A realistic problem of an EXPLOSION-GENERATED relativistic plasma is talked about with respect to the instabilities developed in such systems. For this, the dispersion equation is derived analytically and solved numerically for typical values of physical quantities. Our calculations reveal that two types of instabilities occur in the said plasma if the dust particles and relativistic effects of ions and electrons are considered. Both types of the instabilities are high-frequency instabilities, which carry growth rates of different magnitudes. In view of the magnitudes, the instability having higher/lower growth rate is called as high-frequency higher/lower growth rate instability. The relativistic effects of ions support the growth of these instabilities, whereas those of electrons suppress the growth of the instabilities. The WAVES propagating with larger phase velocity are found to grow at higher rates. There exists a critical value of the drift velocity of dust particles, above which another instability starts growing but with significantly lower growth rate.

The current manuscript presents the validation of Smoothed Particle Hydrodynamics (SPH) techniques for wave generation by underWATER EXPLOSION, utilizing the so-called Duals Physics numerical model. This numerical method is used to analyze GENERATED WAVES which are initiated by man-made or natural EXPLOSIONs below free surface level of sea. In spite of the modeling limitations (e.g. absence of open boundary conditions), reasonable agreement is accomplished with predictions of the existing formula as well as experimental results. This proved that SPH techniques such as incorporated in Duals Physics are becoming a suitable alternative to existing classical approaches to this particular WATER WAVES problem. It is also provided an inherently more accurate computational for the prediction of wave characteristics GENERATED by underWATER EXPLOSIONs.

When gravitational mass flows hit WATER bodies, they create WATER WAVES, called tsunami. The slopes of the mountain flanks surrounding a glacial lake or the slopes of the side walls of artificially constructed reservoirs play important roles in the intensity of splash on landslide impact, amplitudes and propagation speeds of the resulting WATER WAVES and possible dam breaching or overspilling of WATER. The proper analyses of such dynamics are useful for the possible mitigation measures. Here, we apply a general two-phase mass flow model to perform several numerical experiments and present geometrically three-dimensional, high-resolution simulation results for rapidly moving two-phase landslide/debris flow down a plane with varying slopes at its different parts, impacting a fluid reservoir. First, the upstream slope is kept constant, later to make it closer to reality, sudden changes in slopes are imposed one after another at different parts of the topography. The results focus on the effects of the sudden slope changes in the formation and propagation of dynamically different solid-and fluid wave-structures in the reservoir. Results show that steeper upper part of the topography produces more highly intensified tsunami that propagates more longitudinally than the steeper lower part. Thus, steeper upper parts need stronger right coast and steeper lower parts demand stronger side walls in mountain reservoirs to withstand the wave impacts. The results may help for the proper modeling of landslide and debris induced mountain tsunamis in rapidly changing slopes, the dynamics of turbidity currents and sediment transports in fluid reservoirs in high mountain slopes.

An EXPLOSION-GENERATED-plasma is explored for low and high frequency instabilities by taking into account the drift of all the plasma species together with the dust particles which are charged. The possibility of wave triplet is also discussed based on the solution of dispersion equation and synchronism conditions. High frequency instability (HFI) and low frequency instability (LFI) are found to occur in this system. LFI grows faster with the higher concentration of dust particles, whereas its growth rate goes down if the mass of the dust is higher. The ion and electron temperatures affect its growth in opposite manner and the electron temperature causes this instability to grow. In addition to the instabilities, a simple wave is also observed to propagate, whose velocity is larger for larger wave number, smaller mass of the dust and higher ion temperature.

The current paper discusses the physical impacts of the various initial boundary conditions of the free surface of a WATERbody on the initiation and propagation characteristics of WATER WAVES due to the underWATER perturbations. Differences between traditional point of view and applied numerical method in this paper for exertion the initial conditions of the GENERATED WAVES by surface deformation were surveyed in the Lagrangian domain vs. Eulerian. In this article, the smoothed-particle hydrodynamics (SPH) technique was applied for simulating of wave generation process using initial boundary condition of WATER surface deformation through utilizing DualSPHysics numerical code and comparing the modeling results with recorded data. As a distinct approach, we studied the effects of discrete WATER particles on properties of produced surface WAVES by using the Lagrangian analytical capability of SPH model. Illustrative compatibility on simulation results with experimental data proves that meshless techniques such as applied in DualSPHysics software can reproduce physical properties of the event very well, and this is a suitable alternative to existing classical approaches for prediction of shock occurrences with nonlinear behavior such as GENERATED surface WATER WAVES by underWATER disturbance. Besides, the waveforms and their characteristics behave more realistic by considering the thrown upward WATER mass which was not directly considered in old formula and theories. The results of numerical modeling indicated rational agreement between numerical and empirical data proving that a complicated nonlinear phenomenon could be predicted by an SPH model which modified initial boundary conditions were supposed into the model with actual assumptions.

This work regards the extension of the Miles’ and Jeffreys’ theories of growth of wind-WAVES in WATER of finite depth. It is divided in two major sections. The first one corresponds to the surface WATER WAVES in a linear regimes and the second one to the surface WATER waver considered in a weak nonlinear, dispersive and antidissipative regime. In the linear regime, we extend the Miles’ theory of wind wave amplification to finite depth. The dispersion relation provides a wave growth rate depending to depth. A dimensionless WATER depth parameter depending to depth and a characteristic wind speed, induces a family of curves representing the wave growth as a function of the wave phase velocity and the wind speed. We obtain a good agreement between our theoretical results and the data from the Australian Shallow WATER Experiment as well as the data from the Lake George experiment. In a weakly nonlinear regime the evolution of wind WAVES in finite depth is reduced to an anti-dissipative Kortewegde Vries-Burgers equation and its solitary wave solution is exhibited. Anti-dissipation phenomenon accelerates the solitary wave and increases its amplitude which leads to its blow-up and breaking. Blow-up is a nonlinear, dispersive and anti-dissipative phenomenon which occurs in finite time. A consequence of anti-dissipation is that any solitary WAVES’ adjacent planes of constants phases acquire different velocities and accelerations and ends to breaking which occurs in finite space and in a finite time prior to the blow-up. It worth remarking that the theoretical amplitude growth breaking time are both testable in the usual experimental facilities. At the end, in the context of wind forced WAVES in finite depth, the nonlinear Schrö dinger equation is derived and for weak wind inputs, the Akhmediev, Peregrine and Kuznetsov-Ma breather solutions are obtained.