ABOUT CONICAL CUMULATION IN STORAGE AMPOULES

Conical cumulation in storage ampoules consists of a periodically repeating wave pattern - the formation of an axial high-pressure region as a result of the focusing of oblique waves and its unloading. In this case, the convergence of the oblique wave is accompanied by a loss of stability - protrusions appear at the wave front, the collision of which leads to an increase in pressure. The expansion of the high-pressure region is accompanied by the formation of an axial crack and continues until its pressure becomes lower than the pressure of the incoming oblique waves, after which the flow pattern is repeated.

Step Approximation for Water Wave Scattering by Multiple Thin Barriers over Undulated Bottoms

This paper investigates the scattering of oblique water waves by multiple thin barriers over undulation bottoms using the eigenfunction matching method (EMM). In the solution procedures of the EMM, the bottom topographies are sliced into shelves separated by steps. On each step, surface-piercing or/and bottom-standing barriers can be presented or not. For each shelf, the solution is composed of eigenfunctions with unknown coefficients representing the wave amplitudes. Then applying the conservations of mass and momentum, a system of linear equations is resulted and can be solved by a sparse-matrix solver. If no barriers are presented on the steps, the proposed EMM formulation degenerates to the water wave scattering over undulating bottoms. The effects on the barrier lengths, barrier positions and oblique wave incidences by different undulated bottoms are studied. In addition, the EMM is also applied to solve the Bragg reflections of normal and oblique water waves by periodic barrier over sinusoidal bottoms. The accuracy of the solution is demonstrated by comparing it with the results in the literature.

New and more fractional soliton solutions related to generalized Davey–Stewartson equation using oblique wave transformation

The generalized fractional Davey–Stewartson (DSS) equation with fractional temporal derivative, which is used to explore the trends of wave propagation in water of finite depth under the effects of gravity force and surface tension, is considered in this paper. The paper addresses the full nonlinearity of the proposed model. To extract the oblique soliton solutions of the generalized fractional DSS (FDSS) equation is the dominant feature of this research. The conformable fractional derivative is used for fractional temporal derivative and oblique wave transformation is used for converting the proposed model into ordinary differential equation. Two state-of-the-art integration schemes, modified auxiliary equation (MAE) and generalized projective Riccati equations (GPREs) method have been employed for obtaining the desired oblique soliton solutions. The proposed methods successfully attain different structures of explicit solutions such as bright, dark, singular, and periodic solitary wave solutions. The occurrence of these results ensured by the limitations utilized is also exceptionally promising to additionally investigate the propagation of waves of finite depth. The latest found solutions with their existence criteria are considered. The 2D and 3D portraits are also shown for some of the reported solutions. From the graphical representations, it have been illustrated that the descriptions of waves are changed along with the change in fractional and obliqueness parameters.