In the cylindrical coordinate system,a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rig...In the cylindrical coordinate system,a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subject to a vertical oscillation.It is assumed that the fluid in the circular cylindrical vessel is inviscid,incompressible and the motion is irrotational, a nonlinear amplitude equation with cubic and vertically excited terms of the vessel was derived by expansion of two-time scales without considering the effect of surface tension.It is shown by numerical computation that different free surface standing wave patterns will be formed in different excited frequencies and amplitudes.The contours of free surface waves are agreed well with the experimental results which were carried out several years ago.展开更多
In this paper, we experimentally investigate the pattern transition of two-dimensional Faraday waves at an extremely shallow depth in a Hele-Shaw cell. Several patterns of Faraday waves are observed, which have some s...In this paper, we experimentally investigate the pattern transition of two-dimensional Faraday waves at an extremely shallow depth in a Hele-Shaw cell. Several patterns of Faraday waves are observed, which have some significant differences in wave profile,wave height and wave length. It is found that, in a wide range of the forcing frequency f, there always exists a region of the acceleration amplitude A, in which there exist the so-called hysteretic jumps between different patterns of Faraday waves. All of these experimental observations could enrich our knowledges about the Faraday waves and would be helpful to the further theoretical studies on the related topic in future.展开更多
When a partially loaded liquid container vibrates along the vertical direction,the liquid inside will oscillate regularly,which is called Faraday wave.In some cases,the wave form of the Faraday wave is stable and smoo...When a partially loaded liquid container vibrates along the vertical direction,the liquid inside will oscillate regularly,which is called Faraday wave.In some cases,the wave form of the Faraday wave is stable and smooth,and sometimes there is violent wave breaking and liquid splashing.In this paper,the Faraday waves inside the cylindrical tank and the hexagonal tanks are simulated by the in-house solver MLParticle-SJTU base on the moving particle semi-implicit(MPS)method.The surface tension model is used to better model the free surfaces with large deformations.Phenomena such as wave breaking and liquid splashing are well captured and simulated.The results show that the waveforms are significantly different at different excitation frequencies.And the tank shape also has an obvious effect on the waveform.展开更多
An experimental investigation of the dynamics of the interface between two low-viscosity fluids with high density contrast oscillating in a fixed vertical slotted channel has been conducted.It has been found that as t...An experimental investigation of the dynamics of the interface between two low-viscosity fluids with high density contrast oscillating in a fixed vertical slotted channel has been conducted.It has been found that as the amplitude of the liquid column oscillations increases,parametric oscillations of the interface are excited in the form of a standing wave located in the channel plane.In particular,depending on the interfacial tension,the standing waves have a frequency equal to that of liquid piston oscillations(harmonic response),or half of the frequency of oscillations of the liquid column in the channel(subharmonic response).The detected type of instability has a gravitational-capillary nature and is analogous to Faraday waves.The analysis of the overcritical dynamics of wave oscillations indicates that interfacial tension plays a crucial role in determining the type of parametric instability.At high interfacial tension,only synchronous(harmonic)wave modes are observed,and the threshold of the wave excitation is determined by the amplitude of piston oscillations of the liquid column.In this case,the oscillation acceleration does not play a role and has a small value in the threshold of the synchronous mode response.In the case of weak surface tension,subharmonic oscillations are observed.The threshold for the development of these oscillations is determined by the dimensionless acceleration of the oscillating liquid column and remains almost constant with variations in the dimensionless frequency of oscillations.At moderate values of interfacial tension(in the region of moderate dimensionless frequencies),a synchronous wave mode emerges in the stability threshold of the oscillating interface.As the dimensionless acceleration is increased further,a subharmonic mode is excited.The growth of subharmonic oscillations occurs against the background of harmonic wave oscillations,with the oscillations of the interface representing a combination of two standing waves.展开更多
Faraday wave is a phenomenon of sloshing due to a heave motion of a partially filled tank,which is also called parametric instability or parametric resonance.In the present paper,the phenomenon of faraday wave in a pu...Faraday wave is a phenomenon of sloshing due to a heave motion of a partially filled tank,which is also called parametric instability or parametric resonance.In the present paper,the phenomenon of faraday wave in a pure heave excited square tank is numerically simulated through the moving particle semi-implicit(MPS)method.The surface tension effect and a new Dirichlet boundary condition for the pressure Poisson equation are considered to avert unphysical fragmentation and clustering of particles in splash simulation.In the numerical simulation,the evolution of wave motion,and the non-linearity together with breaking phenomenon of faraday wave can be observed.The agreement is good in general,both amplitude and phase.Besides,the parameter studies including the excitation frequency and the forcing amplitude are carried out to analyses the mechanism of resonances response.展开更多
文摘In the cylindrical coordinate system,a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subject to a vertical oscillation.It is assumed that the fluid in the circular cylindrical vessel is inviscid,incompressible and the motion is irrotational, a nonlinear amplitude equation with cubic and vertically excited terms of the vessel was derived by expansion of two-time scales without considering the effect of surface tension.It is shown by numerical computation that different free surface standing wave patterns will be formed in different excited frequencies and amplitudes.The contours of free surface waves are agreed well with the experimental results which were carried out several years ago.
基金supported by the National Key Basic Research Program of China(Grant No.2014CB046801)
文摘In this paper, we experimentally investigate the pattern transition of two-dimensional Faraday waves at an extremely shallow depth in a Hele-Shaw cell. Several patterns of Faraday waves are observed, which have some significant differences in wave profile,wave height and wave length. It is found that, in a wide range of the forcing frequency f, there always exists a region of the acceleration amplitude A, in which there exist the so-called hysteretic jumps between different patterns of Faraday waves. All of these experimental observations could enrich our knowledges about the Faraday waves and would be helpful to the further theoretical studies on the related topic in future.
基金Project supported by the National Natural Science Foundation of China(Grant No.52131102)the National Key Research and Development Program of China(Grant Nos.2022YFC2806705,2019YFB1704200).
文摘When a partially loaded liquid container vibrates along the vertical direction,the liquid inside will oscillate regularly,which is called Faraday wave.In some cases,the wave form of the Faraday wave is stable and smooth,and sometimes there is violent wave breaking and liquid splashing.In this paper,the Faraday waves inside the cylindrical tank and the hexagonal tanks are simulated by the in-house solver MLParticle-SJTU base on the moving particle semi-implicit(MPS)method.The surface tension model is used to better model the free surfaces with large deformations.Phenomena such as wave breaking and liquid splashing are well captured and simulated.The results show that the waveforms are significantly different at different excitation frequencies.And the tank shape also has an obvious effect on the waveform.
基金supported by the Ministry of Education of the Russian Federation(Project No.1023032300071-6-2.3.1).
文摘An experimental investigation of the dynamics of the interface between two low-viscosity fluids with high density contrast oscillating in a fixed vertical slotted channel has been conducted.It has been found that as the amplitude of the liquid column oscillations increases,parametric oscillations of the interface are excited in the form of a standing wave located in the channel plane.In particular,depending on the interfacial tension,the standing waves have a frequency equal to that of liquid piston oscillations(harmonic response),or half of the frequency of oscillations of the liquid column in the channel(subharmonic response).The detected type of instability has a gravitational-capillary nature and is analogous to Faraday waves.The analysis of the overcritical dynamics of wave oscillations indicates that interfacial tension plays a crucial role in determining the type of parametric instability.At high interfacial tension,only synchronous(harmonic)wave modes are observed,and the threshold of the wave excitation is determined by the amplitude of piston oscillations of the liquid column.In this case,the oscillation acceleration does not play a role and has a small value in the threshold of the synchronous mode response.In the case of weak surface tension,subharmonic oscillations are observed.The threshold for the development of these oscillations is determined by the dimensionless acceleration of the oscillating liquid column and remains almost constant with variations in the dimensionless frequency of oscillations.At moderate values of interfacial tension(in the region of moderate dimensionless frequencies),a synchronous wave mode emerges in the stability threshold of the oscillating interface.As the dimensionless acceleration is increased further,a subharmonic mode is excited.The growth of subharmonic oscillations occurs against the background of harmonic wave oscillations,with the oscillations of the interface representing a combination of two standing waves.
基金supported by the National Natural Science Foundation of China(Grant Nos.52131102,51909160 and 51879159)the National Key Research and Development Program of China(Grant No.2019YFB1704200).
文摘Faraday wave is a phenomenon of sloshing due to a heave motion of a partially filled tank,which is also called parametric instability or parametric resonance.In the present paper,the phenomenon of faraday wave in a pure heave excited square tank is numerically simulated through the moving particle semi-implicit(MPS)method.The surface tension effect and a new Dirichlet boundary condition for the pressure Poisson equation are considered to avert unphysical fragmentation and clustering of particles in splash simulation.In the numerical simulation,the evolution of wave motion,and the non-linearity together with breaking phenomenon of faraday wave can be observed.The agreement is good in general,both amplitude and phase.Besides,the parameter studies including the excitation frequency and the forcing amplitude are carried out to analyses the mechanism of resonances response.
