Evolution of wide-spectrum unidirectional wave groups in a tank: an experimental and numerical study

Evolution of unidirectional nonlinear wave groups with wide spectra is studied experimentally and numerically. As an example of such an evolution, focusing of an initially wide wave train that is modulated both in amplitude and in frequency, to a single steep wave at a prescribed location along the laboratory wave tank is investigated. When numerous frequency harmonics arrive at the focusing location in phase, a very wave steep single emerges. The experimental study was carried out in two wave flumes that differ in size by an order of magnitude: a 330 m long Large Wave Channel in Hanover, and in 18 m long Tel-Aviv University wave tank. The spatial version of the Zakharov equation was applied in the numerical simulations. Detailed quantitative comparison is carried out between the experimental results and the numerical simulations. Spectra of the 2nd order bound waves are calculated using the theoretical model adopted. It is demonstrated that with the contribution of bound waves accounted for, a very good agreement between experiments and simulations is achieved.     

Structure of an oblique detonation wave induced by a wedge

The structure of an oblique detonation wave (ODW) induced by a wedge is investigated via numerical simulations and Rankine–Hugoniot analysis. The two-dimensional Euler equations coupled with a two-step chemical reaction model are solved. In the numerical results, four configurations of the Chapman–Jouguet (CJ) ODW reflection (overall Mach reflection, Mach reflection, regular reflection, and non-reflection) are observed to take place sequentially as the inflow Mach number increases. According to the numerical and analytical results, the change of the CJ ODW reflection configuration results from the interaction among the ODW, the CJ ODW, and the centered expansion wave.     

Application of a thermodynamically compatible two‐phase flow model to the high‐resolution simulations of compressible gas–magma flow

This paper reports on the application and development of a fully hyperbolic and fully conservative two‐phase flow model for the simulation of gas and magma flow within volcanic processes. The model solves a set of mixture conservation equations for the gas and magma two‐phase flow with velocity non‐equilibrium. In this model, the effect of the relative velocity is introduced by a kinetic constitutive equation with other equations for volume and mass fractions of the gas phase. The model is examined numerically by the widely used finite volume Godunov methods of centered‐type. Using the Riemann problem, we numerically simulate wave propagation and the development of shocks and rarefactions in volcanic eruptions. These simulations are of magma fragmentation type where the relative velocity continues to dominate. A series of test cases whose solution contains features relevant to gas–magma mixtures are conducted. In particular, numerical results indicate that the model implementation predicts key features of the relative velocity within volcanic processes without any mathematical or physical simplifications. Simulation results are sharply and accurately provided without any spurious oscillations in all of the flow variables. The numerical methods and results are also compared with other numerical methods available in the literature. It is found that the provided resolutions are more accurate for the considered test cases. Copyright © 2014 John Wiley & Sons, Ltd.     

Axi-symmetric wave propagation in a cylinder coated with a piezoelectric layer

This paper presents the wave propagation in a cylinder coated with a thin piezoelectric layer. The piezoelectric coupling effects are fully modeled in the mechanics model for this piezoelectric coupled cylindrical shell with bending resistance. The decoupled torsional wave velocity and the dispersion curves for the two- mode shell model are obtained theoretically. The cut-off frequency and phase velocities at limit wave number are also derived. The numerical simulations are conducted to present the results of wave propagation in this cylindrical shell and as well as to compare the results by the current bending theory and the membrane shell theory. From the comparisons, the results display obvious deference of wave propagations in terms of dispersion characteristics by different shell theories when thicker piezoelectric layer are used and when higher wave number is considered. The results of this paper can serve as a reference for future study on wave propagation in coupled structures as well as in the design of smart structures incorporating piezoelectric materials.     

The numerical simulations of explosion and implosion in air: use of a modified Harten's TVD scheme

Numerical simulations of explosion and implosion in air are carried out with a modified Harten's TVD scheme. The new scheme has a high resolution for contact discontinuities in addition to maintaining the good features of Harten's TVD scheme. In the numerical experiment of spherical explosion in air, the second shock wave (which does not exist in the one‐dimensional shock tube problem) and its subsequent implosion on the origin have been successfully captured. The positions of the main shock wave, the contact discontinuity and the second shock wave have shown satisfactory agreement with those predicted from previous analysis. The numerical results are also compared with those obtained experimentally. Finally, simulations of a cylindrical explosion and implosion in air are carried out. Results of the cylindrical implosion in air are compared with those of previous work, including the interaction of the reflected main shock wave with the contact discontinuity and the formation of a second shock wave. All these attest to the successful use of the modified Harten's TVD scheme for the simulations of shock waves arising from explosion and implosion. Copyright © 1999 John Wiley & Sons, Ltd.     

On one model of cyclic ejections of magma in the process of the explosive volcanic eruption

The dynamics of the structure of a cavitating magma flow behind the decompression wave front is experimentally studied by the method of hydrodynamic shock tubes. It is demonstrated that a discrete system of intensely cavitating zones with alternation of low and high densities of the gas phase can be formed at a certain regime of shock-wave loading of the examined fluid sample. Based on the results of a numerical analysis of the formation of an anomalous zone in the cavitating magma flow with anomalously high flow characteristics exceeding the values of these characteristics outside this zone at least by an order of magnitude, a model of an instantaneous transformation of the cavitating magma in the anomalous zone to a gas-droplet system, its ejections, and formation of a free surface on the interface is proposed. A numerical analysis shows that the characteristic wave structure and the anomalous saturation zone are fairly rapidly reconstructed in the vicinity of this free surface of the flow part remaining in the conduit after the ejections, and the above-mentioned jumps of flow characteristics are again formed in the anomalous zone.     

Phase transition and dynamics of iron under ramp wave compression

The ramp wave compression experiments of iron with different thicknesses were performed on the magnetically driven ramp loading device CQ-4. Numerical simulations of this process were done with Hayes multi-phase equation of state (H-MEOS) and dynamic equations of phase transition. The calculated results of H-MEOS are in good agreement with those of shock phase transition, but are different from those under ramp wave compression. The reason for this is that the bulk modulus of the material in the Hayes model and the wave velocity are considered constant. Shock compression is a jump from the initial state to the final state, and the sound speed is related to the slope of the Rayleigh line. However, ramp compression is a continuous process, and the bulk modulus is no longer a constant but a function of pressure and temperature. Based on Murnaghan equation of state, the first-order correction of the bulk modulus on pressure in the Hayes model was carried out. The numerical results of the corrected H-MEOS agree well with those of pure iron in both ramp and shock compression phase transition experiments. The calculated results show that the relaxation time of iron is about 30 ns and the phase transition pressure is about 13 GPa. There are obvious differences between the isentropic and adiabatic process in terms of pressure–specific volume and temperature–pressure. The fluctuation of the sound speed after 13 GPa is caused by the phase transition.     

Opening of a system of cracks—on the mechanism of the cyclic lateral eruption of the St. Helens volcano in 1980

The dynamic behavior of a magma melt filling a slot channel (crack) in a closed explosive hydrodynamic structure is considered. The explosive hydrodynamic structure includes the volcano focal point with a connected vertical channel (conduit) closed by a slug and a system of internal cracks (dikes) near the dome, as well as a crater open into the atmosphere. A two-dimensional model of a slot eruption is constructed with the use of the Iordanskii–Kogarko–van Wijngaarden mathematical model of two-phase media and the kinetics that describes the basic physical processes in a heavy magma saturated by the gas behind the decompression wave front. A numerical scheme is developed for analyzing the influence of the boundary conditions on the conduit walls and scale factors on the melt flow structure, the role of viscosity in static modes, and dynamic formulations with allowance for diffusion processes and increasing (by several orders of magnitude) viscosity. Results of the numerical analysis of the initial stage of cavitation process evolution are discussed.     

Soliton elastic interactions and dynamical analysis of a reduced integrable nonlinear Schrödinger system on a triangular-lattice ribbon

Under investigation in this paper is a discrete reduced integrable nonlinear Schrödinger system on a triangular-lattice ribbon, which may have some prospective applications in modern nanoribbon. First, we construct the infinitely many conservation laws and discrete N-fold Darboux transformation for this system based on its known Lax pair. Then bright–bright multi-soliton and breather solutions in terms of determinants are obtained by means of the resulting Darboux transformation. Moreover, we investigate soliton interactions through asymptotic analysis and analyze some important physical quantities such as amplitudes, wave numbers, wave widths, velocities, energies and initial phases. Finally, the dynamical evolution behaviors are discussed via numerical simulations. It is found that soliton interactions in this system are elastic, and their evolutions are stable against a small noise in a short period of time. Results obtained in this paper may have some prospective applications for understanding some physical phenomena.

     

A numerical model for aerated‐water wave breaking

This work presents a numerical model designed for the simulation of water‐wave impacts on a structure when aeration of the liquid phase is considered. The model is based on a multifluid Navier–Stokes approach in which all fluids are assumed compressible. The numerical method is based on a finite volume algorithm in space and a second order Runge–Kutta method in time. A validation of this model is performed. It shows a good accuracy for acoustic and shock wave propagation in a bubbly liquid and for wave breaking. Copyright © 2011 John Wiley & Sons, Ltd.     

On the role of the smallest scales of a passive scalar field in a near-wall turbulent flow

Role of the smallest diffusive scales of a passive scalar field in the near-wall turbulent flow was examined with pseudo-spectral numerical simulations. Temperature fields were analyzed at friction Reynolds number Re _τ=171 and at Prandtl numbers, Pr=1 and Pr=5.4. Results of direct numerical simulations (DNS) were compared with the under-resolved simulations where the velocity field was still resolved with the DNS accuracy, while a coarser grid was used to describe the temperature fields. Since the smallest temperature scales remained unresolved in these simulations, an appropriate spectral turbulent thermal diffusivity was applied to avoid pile-up at the higher wave numbers. In spite of coarser numerical grids, the temperature fields are still highly correlated with the DNS results, including instantaneous temperature fields. Results point to practically negligible role of the diffusive temperature scales on the macroscopic behavior of the turbulent heat transfer.     

Multi‐scale simulation with a hybrid Boussinesq‐RANS hydrodynamic model

A hybrid wave model is developed for simulation of water wave propagation from deep water to shoreline. The constituent wave models are the irrotational, 1‐D horizontal Boussinesq and 2‐D vertical Reynolds‐averaged Navier–Stokes (RANS). The models are two‐way coupled, and the interface is placed at a location where turbulence is relatively small. Boundary conditions on the interfacing side of each model are provided by its counterpart model through data exchange. Prior to the exchange, a data transformation step is carried out due to the differences in physical variables and approximations employed in both models. The hybrid model is tested for both accuracy and speedup performance. Tests consisting of idealized solitary and standing wave motions and wave overtopping of nearshore structures show that: (1) the simulation results of the current hybrid model compare well with the idealized data, experimental data, and pure RANS model results and (2) the hybrid model saves computational time by a factor proportional to the reduction in the size of the RANS model domain. Finally, a large‐scale tsunami simulation is provided for a numerical setup that is practically unapproachable using RANS model alone; not only does the hybrid model offer more rapid simulation of relatively small‐scale problems, it provides an opportunity to examine very large total domains with the fine resolution typical of RANS simulations. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical study of breaking waves by a two‐phase flow model

A two‐phase flow model, which solves the flow in the air and water simultaneously, is presented for modelling breaking waves in deep and shallow water, including wave pre‐breaking, overturning and post‐breaking processes. The model is based on the Reynolds‐averaged Navier–Stokes equations with the k ?ε turbulence model. The governing equations are solved by the finite volume method in a Cartesian staggered grid and the partial cell treatment is implemented to deal with complex geometries. The SIMPLE algorithm is utilised for the pressure‐velocity coupling and the air‐water interface is modelled by the interface capturing method via a high resolution volume of fluid scheme. The numerical model is validated by simulating overturning waves on a sloping beach and over a reef, and deep‐water breaking waves in a periodic domain, in which good agreement between numerical results and available experimental measurements for the water surface profiles during wave overturning is obtained. The overturning jet, air entrainment and splash‐up during wave breaking have been captured by the two‐phase flow model, which demonstrates the capability of the model to simulate free surface flow and wave breaking problems.Copyright © 2011 John Wiley & Sons, Ltd.     

Modelling of dust lifting using the Lagrangian approach

The subject of this paper is dust lifting behind shock waves, a process that is important for the formation of explosive dust clouds in air. While Eulerian–Eulerian has been the standard numerical technique for such simulations, the Eulerian–Lagrangian technique has been used in this paper, making it possible to take into account more physical phenomena, such as particle–particle and particle–wall collisions. The results of the simulations are shown mainly graphically, as snapshots of particle positions at given times after the passing of the shock wave. The results show that the collisions, and the coefficient of restitution assumed for them, is important in determining the mobility and lifting of dust behind shock waves. The results also show that the idea of a horizontally travelling shock wave is an oversimplification: the strong pressure gradient at the surface results in a series of reflected waves generated at the surface and travelling into the gas phase.     

Long time interaction of envelope solitons and freak wave formations

This paper concerns long time interaction of envelope solitary gravity waves propagating at the surface of a two-dimensional deep fluid in potential flow. Fully nonlinear numerical simulations show how an initially long wave group slowly splits into a number of solitary wave groups. In the example presented, three large wave events are formed during the evolution. They occur during a time scale that is beyond the time range of validity of simplified equations like the nonlinear Schrödinger (NLS) equation or modifications of this equation. A Fourier analysis shows that these large wave events are caused by significant transfer to side-band modes of the carrier waves. Temporary downshiftings of the dominant wavenumber of the spectrum coincide with the formation large wave events. The wave slope at maximal amplifications is about three times higher than the initial wave slope. The results show how interacting solitary wave groups that emerge from a long wave packet can produce freak wave events.Our reference numerical simulation are performed with the fully nonlinear model of Clamond and Grue [D. Clamond, J. Grue, A fast method for fully nonlinear water wave computations, J. Fluid Mech. 447 (2001) 337–355]. The results of this model are compared with that of two weakly nonlinear models, the NLS equation and its higher-order extension derived by Trulsen et al. [K. Trulsen, I. Kliakhandler, K.B. Dysthe, M.G. Velarde, On weakly nonlinear modulation of waves on deep water, Phys. Fluids 12 (10) (2000) 2432–2437]. They are also compared with the results obtained with a high-order spectral method (HOSM) based on the formulation of West et al. [B.J. West, K.A. Brueckner, R.S. Janda, A method of studying nonlinear random field of surface gravity waves by direct numerical simulation, J. Geophys. Res. 92 (C11) (1987) 11 803–11 824]. An important issue concerning the representation and the treatment of the vertical velocity in the HOSM formulation is highlighted here for the study of long-time evolutions.     

正向爆轰驱动高焓激波风洞的数值模拟

对充满氢氧可燃气体、带扩容腔的正向爆轰驱动的激波风洞进行了数值模拟。计算采用了欧拉方程,频散可控耗散差分格式（DCD）和改进的二阶段化学反应模型。在扩容腔附近采用二维轴对称计算模型,而在驱动段和被驱动段的直管道部分则采用一维计算模型。本文分析了爆轰波在管道中的传播、反射和绕射过程。计算结果表明扩容腔的尺寸对爆轰波的传播、反射、汇聚等起着决定性的作用;带扩容腔的正向爆轰驱动的激波风洞能够得到平稳的持续时间较长的气流,提高了实验的精确度和可重复性。     

煤油液滴直径对两相旋转爆轰发动机流场的影响

为探究煤油液滴不同初始直径对气液两相旋转爆轰发动机流场的影响,假设初始注入的煤油液滴具有均匀直径,考虑雾化破碎、蒸发等过程,建立了非定常两相爆轰的Eulerian-Lagrangian模型,进行了液态煤油/高温空气爆轰的非预混二维数值模拟。结果表明：在初始液滴直径为1～70μm的工况范围,燃烧室内均形成了单个稳定传播的旋转爆轰波;全局当量比为1时,爆轰波前的空气区域大于液滴煤油的蒸气区域,导致波前燃料空气混合不均匀,波前均存在富油区和贫油区,两相速度差导致分离出的空气形成低温条带;当煤油液滴的初始直径较小时,波前的反应物混合过程主要受蒸发的影响,爆轰波可稳定传播;当直径减小至1μm时,煤油液滴在入口处即蒸发,旋转爆轰波表现为气相传播的特性,爆轰波结构平整;当煤油液滴的初始直径较大时,波前的反应物混合过程主要受液滴破碎的影响;对于相同的燃料质量流量,在不同初始煤油液滴直径工况下,煤油液滴最大的停留时间均占爆轰波传播时间尺度的80%以上;爆轰波前燃料预蒸发为气相的占比越高,爆轰波的传播速度越高;初始液滴直径为10～70μm的工况范围内,爆轰波的速度随初始直径的增大先升高后降低。