Surface wave methods have received much attention due to their efficient, flexible and convenient characteristics. However, there are still critical issues regarding a key step in surface wave inversion. In most exist...Surface wave methods have received much attention due to their efficient, flexible and convenient characteristics. However, there are still critical issues regarding a key step in surface wave inversion. In most existing methods, the number of layers is assumed to be known prior to the process of inversion. However, improper assignment of this parameter leads to erroneous inversion results. A Bayesian nonparametric method for Rayleigh wave inversion is proposed herein to address this problem. In this method, each model class represents a particular number of layers with unknown S-wave velocity and thickness of each layer. As a result, determination of the number of layers is equivalent to selection of the most applicable model class. Regarding each model class, the optimization search of S-wave velocity and thickness of each layer is implemented by using a genetic algorithm. Then, each model class is assessed in view of its efficiency under the Bayesian framework and the most efficient class is selected. Simulated and actual examples verify that the proposed Bayesian nonparametric approach is reliable and efficient for Rayleigh wave inversion, especially for its capability to determine the number of layers.展开更多
Large eddy simulation is performed to study three-dimensional wave-current interaction with a square cylinder at different Reynolds numbers, ranging from 1,000 to 600,000. The Keulegan-Carpenter number is relevantly a...Large eddy simulation is performed to study three-dimensional wave-current interaction with a square cylinder at different Reynolds numbers, ranging from 1,000 to 600,000. The Keulegan-Carpenter number is relevantly a constant of 0.6 for all cases. The Strouhal number, the mean and the RMS values of the effective drag coefficient in the streamwise and transverse directions are computed for various Reynolds numbers, and the velocity of a rep- resentative point in the turbulent zone is simulated to find the turbulent feature. It is found that the wave-current interaction should be considered as three-dimensional flow when the Reynolds number is high; under wave-current effect, there exists a critical Reynolds number, and when the Reynolds number is smaller than the critical one, current effect on wave can be nearly neglected; conversely, with the Reynolds number increasing, wave-currentstructure interaction is sensitive to the Reynolds number.展开更多
The study of large-scale atmospheric turbulence and transport processes is of vital importance in the general circulation of the atmosphere. The governing equations of the power and cross-spectra for the atmospheric m...The study of large-scale atmospheric turbulence and transport processes is of vital importance in the general circulation of the atmosphere. The governing equations of the power and cross-spectra for the atmospheric motion and transports in the domain of wave number frequency space have been derived. The contributions of the nonlinear interactions of the atmospheric waves in velocity and temperature fields to the conversion of kinetic and potential energies and to the meridional transports of angular momentum and sensible heat in the atmosphere have been discussed.展开更多
Based on the indirect Trefftz approach, a wave number method （WNM） is proposed to deal with three-dimensional steady-state acoustic problems. In the WNM, the dynamic pressure response variable is approximated by a s...Based on the indirect Trefftz approach, a wave number method （WNM） is proposed to deal with three-dimensional steady-state acoustic problems. In the WNM, the dynamic pressure response variable is approximated by a set of wave functions, which exactly satisfy the Helmholtz equation. The set of wave functions comprise the exact solutions of the homogeneous part of the governing equations and some particular solution functions. The unknown coefficients of the wave functions can be obtained by enforcing the pressure approximation to satisfy the boundary conditions. Compared with the boundary element method （BEM）, the WNM have a smaller system matrix, and is applicable to the radiation problems since the wave functions are independent of the domain size. A 3D acoustic cavity is exemplified to show the properties of the method. The results show that the wave number method is more efficient than the BEM, and it is fairly accurate.展开更多
We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on...We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on nonlinear equations. We focus on to describe the analytic solution in the special pattern of travelling wave solutions using tan-cot function method. We discuss about inviscid and viscous version of Burger’s equation for fluid flow and investigate the effects of internal friction of a fluid via Reynolds number. By changing the velocity amplitude, the nature of flows with shock wave and disturbance are observed. For numerical solutions, the Crank-Nicolson scheme is introduced to establish the wave solutions.展开更多
A shallow water tomography scheme based on the modal wave number inversion technique is considered in this paper. The scheme is based on the assumption that modal wave number for trapped modes can be measured in a sui...A shallow water tomography scheme based on the modal wave number inversion technique is considered in this paper. The scheme is based on the assumption that modal wave number for trapped modes can be measured in a suitable way. The tomographic inversion is accomplished in two steps: firstly, the bottom parameters are inverted by using the bottom reflection phase shift with the known sound speed profile; secondly, the variation of sound speed profile at different time is inverted provided the bottom parameters are known. A numerical simulation shows that the proposed scheme works well, and the sensitivity analysis of sound speed profile inversion is performed for shallow water environmental parameters: sound speed, density and attenuation coefficient of the bottom.展开更多
The variations of ocean environmental parameters invariably result in variations of local modal wave numbers of a sound pressure field. The asymptotic Hankel transform with a short sliding window is applied to the com...The variations of ocean environmental parameters invariably result in variations of local modal wave numbers of a sound pressure field. The asymptotic Hankel transform with a short sliding window is applied to the complex sound pressure field in the water containing a mesoscale eddy to examine the variation of local modal wave numbers in such a range-dependent environment. The numerical simulation results show that modal wave number spectra obtained by this method can reflect the location and strength of a mesoscale eddy, therefore it can be used to monitor the strength and spatial scale of ocean mesoscale eddies.展开更多
Effect of the particle number density on the dispersion properties of longitudinal and transverse lattice waves in a two-dimensional Yukawa charged-dust system is investigated using molecular dynamics simulation. The ...Effect of the particle number density on the dispersion properties of longitudinal and transverse lattice waves in a two-dimensional Yukawa charged-dust system is investigated using molecular dynamics simulation. The dispersion relations for the waves are obtained. It is found that the frequencies of both the longitudinal and transverse dust waves increase with the density and when the density is sufficiently high a cutoff region appears at the short wavelength. With the increase of the particle number density, the common frequency tends to increase, and the sound speed of the longitudinal wave also increases, but that of the transverse wave remains low.展开更多
Acoustic fields with impedance boundary conditions have high engineering applications, such as noise control and evaluation of sound insulation materials, and can be approximated by three-dimensional Helmholtz boundar...Acoustic fields with impedance boundary conditions have high engineering applications, such as noise control and evaluation of sound insulation materials, and can be approximated by three-dimensional Helmholtz boundary value problems. Finite difference method is widely applied to solving these problems due to its ease of use. However, when the wave number is large, the pollution effects are still a major difficulty in obtaining accurate numerical solutions. We develop a fast algorithm for solving three-dimensional Helmholtz boundary problems with large wave numbers. The boundary of computational domain is discrete based on high-order compact difference scheme. Using the properties of the tensor product and the discrete Fourier sine transform method, the original problem is solved by splitting it into independent small tridiagonal subsystems. Numerical examples with impedance boundary conditions are used to verify the feasibility and accuracy of the proposed algorithm. Results demonstrate that the algorithm has a fourth- order convergence in and -norms, and costs less CPU calculation time and random access memory.展开更多
Offshore wind power plays a crucial role in energy strategies.The results of traditional small-scale physical models may be unreliable when extrapolated to large field scales.This study addressed this limitation by co...Offshore wind power plays a crucial role in energy strategies.The results of traditional small-scale physical models may be unreliable when extrapolated to large field scales.This study addressed this limitation by conducting large-scale(1:13)experiments to investigate the scour hole pattern and equilibrium scour depth around both slender and large monopiles under irregular waves.The experiments adopted KeuleganeCarpenter number(NKC)values from 1.01 to 8.89 and diffraction parameter(D/L,where D is the diameter of the monopile,and L is the wave length)values from 0.016 to 0.056.The results showed that changes in the maximum scour location and scour hole shape around a slender monopile were associated with NKC,with differences observed between irregular and regular waves.Improving the calculation of NKC enhanced the accuracy of existing scour formulae under irregular waves.The maximum scour locations around a large monopile were consistently found on both sides,regardless of NKC and D/L,but the scour hole topography was influenced by both parameters.Notably,the scour range around a large monopile was at least as large as the monopile diameter.展开更多
Shear-wave velocity is a key parameter for calibrating monitoring time-lapse 4D seismic data during CO2-EOR （Enhanced Oil Recovery） and CO2 sequestration. However, actual S-wave velocity data are lacking, especially...Shear-wave velocity is a key parameter for calibrating monitoring time-lapse 4D seismic data during CO2-EOR （Enhanced Oil Recovery） and CO2 sequestration. However, actual S-wave velocity data are lacking, especially in 4D data for CO2 sequestration because wells are closed after the CO2 injection and seismic monitoring is continued but no well log data are acquired. When CO2 is injected into a reservoir, the pressure and saturation of the reservoirs change as well as the elastic parameters of the reservoir rocks. We propose a method to predict the S-wave velocity in reservoirs at different pressures and porosities based on the Hertz-Mindlin and Gassmann equations. Because the coordination number is unknown in the Hertz Mindlin equation, we propose a new method to predict it. Thus, we use data at different CO2 injection stages in the Gao89 well block, Shengli Oilfield. First, the sand and mud beds are separated based on the structural characteristics of the thin sand beds and then the S-wave velocity as a function of reservoir pressure and porosity is calculated. Finally, synthetic seismic seismograms are generated based on the predicted P- and S-wave velocities at different stages of CO2 injection.展开更多
A new numerical finite difference iteration method for refraction-diffraction of waves ia water of slowly varying current and topography is developed in this paper. And corresponding theoretical model including the di...A new numerical finite difference iteration method for refraction-diffraction of waves ia water of slowly varying current and topography is developed in this paper. And corresponding theoretical model including the dissipation term is briefly described, together with some analysis and comparison of computational results of the model with measurements in a hydraulic scale model (Berkhoff et al., 1982). An example of practical use of the method is given, showing that the present model is useful to engineering practice.展开更多
In the present paper, we endeavor to accomplish a diagram, which demarcates the validity ranges for interfacial wave theories in a two-layer system, to meet the needs of design in ocean engineering. On the basis of th...In the present paper, we endeavor to accomplish a diagram, which demarcates the validity ranges for interfacial wave theories in a two-layer system, to meet the needs of design in ocean engineering. On the basis of the available solutions of periodic and solitary waves, we propose a guideline as principle to identify the validity regions of the interfacial wave theories in terms of wave period T, wave height H, upper layer thickness dl, and lower layer thick-ness d2, instead of only one parameter-water depth d as in the water surface wave circumstance. The diagram proposed here happens to be Le Mehaute＇s plot for free surface waves if water depth ratio r= d1/d2 approaches to infinity and the upper layer water density p1 to zero. On the contrary, the diagram for water surface waves can be used for two-layer interfacial waves if gravity acceleration g in it is replaced by the reduced gravity defined in this study under the condition of σ=（P2 - Pl）/P2 → 1.0 and r 〉 1.0. In the end, several figures of the validity ranges for various interfacial wavetheories in the two-layer fluid are given and compared with the results for surface waves.展开更多
Shock waves can significantly affect the film cooling for supersonic flow and shock waves may have different influence when impinging in different regions.The present study numerically compared the results of shock wa...Shock waves can significantly affect the film cooling for supersonic flow and shock waves may have different influence when impinging in different regions.The present study numerically compared the results of shock wave impinging in three different regions and analyzed the effect of impinging region.The shock wave generators were located at x/s=5,25,45 with 4°,7°and 10°shock wave incidence.The mainstream Mach number was 3.2 and the coolant Mach number was 1.2 or 1.5.The numerical results illustrated that the shock wave impinged in the further upstream region led to a larger high-pressure region and a larger vortex in the boundary layer.Moreover,placing the shock wave generator upstream resulted in the lower mass fraction of coolant in the downstream region.The velocity in the upstream part of the cooling layer was lower than the midstream and downstream part,which resulted in the less ability to resist the shock wave impingement.Therefore,the upstream impingement deteriorated the cooling performance to a greater extent.The study also manifested that the stronger shock wave had a larger effect on supersonic film cooling.Increasing the coolant inlet Mach number can increase the blowing ratio and reduce the mixing,which was of benefit to improve cooling effect.展开更多
The structure and stability of non-adiabatic reverse smolder waves are investigated numerically. First, the 1D steady-state responses of reverse smolder waves in the presence of convective heat losses are studied with...The structure and stability of non-adiabatic reverse smolder waves are investigated numerically. First, the 1D steady-state responses of reverse smolder waves in the presence of convective heat losses are studied with the rate of incoming air flow as the control parameter. Based on the 1D steady solutions, the linear stability and the Lewis number effects on the stability are examined by a numerical normal mode analysis. Finally, the dynamical evolution processes of unstable reverse smolder waves are studied by direct numerical simulations. It is shown that, in comparison with the adiabatic case, the presence of heat losses leads to a backward shift of the extinction limit. For varying Lewis numbers, the extinction limit shifts forward with the increase of the Lewis number while the smolder temperature remains unchanged. Furthermore, results of a linear stability analysis show that the maximum growth rate decreases with the increasing Lewis number, implying that increasing the Lewis number tends to weaken the thermal-diffusive instability of non-adiabatic reverse smolder waves. Direct numerical simulation results show that, on the fuel-rich branch, the unstable plane reverse smolder wave gradually develops to a regular steady fingering pattern, whereas on the fuel-lean branch, similar to the adiabatic case, vigorous fragmentation instability occurs, and is accompanied by a substantial local temperature rise, which may be sufficiently high to trigger the transition to flaming combustion.展开更多
The evolution and breaking of a propagating internal wave are directly numerically simulated using a pseudo-spectral method. The mechanism of PSI （ parametric subharmonic instability） involved in the evolution is te...The evolution and breaking of a propagating internal wave are directly numerically simulated using a pseudo-spectral method. The mechanism of PSI （ parametric subharmonic instability） involved in the evolution is testified clearly. It dominates gradually in nonlinear resonant interactions. As a consequence, the energy cascades to a second plant wave packet which has lower frequencies and higher wavenumbers than that of the primary wave. With the growth of this wave packet, wave breaking occurs and causes strongly nonlinear regime, i.e. stratified turbulence. The strong mixing and intermittent of the turbulence can be learned from the evolution of the total energy and kurtosis of vorticity vs. time. Some statistic properties of the stratified turbulence are also analyzed, including the spectra of KE （kinetic energy） and PE （potential energy）. The results show that the PE spectra display a wavenumber range scaling as 0. 2 N^4ky^-3 （N is the Brunt - Vaisala frequency, k, is the vertical wavenumber）, which is called buoyancy sub-range. However, the KE spectra cannot satisfy the negative cubic law of vertical wavenumber, which have a much larger downtrend than that of the PE spectra, for the potential energy is transferred more efficiently toward small scales than the kinetic energy. The Cox number of diapycnal diffusivity is also calculated, and it shows a good consistency with the observations and deductions in the ocean interior, during the stage of the stratified turbulence maintaining a fairly active level.展开更多
A series solution for surface motion amplification due to underground group cavities for incident plane P waves is derived by Fourier-Bessel series expansion method. It is shown that underground group cavities signifi...A series solution for surface motion amplification due to underground group cavities for incident plane P waves is derived by Fourier-Bessel series expansion method. It is shown that underground group cavities significantly am-plify the surface ground motion nearby. It is suggested that the effect of subways on ground motion should be con-sidered when the subways are planned and designed.展开更多
基金Science and Technology Development Fund of the Macao SAR under research grant SKL-IOTSC-2018-2020the Research Committee of University of Macao under Research Grant MYRG2016-00029-FST。
文摘Surface wave methods have received much attention due to their efficient, flexible and convenient characteristics. However, there are still critical issues regarding a key step in surface wave inversion. In most existing methods, the number of layers is assumed to be known prior to the process of inversion. However, improper assignment of this parameter leads to erroneous inversion results. A Bayesian nonparametric method for Rayleigh wave inversion is proposed herein to address this problem. In this method, each model class represents a particular number of layers with unknown S-wave velocity and thickness of each layer. As a result, determination of the number of layers is equivalent to selection of the most applicable model class. Regarding each model class, the optimization search of S-wave velocity and thickness of each layer is implemented by using a genetic algorithm. Then, each model class is assessed in view of its efficiency under the Bayesian framework and the most efficient class is selected. Simulated and actual examples verify that the proposed Bayesian nonparametric approach is reliable and efficient for Rayleigh wave inversion, especially for its capability to determine the number of layers.
基金supported by the National Natural Science Foundation of China (No. 51178397)Technological Research and Development Programs of the Ministry of Railways (No. 2010G004-L)
文摘Large eddy simulation is performed to study three-dimensional wave-current interaction with a square cylinder at different Reynolds numbers, ranging from 1,000 to 600,000. The Keulegan-Carpenter number is relevantly a constant of 0.6 for all cases. The Strouhal number, the mean and the RMS values of the effective drag coefficient in the streamwise and transverse directions are computed for various Reynolds numbers, and the velocity of a rep- resentative point in the turbulent zone is simulated to find the turbulent feature. It is found that the wave-current interaction should be considered as three-dimensional flow when the Reynolds number is high; under wave-current effect, there exists a critical Reynolds number, and when the Reynolds number is smaller than the critical one, current effect on wave can be nearly neglected; conversely, with the Reynolds number increasing, wave-currentstructure interaction is sensitive to the Reynolds number.
文摘The study of large-scale atmospheric turbulence and transport processes is of vital importance in the general circulation of the atmosphere. The governing equations of the power and cross-spectra for the atmospheric motion and transports in the domain of wave number frequency space have been derived. The contributions of the nonlinear interactions of the atmospheric waves in velocity and temperature fields to the conversion of kinetic and potential energies and to the meridional transports of angular momentum and sensible heat in the atmosphere have been discussed.
文摘Based on the indirect Trefftz approach, a wave number method （WNM） is proposed to deal with three-dimensional steady-state acoustic problems. In the WNM, the dynamic pressure response variable is approximated by a set of wave functions, which exactly satisfy the Helmholtz equation. The set of wave functions comprise the exact solutions of the homogeneous part of the governing equations and some particular solution functions. The unknown coefficients of the wave functions can be obtained by enforcing the pressure approximation to satisfy the boundary conditions. Compared with the boundary element method （BEM）, the WNM have a smaller system matrix, and is applicable to the radiation problems since the wave functions are independent of the domain size. A 3D acoustic cavity is exemplified to show the properties of the method. The results show that the wave number method is more efficient than the BEM, and it is fairly accurate.
文摘We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on nonlinear equations. We focus on to describe the analytic solution in the special pattern of travelling wave solutions using tan-cot function method. We discuss about inviscid and viscous version of Burger’s equation for fluid flow and investigate the effects of internal friction of a fluid via Reynolds number. By changing the velocity amplitude, the nature of flows with shock wave and disturbance are observed. For numerical solutions, the Crank-Nicolson scheme is introduced to establish the wave solutions.
文摘A shallow water tomography scheme based on the modal wave number inversion technique is considered in this paper. The scheme is based on the assumption that modal wave number for trapped modes can be measured in a suitable way. The tomographic inversion is accomplished in two steps: firstly, the bottom parameters are inverted by using the bottom reflection phase shift with the known sound speed profile; secondly, the variation of sound speed profile at different time is inverted provided the bottom parameters are known. A numerical simulation shows that the proposed scheme works well, and the sensitivity analysis of sound speed profile inversion is performed for shallow water environmental parameters: sound speed, density and attenuation coefficient of the bottom.
文摘The variations of ocean environmental parameters invariably result in variations of local modal wave numbers of a sound pressure field. The asymptotic Hankel transform with a short sliding window is applied to the complex sound pressure field in the water containing a mesoscale eddy to examine the variation of local modal wave numbers in such a range-dependent environment. The numerical simulation results show that modal wave number spectra obtained by this method can reflect the location and strength of a mesoscale eddy, therefore it can be used to monitor the strength and spatial scale of ocean mesoscale eddies.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11675261 and 21403297the Scientific Research Foundation of Ludong University under Grant No LY2014010
文摘Effect of the particle number density on the dispersion properties of longitudinal and transverse lattice waves in a two-dimensional Yukawa charged-dust system is investigated using molecular dynamics simulation. The dispersion relations for the waves are obtained. It is found that the frequencies of both the longitudinal and transverse dust waves increase with the density and when the density is sufficiently high a cutoff region appears at the short wavelength. With the increase of the particle number density, the common frequency tends to increase, and the sound speed of the longitudinal wave also increases, but that of the transverse wave remains low.
文摘Acoustic fields with impedance boundary conditions have high engineering applications, such as noise control and evaluation of sound insulation materials, and can be approximated by three-dimensional Helmholtz boundary value problems. Finite difference method is widely applied to solving these problems due to its ease of use. However, when the wave number is large, the pollution effects are still a major difficulty in obtaining accurate numerical solutions. We develop a fast algorithm for solving three-dimensional Helmholtz boundary problems with large wave numbers. The boundary of computational domain is discrete based on high-order compact difference scheme. Using the properties of the tensor product and the discrete Fourier sine transform method, the original problem is solved by splitting it into independent small tridiagonal subsystems. Numerical examples with impedance boundary conditions are used to verify the feasibility and accuracy of the proposed algorithm. Results demonstrate that the algorithm has a fourth- order convergence in and -norms, and costs less CPU calculation time and random access memory.
基金supported by the National Nature Science Foundation of China National Outstanding Youth Science Fund Project(Grant No.52122109)the National Natural Science Foundation of China(Grants No.51861165102 and 52039005).
文摘Offshore wind power plays a crucial role in energy strategies.The results of traditional small-scale physical models may be unreliable when extrapolated to large field scales.This study addressed this limitation by conducting large-scale(1:13)experiments to investigate the scour hole pattern and equilibrium scour depth around both slender and large monopiles under irregular waves.The experiments adopted KeuleganeCarpenter number(NKC)values from 1.01 to 8.89 and diffraction parameter(D/L,where D is the diameter of the monopile,and L is the wave length)values from 0.016 to 0.056.The results showed that changes in the maximum scour location and scour hole shape around a slender monopile were associated with NKC,with differences observed between irregular and regular waves.Improving the calculation of NKC enhanced the accuracy of existing scour formulae under irregular waves.The maximum scour locations around a large monopile were consistently found on both sides,regardless of NKC and D/L,but the scour hole topography was influenced by both parameters.Notably,the scour range around a large monopile was at least as large as the monopile diameter.
基金supported by the National High Techology Research and Development Program(No.2012AA050103)
文摘Shear-wave velocity is a key parameter for calibrating monitoring time-lapse 4D seismic data during CO2-EOR （Enhanced Oil Recovery） and CO2 sequestration. However, actual S-wave velocity data are lacking, especially in 4D data for CO2 sequestration because wells are closed after the CO2 injection and seismic monitoring is continued but no well log data are acquired. When CO2 is injected into a reservoir, the pressure and saturation of the reservoirs change as well as the elastic parameters of the reservoir rocks. We propose a method to predict the S-wave velocity in reservoirs at different pressures and porosities based on the Hertz-Mindlin and Gassmann equations. Because the coordination number is unknown in the Hertz Mindlin equation, we propose a new method to predict it. Thus, we use data at different CO2 injection stages in the Gao89 well block, Shengli Oilfield. First, the sand and mud beds are separated based on the structural characteristics of the thin sand beds and then the S-wave velocity as a function of reservoir pressure and porosity is calculated. Finally, synthetic seismic seismograms are generated based on the predicted P- and S-wave velocities at different stages of CO2 injection.
基金Science Foundation of National Education Committee of China
文摘A new numerical finite difference iteration method for refraction-diffraction of waves ia water of slowly varying current and topography is developed in this paper. And corresponding theoretical model including the dissipation term is briefly described, together with some analysis and comparison of computational results of the model with measurements in a hydraulic scale model (Berkhoff et al., 1982). An example of practical use of the method is given, showing that the present model is useful to engineering practice.
基金the Knowledge Innovation Project of CAS(KJCX-YW-L02)the National 863 Project of China(2006AAO9A103-4)+1 种基金China National Oil Corporation in Beijing(CNOOC)the National Natural Science Foundation of China(10672056).
文摘In the present paper, we endeavor to accomplish a diagram, which demarcates the validity ranges for interfacial wave theories in a two-layer system, to meet the needs of design in ocean engineering. On the basis of the available solutions of periodic and solitary waves, we propose a guideline as principle to identify the validity regions of the interfacial wave theories in terms of wave period T, wave height H, upper layer thickness dl, and lower layer thick-ness d2, instead of only one parameter-water depth d as in the water surface wave circumstance. The diagram proposed here happens to be Le Mehaute＇s plot for free surface waves if water depth ratio r= d1/d2 approaches to infinity and the upper layer water density p1 to zero. On the contrary, the diagram for water surface waves can be used for two-layer interfacial waves if gravity acceleration g in it is replaced by the reduced gravity defined in this study under the condition of σ=（P2 - Pl）/P2 → 1.0 and r 〉 1.0. In the end, several figures of the validity ranges for various interfacial wavetheories in the two-layer fluid are given and compared with the results for surface waves.
基金supported by the the National Science and Technology Major Project of China(No.2017-III-0003-0027)the Science Fund for Creative Research Groups of the NSFC(No.51621062)Tsinghua University-Zhang Jiagang Joint Institute for Hydrogen Energy and Lithium-Ion Battery Technology。
文摘Shock waves can significantly affect the film cooling for supersonic flow and shock waves may have different influence when impinging in different regions.The present study numerically compared the results of shock wave impinging in three different regions and analyzed the effect of impinging region.The shock wave generators were located at x/s=5,25,45 with 4°,7°and 10°shock wave incidence.The mainstream Mach number was 3.2 and the coolant Mach number was 1.2 or 1.5.The numerical results illustrated that the shock wave impinged in the further upstream region led to a larger high-pressure region and a larger vortex in the boundary layer.Moreover,placing the shock wave generator upstream resulted in the lower mass fraction of coolant in the downstream region.The velocity in the upstream part of the cooling layer was lower than the midstream and downstream part,which resulted in the less ability to resist the shock wave impingement.Therefore,the upstream impingement deteriorated the cooling performance to a greater extent.The study also manifested that the stronger shock wave had a larger effect on supersonic film cooling.Increasing the coolant inlet Mach number can increase the blowing ratio and reduce the mixing,which was of benefit to improve cooling effect.
基金Project supported by the Shanghai Rising Star Program (No. 09QA1402300)the Scientific Research Innovation Program of Shanghai Education Commission
文摘The structure and stability of non-adiabatic reverse smolder waves are investigated numerically. First, the 1D steady-state responses of reverse smolder waves in the presence of convective heat losses are studied with the rate of incoming air flow as the control parameter. Based on the 1D steady solutions, the linear stability and the Lewis number effects on the stability are examined by a numerical normal mode analysis. Finally, the dynamical evolution processes of unstable reverse smolder waves are studied by direct numerical simulations. It is shown that, in comparison with the adiabatic case, the presence of heat losses leads to a backward shift of the extinction limit. For varying Lewis numbers, the extinction limit shifts forward with the increase of the Lewis number while the smolder temperature remains unchanged. Furthermore, results of a linear stability analysis show that the maximum growth rate decreases with the increasing Lewis number, implying that increasing the Lewis number tends to weaken the thermal-diffusive instability of non-adiabatic reverse smolder waves. Direct numerical simulation results show that, on the fuel-rich branch, the unstable plane reverse smolder wave gradually develops to a regular steady fingering pattern, whereas on the fuel-lean branch, similar to the adiabatic case, vigorous fragmentation instability occurs, and is accompanied by a substantial local temperature rise, which may be sufficiently high to trigger the transition to flaming combustion.
基金The National Nature Science Foundation of China under contract No.40706002the National High Technology Development Project of China under contract No.2007AA09Z122.
文摘The evolution and breaking of a propagating internal wave are directly numerically simulated using a pseudo-spectral method. The mechanism of PSI （ parametric subharmonic instability） involved in the evolution is testified clearly. It dominates gradually in nonlinear resonant interactions. As a consequence, the energy cascades to a second plant wave packet which has lower frequencies and higher wavenumbers than that of the primary wave. With the growth of this wave packet, wave breaking occurs and causes strongly nonlinear regime, i.e. stratified turbulence. The strong mixing and intermittent of the turbulence can be learned from the evolution of the total energy and kurtosis of vorticity vs. time. Some statistic properties of the stratified turbulence are also analyzed, including the spectra of KE （kinetic energy） and PE （potential energy）. The results show that the PE spectra display a wavenumber range scaling as 0. 2 N^4ky^-3 （N is the Brunt - Vaisala frequency, k, is the vertical wavenumber）, which is called buoyancy sub-range. However, the KE spectra cannot satisfy the negative cubic law of vertical wavenumber, which have a much larger downtrend than that of the PE spectra, for the potential energy is transferred more efficiently toward small scales than the kinetic energy. The Cox number of diapycnal diffusivity is also calculated, and it shows a good consistency with the observations and deductions in the ocean interior, during the stage of the stratified turbulence maintaining a fairly active level.
基金Supported by National Natural Science Foundation of China (50378063), Excellent Young Teachers Program of MOE and SRF for ROCS, MOE.
文摘A series solution for surface motion amplification due to underground group cavities for incident plane P waves is derived by Fourier-Bessel series expansion method. It is shown that underground group cavities significantly am-plify the surface ground motion nearby. It is suggested that the effect of subways on ground motion should be con-sidered when the subways are planned and designed.
