Tight sandstone has a certain anisotropy. Using ultrasonic measurements of samples in three different directions and related matched experiments, this study systematically analyzes the pore structure and anisotropy of...Tight sandstone has a certain anisotropy. Using ultrasonic measurements of samples in three different directions and related matched experiments, this study systematically analyzes the pore structure and anisotropy of tight sandstone samples obtained from oil fields and compares results with those of shale. Results firstly show that the anisotropy of tight sandstone is mainly related to the compositional layering and thin interbedding which occur in different sedimentary environments. Tight sandstone has typical transverse isotropic medium characteristics, Young’s modulus increases in different directions with increasing confining pressure, Poisson’s ratio change is not obvious, anisotropic coefficients decrease with increasing effective pressure, and a certain linear relationship exists between ε, γ, and δ. This article finally summarizes anisotropy in different areas, thereby providing a foundation for the use of suitable appraisal models in different regions. This research can be used as an experimental reference for logging evaluation, seismic data interpretation, and fracturing develop of tight sandstones.展开更多
Based on the method of linear trending,analysis was made upon the daily temperature statistics of Meitan County from 1951 to 2009,and the results showed that the temperature in general was on the rise.With 1980 as the...Based on the method of linear trending,analysis was made upon the daily temperature statistics of Meitan County from 1951 to 2009,and the results showed that the temperature in general was on the rise.With 1980 as the turning point,it was on the decline before while later the temperature increased quickly.Among these figures,the variation rates of annual average temperature,annual maximum temperature,and annual minimum temperature are 0.11 ℃/10 a,0.08 ℃/10 a,and 0.36 ℃/10 a.The variation rates of average temperature in spring,summer,fall and winter are respectively 0.12 ℃/10 a,0.07 ℃/10 a,0.12 ℃/10 a,and 0.13 ℃/10 a.Morlet wavelet was adopted to analyze the periodicity of temperature change which has periods of different scales.But since 2000,during different time scales most of the areas have been in the period of temperature rises.Besides,certain rule exists in the periodicity of maximum temperature and minimum temperature.Before 1970s,they had opposite changing rules,and the alteration of the peak value occurred.However,in the late 1980s,they had similar changing rules,and their peak values appeared at the same time.It means that against the background of global warming,the reaction of temperature evolution in Meitan County is quite remarkable.展开更多
Ocean waves are the core environmental elements affecting the movements and structure design of ships. Statistical analysis of wave parameters is the basis for the establishment of long-term ship environmental adaptab...Ocean waves are the core environmental elements affecting the movements and structure design of ships. Statistical analysis of wave parameters is the basis for the establishment of long-term ship environmental adaptability prediction model. The observations from coastal stations, buoys, altimeters and volunteer ships that cover from 1993 to 2011 were interpolated into miller Ion-lat grids by using bilinear method and the analytical fields of ocean waves were given. By using optimal interpolation, the analysis wave fields were assimilated into the WAVEWATCH III (WW3) simulation results. From the assimilated results, the wave rose statistics, the wave height of muitiyear return period and the extreme 2-D wave spectrum are related to the ship seakeeping were calculated. Finally, the wave statistics in China offshore were analyzed in detail.展开更多
Finding channel sandbodies is an important task in oil and gas exploration due to the importance of fluvial reservoirs. It is difficult to describe fluvial reservoirs in detail owing to their frequent changes and seri...Finding channel sandbodies is an important task in oil and gas exploration due to the importance of fluvial reservoirs. It is difficult to describe fluvial reservoirs in detail owing to their frequent changes and serious intersections, as well as limitations of S/N ratio and seismic data resolution. Based on the Laohekou 3D data in Shengli Oilfield, we analyze the general characteristics of fluvial reservoirs in this area, from which we find that they are characterized by strong amplitudes on seismic profiles, high continuity on time slices, and low frequency in the frequency domain. In addition, a cluster of strong string-bead- like reflections was found after color processing and detailed interpretation. To understand this observation, we conduct forward modeling to explain the mechanism. This provides a new way to identify ancient channels in similar areas. By using the multi-attribute fusion and RGB display techniques, channel incision is more obvious and the characteristics of the channel structures are manifested much better. Finally, we introduce and apply multi-wavelet detection technology to identify weaker fluvial reservoir signals.展开更多
The flooding characteristics of hydrofoil impeller were systematically investigated in a two-and three-phase 383 mm i.d. stirred tank operated on air, water and spherical glass beads. The volumetric solid concen-trati...The flooding characteristics of hydrofoil impeller were systematically investigated in a two-and three-phase 383 mm i.d. stirred tank operated on air, water and spherical glass beads. The volumetric solid concen-tration Cs was varied from 0 to 25%. And the superficial gas velocity Ug was at the range of 0-0.096 m·s-1. A fast and objective method for identifying flooding point NF is developed based on the statistical analysis of the pressure fluctuation signals. It is found, the effect of solid concentration on the flooding point NF depends on the gas velocity. At the lower gas velocity (Ug = 0.010 m·s-1), the solid concentration has only a minor effect. However, it displays a very significant effect on the flooding point NF at the medium and high gas velocity. The flooding point NF linearly increases with the gas velocity Ug, at lower solid concentration (Cs = 0, 10%). When Cs = 20%, the behavior of NF versus Ug becomes more complex. The correlations of the flooding characteristics in the slurry stirred tank are proposed by considering the solid concentration effect.展开更多
Biot' s two-phase theory for fluid-saturated porous media was applied in a study carried out to investigate the influence of water saturation on propagation of elastic wave in transversely isotropic nearly saturat...Biot' s two-phase theory for fluid-saturated porous media was applied in a study carried out to investigate the influence of water saturation on propagation of elastic wave in transversely isotropic nearly saturated soil. The characteristic equations for wave propagation were derived and solved analytically. The results showed that there are four waves: the first and second quasi-longitudinal waves (QP1 and QP2), the quasitransverse wave (QSV) and the anti-plane transverse wave (SH) . Numerical results are given to illustrate theinfluence of saturation on the velocity, dispersion and attenuation of the four body waves. Some typical numerical results are discussed and plotted. The results can be meaningful for soil dynamics and earthquake engineering.展开更多
Determination of relative three-dimensional (3D) position, orientation, and relative motion between two reference frames is an important problem in robotic guidance, manipulation, and assembly as well as in other fi...Determination of relative three-dimensional (3D) position, orientation, and relative motion between two reference frames is an important problem in robotic guidance, manipulation, and assembly as well as in other fields such as photogrammetry. A solution to pose and motion estimation problem that uses two-dimensional (2D) intensity images from a single camera is desirable for real-time applications. The difficulty in performing this measurement is that the process of projecting 3D object features to 2D images is a nonlinear transformation. In this paper, the 3D transformation is modeled as a nonlinear stochastic system with the state estimation providing six degrees-of-freedom motion and position values, using line features in image plane as measuring inputs and dual quaternion to represent both rotation and translation in a unified notation. A filtering method called the Gaussian particle filter (GPF) based on the panicle filtering concept is presented for 3D pose and motion estimation of a moving target from monocular image sequences. The method has been implemented with simulated data, and simulation results are provided along with comparisons to the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) to show the relative advantages of the GPF. Simulation results showed that GPF is a superior alternative to EKF and UKF.展开更多
The internal energy and specific heat of a Heisenberg ferro- antiferromagnetic double-layer system are studied by using spin-wave theory and the retarded Green function method at low temperatures. Numerical results sh...The internal energy and specific heat of a Heisenberg ferro- antiferromagnetic double-layer system are studied by using spin-wave theory and the retarded Green function method at low temperatures. Numerical results show that the antiferromagnetic intralayer coupling J2 has an important influence on internal energy and specific heat for a four-sublattice system with antiferromagnetic (or ferrimagnetic) interlayer couplings.展开更多
This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes seco...This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes second-order waves. The numerical results obtained for limiting cases of double-row and triple-row walls are in good agreement with results of previous studies and experimental results. Comparisons with experimental measurements of the reflection, transmission, and dissipation coefficients (CR, Cr, and CE) for double-row walls show that the proposed mathematical model adequately reproduces most of the important features. We found that for double-row walls, the CR increases with increasing wave number, kd, and with a decreasing permeable wall part, din. The Cr follows the opposite trend. The CE slowly increases with an increasing kd for lower kd values, reaches a maximum, and then decreases again. In addition, an increasing porosity of dm would significantly decrease the CR while increasing the Cr. At lower values of kd, a decreasing porosity increases the CE, but for high values of kd, a decreasing porosity reduces the Ce. The numerical results indicate that, for triple-row walls, the effect of the arrangement of the chamber widths on hydrodynamic characteristics is not significant, except when kd〈0.5 Double-row slotted breakwaters may exhibit a good wave-absorbing performance at kd〉0.5, where by the horizontal wave force may be smaller than that of a single wall. On the other hand, the difference between double-row and triple-row vertical slotted breakwaters is marginal.展开更多
This paper introduces a novel clutter power model of coastal compound and deduces the statistic characteristics and the arithmetics of model parameter estimation algorithm. Then, a novel coastal compound distributed m...This paper introduces a novel clutter power model of coastal compound and deduces the statistic characteristics and the arithmetics of model parameter estimation algorithm. Then, a novel coastal compound distributed model of the clutter amplitude is proposed and its statistic character- istics are studied. Subsequently, the nonlinear relation of autocorrelation function is deduced between the coastal compound clutter random sequences and the correlated Gaussian random sequences, which is the important prerequisite for the clutter simulation based on the ZMNL (Zero Memory NonLin- earity). Lastly, the advantage of the algorithm is demonstrated by a feasible simulation of the gen- eration of the random coastal compound clutter sequences.展开更多
We obtain. the exact analytical results of all the eigenvalues and eigenstates for three kinds of models describing N-mode multiphoton process without using the assumption of the Bethe ansatz. The exact analytical res...We obtain. the exact analytical results of all the eigenvalues and eigenstates for three kinds of models describing N-mode multiphoton process without using the assumption of the Bethe ansatz. The exact analytical results of all the eigenstates and eigenvalues are in terms of a parameter lambda for three kinds of models describing N-mode multiphoton process. The parameter is shown to be determined by the roots of a polynomial and is solvable analytically or numerically. Moreover, these three kinds of models can be processed with the same procedure.展开更多
An analytical method is developed for the hydroelastic interaction between surface incident waves and a thin elastic plate of arbitrary geometry floating on an inviscid fluid of finite depth in the framework of linear...An analytical method is developed for the hydroelastic interaction between surface incident waves and a thin elastic plate of arbitrary geometry floating on an inviscid fluid of finite depth in the framework of linear potential flow.Three kinds of edge conditions are considered and the corresponding analytical representations are derived in the polar coordinate system.According to the surface boundary conditions,the fluid domain is divided into two regions,namely,an open water region and a plate-covered region.With the assumption that all the motion is time-harmonic,the series solutions for the spatial velocity potentials are derived by the method of eigenfunction expansion.The matching conditions for the continuities of the velocity and pressure are transformed by taking the inner products successively with respect to the vertical eigenfunction for the free surface and the angular eigenfunction.A system of simultaneous equations,including two edge conditions and two matching conditions,is set up for deriving the expansion coefficients.As an example,numerical computation for the expansion coefficients of truncated series is performed for an elliptic plate.The results show that the method suggested here is useful to revealing the physical features of the gravity wave scattering in the open water and the hydroelastic response in the plate.展开更多
The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al. using direct numerical simulation (DNS). It was found that certain sma...The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al. using direct numerical simulation (DNS). It was found that certain small-scale 3-D disturbances amplified rapidly. These disturbances exhibit the characteristics of second modes, and the most amplified components have a well- defined spanwise wavelength, indicating a clear selectivity of the amplification. In the case of a cone, the three-dimensionality of the base flow and the disturbances themselves may be responsible for the rapid amplification. In order to ascertain which of these two effects are essential, in this study we carried out DNS of the nonlinear evolution of a spanwise localized disturbance (wavepacket) in a flat-plate boundary layer. A similar amplification of small-scale disturbances was observed, suggesting that the direct reason for the rapid amplification is the three-dimensionality of the disturbances rather than the three-dimensional nature of the base flow, even though the latter does alter the spanwise distribution of the disturbance. The rapid growth of 3-D waves may be attributed to the secondary instability mechanism. Further simulations were performed for a wavepacket of first modes in a supersonic boundary layer and of Tollmien-Schlichting (T-S) waves in an incompressible boundary layer. The re- suits show that the amplifying components are in the band centered at zero spanwise wavenumber rather than at a finite spanwise wavenumber. It is therefore concluded that the rapid growth of 3-D disturbances in a band centered at a preferred large spanwise wavenumber is the main characteristic of nonlinear evolution of second mode disturbances in supersonic boundary layers.展开更多
基金sponsored by the National Key Technology R&D Program for the 12th five-year plan(No.2011ZX05020-008)the China National Petroleum Corporation Logging Basic Research Project(No.2014A-3910)
文摘Tight sandstone has a certain anisotropy. Using ultrasonic measurements of samples in three different directions and related matched experiments, this study systematically analyzes the pore structure and anisotropy of tight sandstone samples obtained from oil fields and compares results with those of shale. Results firstly show that the anisotropy of tight sandstone is mainly related to the compositional layering and thin interbedding which occur in different sedimentary environments. Tight sandstone has typical transverse isotropic medium characteristics, Young’s modulus increases in different directions with increasing confining pressure, Poisson’s ratio change is not obvious, anisotropic coefficients decrease with increasing effective pressure, and a certain linear relationship exists between ε, γ, and δ. This article finally summarizes anisotropy in different areas, thereby providing a foundation for the use of suitable appraisal models in different regions. This research can be used as an experimental reference for logging evaluation, seismic data interpretation, and fracturing develop of tight sandstones.
基金Supported by National Basic Research Program of China (973 Pro-gram) (2010CB951102 )Program of Innovation ResearchGroup (51021006),National Natural Science Foundation of China~~
文摘Based on the method of linear trending,analysis was made upon the daily temperature statistics of Meitan County from 1951 to 2009,and the results showed that the temperature in general was on the rise.With 1980 as the turning point,it was on the decline before while later the temperature increased quickly.Among these figures,the variation rates of annual average temperature,annual maximum temperature,and annual minimum temperature are 0.11 ℃/10 a,0.08 ℃/10 a,and 0.36 ℃/10 a.The variation rates of average temperature in spring,summer,fall and winter are respectively 0.12 ℃/10 a,0.07 ℃/10 a,0.12 ℃/10 a,and 0.13 ℃/10 a.Morlet wavelet was adopted to analyze the periodicity of temperature change which has periods of different scales.But since 2000,during different time scales most of the areas have been in the period of temperature rises.Besides,certain rule exists in the periodicity of maximum temperature and minimum temperature.Before 1970s,they had opposite changing rules,and the alteration of the peak value occurred.However,in the late 1980s,they had similar changing rules,and their peak values appeared at the same time.It means that against the background of global warming,the reaction of temperature evolution in Meitan County is quite remarkable.
基金supports from National Natural Science Foundation of China (No. 41406032 and No. 41376014)Open Fund of State Key Laboratory of Satellite Ocean Environment Dynamics (No. SOED1305)
文摘Ocean waves are the core environmental elements affecting the movements and structure design of ships. Statistical analysis of wave parameters is the basis for the establishment of long-term ship environmental adaptability prediction model. The observations from coastal stations, buoys, altimeters and volunteer ships that cover from 1993 to 2011 were interpolated into miller Ion-lat grids by using bilinear method and the analytical fields of ocean waves were given. By using optimal interpolation, the analysis wave fields were assimilated into the WAVEWATCH III (WW3) simulation results. From the assimilated results, the wave rose statistics, the wave height of muitiyear return period and the extreme 2-D wave spectrum are related to the ship seakeeping were calculated. Finally, the wave statistics in China offshore were analyzed in detail.
基金sponsored by The Science and Technology Research Project,Shengli Oilfield (Grant No. YKW1002)
文摘Finding channel sandbodies is an important task in oil and gas exploration due to the importance of fluvial reservoirs. It is difficult to describe fluvial reservoirs in detail owing to their frequent changes and serious intersections, as well as limitations of S/N ratio and seismic data resolution. Based on the Laohekou 3D data in Shengli Oilfield, we analyze the general characteristics of fluvial reservoirs in this area, from which we find that they are characterized by strong amplitudes on seismic profiles, high continuity on time slices, and low frequency in the frequency domain. In addition, a cluster of strong string-bead- like reflections was found after color processing and detailed interpretation. To understand this observation, we conduct forward modeling to explain the mechanism. This provides a new way to identify ancient channels in similar areas. By using the multi-attribute fusion and RGB display techniques, channel incision is more obvious and the characteristics of the channel structures are manifested much better. Finally, we introduce and apply multi-wavelet detection technology to identify weaker fluvial reservoir signals.
文摘The flooding characteristics of hydrofoil impeller were systematically investigated in a two-and three-phase 383 mm i.d. stirred tank operated on air, water and spherical glass beads. The volumetric solid concen-tration Cs was varied from 0 to 25%. And the superficial gas velocity Ug was at the range of 0-0.096 m·s-1. A fast and objective method for identifying flooding point NF is developed based on the statistical analysis of the pressure fluctuation signals. It is found, the effect of solid concentration on the flooding point NF depends on the gas velocity. At the lower gas velocity (Ug = 0.010 m·s-1), the solid concentration has only a minor effect. However, it displays a very significant effect on the flooding point NF at the medium and high gas velocity. The flooding point NF linearly increases with the gas velocity Ug, at lower solid concentration (Cs = 0, 10%). When Cs = 20%, the behavior of NF versus Ug becomes more complex. The correlations of the flooding characteristics in the slurry stirred tank are proposed by considering the solid concentration effect.
文摘Biot' s two-phase theory for fluid-saturated porous media was applied in a study carried out to investigate the influence of water saturation on propagation of elastic wave in transversely isotropic nearly saturated soil. The characteristic equations for wave propagation were derived and solved analytically. The results showed that there are four waves: the first and second quasi-longitudinal waves (QP1 and QP2), the quasitransverse wave (QSV) and the anti-plane transverse wave (SH) . Numerical results are given to illustrate theinfluence of saturation on the velocity, dispersion and attenuation of the four body waves. Some typical numerical results are discussed and plotted. The results can be meaningful for soil dynamics and earthquake engineering.
基金Project (No. 2006J0017) supported by the Natural Science Foundation of Fujian Province, China
文摘Determination of relative three-dimensional (3D) position, orientation, and relative motion between two reference frames is an important problem in robotic guidance, manipulation, and assembly as well as in other fields such as photogrammetry. A solution to pose and motion estimation problem that uses two-dimensional (2D) intensity images from a single camera is desirable for real-time applications. The difficulty in performing this measurement is that the process of projecting 3D object features to 2D images is a nonlinear transformation. In this paper, the 3D transformation is modeled as a nonlinear stochastic system with the state estimation providing six degrees-of-freedom motion and position values, using line features in image plane as measuring inputs and dual quaternion to represent both rotation and translation in a unified notation. A filtering method called the Gaussian particle filter (GPF) based on the panicle filtering concept is presented for 3D pose and motion estimation of a moving target from monocular image sequences. The method has been implemented with simulated data, and simulation results are provided along with comparisons to the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) to show the relative advantages of the GPF. Simulation results showed that GPF is a superior alternative to EKF and UKF.
基金Project supported by the Natural Science Foundation of Liaoning Province (Grant No 20041021), the Scientific Foundation of the Educational Department of Liaoning Province (Grant No 2004C006) and the Postdoctoral Foundation of Shenyang University of Technology.
文摘The internal energy and specific heat of a Heisenberg ferro- antiferromagnetic double-layer system are studied by using spin-wave theory and the retarded Green function method at low temperatures. Numerical results show that the antiferromagnetic intralayer coupling J2 has an important influence on internal energy and specific heat for a four-sublattice system with antiferromagnetic (or ferrimagnetic) interlayer couplings.
文摘This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes second-order waves. The numerical results obtained for limiting cases of double-row and triple-row walls are in good agreement with results of previous studies and experimental results. Comparisons with experimental measurements of the reflection, transmission, and dissipation coefficients (CR, Cr, and CE) for double-row walls show that the proposed mathematical model adequately reproduces most of the important features. We found that for double-row walls, the CR increases with increasing wave number, kd, and with a decreasing permeable wall part, din. The Cr follows the opposite trend. The CE slowly increases with an increasing kd for lower kd values, reaches a maximum, and then decreases again. In addition, an increasing porosity of dm would significantly decrease the CR while increasing the Cr. At lower values of kd, a decreasing porosity increases the CE, but for high values of kd, a decreasing porosity reduces the Ce. The numerical results indicate that, for triple-row walls, the effect of the arrangement of the chamber widths on hydrodynamic characteristics is not significant, except when kd〈0.5 Double-row slotted breakwaters may exhibit a good wave-absorbing performance at kd〉0.5, where by the horizontal wave force may be smaller than that of a single wall. On the other hand, the difference between double-row and triple-row vertical slotted breakwaters is marginal.
基金the National Natural Science Foundation of China (No.60402032).
文摘This paper introduces a novel clutter power model of coastal compound and deduces the statistic characteristics and the arithmetics of model parameter estimation algorithm. Then, a novel coastal compound distributed model of the clutter amplitude is proposed and its statistic character- istics are studied. Subsequently, the nonlinear relation of autocorrelation function is deduced between the coastal compound clutter random sequences and the correlated Gaussian random sequences, which is the important prerequisite for the clutter simulation based on the ZMNL (Zero Memory NonLin- earity). Lastly, the advantage of the algorithm is demonstrated by a feasible simulation of the gen- eration of the random coastal compound clutter sequences.
文摘We obtain. the exact analytical results of all the eigenvalues and eigenstates for three kinds of models describing N-mode multiphoton process without using the assumption of the Bethe ansatz. The exact analytical results of all the eigenstates and eigenvalues are in terms of a parameter lambda for three kinds of models describing N-mode multiphoton process. The parameter is shown to be determined by the roots of a polynomial and is solvable analytically or numerically. Moreover, these three kinds of models can be processed with the same procedure.
基金supported by the National Natural Science Foundation of China (Grant No. 11072140)the State Key Laboratory of Ocean Engineering (Shanghai Jiao Tong University) (Grant No. 0803)+1 种基金the Innovation Program of Shanghai Municipal Education Commission (Grant No.09YZ04)The Shanghai Program for Innovative Research Team in Universities is also acknowledged
文摘An analytical method is developed for the hydroelastic interaction between surface incident waves and a thin elastic plate of arbitrary geometry floating on an inviscid fluid of finite depth in the framework of linear potential flow.Three kinds of edge conditions are considered and the corresponding analytical representations are derived in the polar coordinate system.According to the surface boundary conditions,the fluid domain is divided into two regions,namely,an open water region and a plate-covered region.With the assumption that all the motion is time-harmonic,the series solutions for the spatial velocity potentials are derived by the method of eigenfunction expansion.The matching conditions for the continuities of the velocity and pressure are transformed by taking the inner products successively with respect to the vertical eigenfunction for the free surface and the angular eigenfunction.A system of simultaneous equations,including two edge conditions and two matching conditions,is set up for deriving the expansion coefficients.As an example,numerical computation for the expansion coefficients of truncated series is performed for an elliptic plate.The results show that the method suggested here is useful to revealing the physical features of the gravity wave scattering in the open water and the hydroelastic response in the plate.
基金supported by the National Basic Research Program of China (Grant No. 2009CB724103)
文摘The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al. using direct numerical simulation (DNS). It was found that certain small-scale 3-D disturbances amplified rapidly. These disturbances exhibit the characteristics of second modes, and the most amplified components have a well- defined spanwise wavelength, indicating a clear selectivity of the amplification. In the case of a cone, the three-dimensionality of the base flow and the disturbances themselves may be responsible for the rapid amplification. In order to ascertain which of these two effects are essential, in this study we carried out DNS of the nonlinear evolution of a spanwise localized disturbance (wavepacket) in a flat-plate boundary layer. A similar amplification of small-scale disturbances was observed, suggesting that the direct reason for the rapid amplification is the three-dimensionality of the disturbances rather than the three-dimensional nature of the base flow, even though the latter does alter the spanwise distribution of the disturbance. The rapid growth of 3-D waves may be attributed to the secondary instability mechanism. Further simulations were performed for a wavepacket of first modes in a supersonic boundary layer and of Tollmien-Schlichting (T-S) waves in an incompressible boundary layer. The re- suits show that the amplifying components are in the band centered at zero spanwise wavenumber rather than at a finite spanwise wavenumber. It is therefore concluded that the rapid growth of 3-D disturbances in a band centered at a preferred large spanwise wavenumber is the main characteristic of nonlinear evolution of second mode disturbances in supersonic boundary layers.