analysis shows that both supercritical stability and subcritical instability are possible for the film flow system. The results indicate the existence of finite-amplitude waves, and the threshold amplitude and nonlinear speed of these waves are influenced by thermocapillarity. The nonlinear evolution equation for the film thickness is solved numerically in a periodic domain in the supercritical stable region, and the results show that the shape of the wave is influenced by the choice of wave number, non-Newtonian rheology, and nonuniform heating.

Front propagation under periodic forcing in reaction-diffusion systems

One- and two-component bistable reaction-diffusion systems under external force are considered. The simplest case of a periodic forcing of cosine type is chosen. Exact analytical solutions for the traveling fronts are obtained for a piecewise linear approximation of the non-linear reaction term. Velocity equations are derived from the matching conditions. It is found that in the presence of forcing there exists a set of front solutions with different phases (matching point coordinates $\xi_0$ ) leading to velocity dependencies on the wavenumber that are either monotonic or oscillating. The general characteristic feature is that the nonmoving front becomes movable under forcing. However, for a specific choice of wavenumber and phase, there is a nonmoving front at any value of the forcing amplitude. When the forcing amplitude is large enough, the velocity bifurcates to form two counterpropagating fronts. The phase portraits of specific types of solutions are shown and briefly discussed.

On the choice of wavenumbers in viscoelastic seismic modelling with discrete wavenumber-frequency methods

Abstract Seismic wave propagation through an attenuating medium has a unique description in the linear viscoelastic model which, by the correspondence principle, is a direct extension of the elastic model. Horizontal wavenumbers are constant across a horizontal boundary, but the vertical wavenumbers are ambiguously defined when incidence is from a layer with relatively low velocity or strong attenuation. The direct choice of vertical wavenumber in a horizontally stratified model implies increasing amplitudes with depth and reflection coefficients which are qualitatively different from the corresponding elastic coefficients. This is unacceptable. It can be avoided by choosing a non-attenuating source layer for modelling near vertical reflections in low-loss media. However, when layers exhibit strong attenuation, the ‘conjugated viscoelastic model’ should be used instead. This has the advantages that we stay within the framework of the viscoelastic model, increasing amplitudes are avoided and the reflection coefficients are realistic smooth deviations from the corresponding elastic coefficients.

Resonance properties of two-dimensional wave disturbances in a boundary layer

The nonlinear development of disturbances of the traveling wave type in the boundary layer on a flat plate is examined. The investigation is restricted to two-dimensional disturbances periodic with respect to the longitudinal space coordinate and evolving in time. Attention is concentrated on the interactions of two waves of finite amplitude with multiple wave numbers. The problem is solved by numerically integrating the Navier-Stokes equations for an incompressible fluid. The pseudospectral method used in the calculations is an extension to the multidimensional case of a method previously developed by the authors [1, 2] in connection with the study of nonlinear wave processes in one-dimensional systems. Its use makes it possible to obtain reliable results even at very large amplitudes of the velocity perturbations (up to 20% of the free-stream velocity). The time dependence of the amplitudes of the disturbances and their phase velocities is determined. It is shown that for a fairly large amplitude of the harmonic and a particular choice of wave number and Reynolds number the interacting waves are synchronized. In this case the amplitude of the subharmonic grows strongly and quickly reaches a value comparable with that for the harmonic. As distinct from the resonance effects reported in [3, 4], which are typical only of the three-dimensional problem, the effect described is essentially two-dimensional.