Influence of Nonlinear Terms on Orbital Stability of Solitary Wave Solutions to the Generalized Symmetric Regularized-Long-Wave Equation

The influence of two nonlinear terms on the orbital stability of solitary wave solutions to the generalized symmetric regularized-long-wave(gsrlw) equation is investigated in this paper. Based on the general conclusion to judge the orbit stability of solitary wave solution to the equation, the stable and unstable wave velocity intervals of solitary wave solutions to the gsrlw equation with two low order nonlinear terms are given. By appropriate transformation and scaling, the complexity caused by two high-order nonlinear terms is overcome, and the stable and unstable wave velocity intervals of solitary wave solutions to the gsrlw equation with high-order nonlinear terms are also obtained. Last, the influences of the coefficients and the order of the nonlinear terms on the stability of solitary wave solutions are studied.

Effects of Cowl-Induced Expansion on the Wave Complex Induced by Oblique Detonation Wave Reflection

Oblique detonation wave (ODW) reflection on the upper wall leads to a sophisticated wave complex, whose stability is critical to the application of oblique detonation engines. The unstable wave complex characterized with a continuous moving Mach stem has been observed, but the corresponding re-stability adjusting method is still unclear so far. In this study, the cowl-induced expansion wave based on the model with an upper-side expansion wall is introduced, and the ODW dynamics have been analyzed using the reactive Euler equations with a two-step induction–reaction kinetic model. With the addition of a cowl-induced expansion wave, the re-stabilized Mach stem has been distinguished. This re-stability is determined by the weakened secondary reflection wave of lower wall, while the final location of Mach stem is not sensitive to the position of the expansion corner. The re-stabilized ODW structure is also basically irrelevant to the expansion angle, while it may shift to unstable due to the merging of subsonic zones. Transient phenomena for the unstable state have been also discussed, clarifying fine wave structures further.

Centrifugal Waves in Tornado-like Vortices: Kelvin’s solutions and their Applications to Multiple-Vortex Development and Vortex Breakdown

About 140 years ago, Lord Kelvin derived the equations describing waves that travel along the axis of concentrated vortices such as tornadoes. Although Kelvin’s vortex waves, also known as centrifugal waves, feature prominently in the engineering and uid dynamics literature, they have not attracted as much attention in the field of atmospheric science. To remedy this circumstance, Kelvin’s elegant derivation is retraced, and slightly generalized, to obtain solutions for a hierarchy of vortex ows that model basic features of tornado-like vortices. This treatment seeks to draw attention to the important work that Lord Kelvin did in this field, and reveal the remarkably rich structure and dynamics of these waves. Kelvin’s solutions help explain the vortex breakdown phenomenon routinely observed in modeled tornado-like vortices, and it is shown that his work is compatible with the widely used criticality condition put forth by Benjamin in 1962. Moreover, it is demonstrated that Kelvin’s treatment, with the slight generalization, includes unstable wave solutions that have been invoked to explain some aspects of the formation of multiple-vortex tornadoes. The analysis of the unstable solutions also forms the basis for determining whether e.g., an axisymmetric or a spiral vortex breakdown occurs. Kelvin’s work thus helps understand some of the visible features of tornado-like vortices.

General dispersion properties of magnetized plasmas with drifting bi-Kappa distributions. DIS-K: Dispersion Solver for Kappa Plasmas

Space plasmas are known to be out of (local) thermodynamic equilibrium, as observations show direct or indirect evidences of non-thermal velocity distributions of plasma particles. Prominent are the anisotropies relative to the magnetic field, anisotropic temperatures, field-aligned beams or drifting populations, but also, the suprathermal populations enhancing the high-energy tails of the observed distributions. Drifting bi-Kappa distribution functions can provide a good representation of these features and enable for a kinetic fundamental description of the dispersion and stability of these collision-poor plasmas, where particle–particle collisions are rare but wave–particle interactions appear to play a dominant role in the dynamics. In the present paper we derive the full set of components of the dispersion tensor for magnetized plasma populations modelled by drifting bi-Kappa distributions. A new solver called DIS-K (DIspersion Solver for Kappa plasmas) is proposed to solve numerically the dispersion relations of high complexity. The solver is validated by comparing with the damped and unstable wave solutions obtained with other codes, operating in the limits of drifting Maxwellian and non-drifting Kappa models. These new theoretical tools enable more realistic characterizations, both analytical and numerical, of wave fluctuations and instabilities in complex kinetic configurations measured in-situ in space plasmas.

Direct measurements of cold and hot plasma composition and EMIC waves in the outer magnetosphere: Implications for inner magnetosphere wave-particle interactions

<p>Although thorough characterization of magnetospheric ion composition is rare for EMIC wave studies, convective processes that occur more frequently in Earth’s outer magnetosphere have allowed the Magnetospheric Multiscale (MMS) satellites to make direct measurements of the cold and hot plasma composition during EMIC wave activity. We will present an observation and linear wave modeling case study conducted on EMIC waves observed during a perturbed activity period in the outer dusk-side magnetosphere. During the two intervals investigated for the case study, the MMS satellites made direct measurements of cold plasmaspheric plasma in addition to multiple hot ion components at the same time as EMIC wave emissions were observed. Applying the in-situ plasma composition data to wave modeling, we find that wave growth rate is impacted by the complex interactions between the cold as well as the hot ion components and ambient plasma conditions. In addition, we observe that linear wave properties (unstable wave numbers and band structure) can significantly evolve with changes in cold and hot ion composition. Although the modeling showed the presence of dense cold ions can broaden the range of unstable wave numbers, consistent with previous work, the hot heavy ions that were more abundant nearer storm main phase could limit the growth of EMIC waves to smaller wave numbers. In the inner magnetosphere, where higher cold ion density is expected, the ring current heavy ions could also be more intense near storm-time, possibly resulting in conditions that limit the interactions of EMIC waves with trapped radiation belt electrons to multi-MeV energies. Additional investigation when direct measurements of cold and hot plasma composition are available could improve understanding of EMIC waves and their interactions with trapped energetic particles in the inner magnetosphere.</p>

CONSTRUCTION OF LOW-RISE BUILDINGS IN THE COASTLAND AND WATER AREAS

Introduction: Artificial islands for new construction and works in a dry environment are created in water areas by installing enclosures, which allow buildings to remain rigid and stable and withstand the influence of climatic factors. Purpose of the study: We aim to develop a method for the construction of low-rise buildings in the coastland and water areas with the least labor effort required to erect buildings and ensure their safe operation. Methods: In the course of the research, we have performed theoretical studies in the field of experimental construction and analyzed the results of Russian and foreign scientific research related to the construction of buildings in water areas. Results: We have examined methods for the construction of waterproof enclosures in water areas that make it possible to erect buildings in a dry environment in open water areas with unstable wave conditions. Such methods reduce labor efforts, decrease the term of construction, and improve performance indicators.

CONSTRUCTION OF LOW-RISE BUILDINGS IN THE COASTLAND AND WATER AREAS

Introduction: Artificial islands for new construction and works in a dry environment are created in water areas by installing enclosures, which allow buildings to remain rigid and stable and withstand the influence of climatic factors. Purpose of the study: We aim to develop a method for the construction of low-rise buildings in the coastland and water areas with the least labor effort required to erect buildings and ensure their safe operation. Methods: In the course of the research, we have performed theoretical studies in the field of experimental construction and analyzed the results of Russian and foreign scientific research related to the construction of buildings in water areas. Results: We have examined methods for the construction of waterproof enclosures in water areas that make it possible to erect buildings in a dry environment in open water areas with unstable wave conditions. Such methods reduce labor efforts, decrease the term of construction, and improve performance indicators.

EVOLUTION OF UNSTABLE WAVE PACKETS OVER VARIABLE BATHYMETRY

Several field observations have reported the formation of rogue waves in coastal zones, see Chien et al. (2002) for an example in Taiwanese sea. The mechanisms that lead to the occurrence of rogue waves in finite water depth to shallow water are not well understood yet under the conjecture of modulation instability. Indeed, this theory for uni-directional waves shows that when kh is lower than a threshold of 1.363 in homogeneous water depth conditions, the wave train becomes stable to side-band perturbations. Then if the wave train is stable, the appearance of rogue waves is not possible within this linear stability framework. One explanation may come from the complex wave transformation mechanisms in variable bathymetry, especially, for cases of steep slopes or near the edge between a steep slope and a gentle slope as it is the case of the continental shelf. Very few laboratory experiments have been so far addressing the influence of the bathymetry on extreme wave occurrence (Baldock and Swan (1996), Kashima et al. (2012), Ma et al. (2015)).Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/a5M4PS-Lo4Q