On the basis of the perturbation, we present an approach to approximating rational surfaces by the interval Btzier surfaces using energy minimization method. The approach makes the perturbation surfaces have more rest...On the basis of the perturbation, we present an approach to approximating rational surfaces by the interval Btzier surfaces using energy minimization method. The approach makes the perturbation surfaces have more restrictions than the original surfaces. It could be combined with subdivision method to obtain a piecewise interval polynomial approximation for a rational surface. The applications of this approach are illustrated too.展开更多
Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investi...Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investigated within the framework of linearized water wave theory. The effect of surface tension at the surface below the ice-cover is neglected. There exists only one wave number propagating at just below the ice-cover. A perturbation analysis is employed to solve the boundary value problem governed by Laplace＇s equation by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function and thereby evaluating the reflection and transmission coefficients approximately up to first order. A patch of sinusoidal ripples is considered as an example and the related coefficients are determined.展开更多
Atmospheric variability is driven not only by internal dynamics, but also by external forcing, such as soil states, SST, snow, sea-ice cover, and so on. To investigate the forecast uncertainties and effects of land su...Atmospheric variability is driven not only by internal dynamics, but also by external forcing, such as soil states, SST, snow, sea-ice cover, and so on. To investigate the forecast uncertainties and effects of land surface processes on numerical weather prediction, we added modules to perturb soil moisture and soil temperature into NCEP＇s Global Ensemble Forecast System （GEFS）, and compared the results of a set of experiments involving different configurations of land surface and atmospheric perturbation. It was found that uncertainties in different soil layers varied due to the multiple timescales of interactions between land surface and atmospheric processes. Perturbations of the soil moisture and soil temperature at the land surface changed sensible and latent heat flux obviously, as compared to the less or indirect land surface perturbation experiment from the day-to-day forecasts. Soil state perturbations led to greater variation in surface heat fluxes that transferred to the upper troposphere, thus reflecting interactions and the response to atmospheric external forcing. Various verification scores were calculated in this study. The results indicated that taking the uncertainties of land surface processes into account in GEFS could contribute a slight improvement in forecast skill in terms of resolution and reliability, a noticeable reduction in forecast error, as well as an increase in ensemble spread in an under-dispersive system. This paper provides a preliminary evaluation of the effects of land surface processes on predictability. Further research using more complex and suitable methods is needed to fully explore our understanding in this area.展开更多
In this paper, sound scattering from the sea surface in the Persian Gulf region is investigated. Chapman-Harris and Ogden-Erskine empirical relations coupled with perturbation theory are implemented. Based on the Ogde...In this paper, sound scattering from the sea surface in the Persian Gulf region is investigated. Chapman-Harris and Ogden-Erskine empirical relations coupled with perturbation theory are implemented. Based on the Ogden and Erskine＇s experiments, sound scattering from the sea surface has three different regimes in which two mechanisms of surface roughness and subsurface bubble clouds are involved. Ogden-Erskine＇s scattering relation which consists of perturbation theory and Chapman-Harris＇s scattering terms are verified by the experimental data of Critical Sea Tests 7. Subsequently, wind speed in the Persian Gulf is provided based on three data bases of Arzanah station, ERA40, and PERGOS. Accordingly, surface scattering strength in the Persian Gulf region is calculated at different grazing angles, frequencies and provided wind speeds. Based on the resulted values of scattering strength, scattered intensity from the sea surface is also studied. These studies indicate that both scattering strength and scattered intensity generally increase as grazing angle, frequency and wind speed increase.展开更多
For surface gravity waves propagating over a horizontal bottom that consists of a patch of sinusoidal ripples,strong wave reflection occurs under the Bragg resonance condition.The critical wave frequency,at which the ...For surface gravity waves propagating over a horizontal bottom that consists of a patch of sinusoidal ripples,strong wave reflection occurs under the Bragg resonance condition.The critical wave frequency,at which the peak reflection coefficient is obtained,has been observed in both physical experiments and direct numerical simulations to be downshifted from the well-known theoretical prediction.It has long been speculated that the downshift may be attributed to higher-order rippled bottom and free-surface boundary effects,but the intrinsic mechanism remains unclear.By a regular perturbation analysis,we derive the theoretical solution of frequency downshift due to third-order nonlinear effects of both bottom and free-surface boundaries.It is found that the bottom nonlinearity plays the dominant role in frequency downshift while the free-surface nonlinearity actually causes frequency upshift.The frequency downshift/upshift has a quadratic dependence in the bottom/free-surface steepness.Polychromatic bottom leads to a larger frequency downshift relative to the monochromatic bottom.In addition,direct numerical simulations based on the high-order spectral method are conducted to validate the present theory.The theoretical solution of frequency downshift compares well with the numerical simulations and available experimental data.展开更多
The main goal of this paper is to investigate sound scattering from the sea surface, by Kuo＇s small perturbation method （SPM）, in the Persian Gulf＇s environmental conditions. Accordingly the SPM method is reviewed...The main goal of this paper is to investigate sound scattering from the sea surface, by Kuo＇s small perturbation method （SPM）, in the Persian Gulf＇s environmental conditions. Accordingly the SPM method is reviewed, then it is demonstrated how it can accurately model sound scattering from the sea surface. Since in Kuo＇s approach, the effects of surface roughness and sub-surface bubble plumes on incident sounds can be studied separately, it is possible to investigate the importance of each mechanism in various scattering regimes. To conduct this study, wind and wave information reported by Arzanah station as well as some numerical atmospheric models for the Persian Gulf are presented and applied to examine sound scattering from the sea surface in the Persian Gulf region. Plots of scattering strength by Kuo＇s SPM method versus grazing angle for various frequencies, wave heights, and wind speeds are presented. The calculated scattering strength by the SPM method for various frequencies and wind speeds are compared against the results of critical sea tests 7 （CST-7）. The favorable agreement achieved for sound scattering in the Persian Gulf region is indicative of the fact that the SPM method can quite accurately model and predict sound scattering from the sea surface.展开更多
We present the results of an investigation into the behavior of the unsteady flow of a Casson Micropolar nanofluid over a shrinking/stretching curved surface,together with a heat transfer analysis of the same problem....We present the results of an investigation into the behavior of the unsteady flow of a Casson Micropolar nanofluid over a shrinking/stretching curved surface,together with a heat transfer analysis of the same problem.The body force acting perpendicular to the surface wall is in charge of regulating the fluid flow rate.Curvilinear coordinates are used to account for the considered curved geometry and a set of balance equations for mass,momentum,energy and concentration is obtained accordingly.These are turned into ordinary differential equations using a similarity transformation.We show that these equations have dual solutions for a number of different combinations of various parameters.The stability of such solutions is investigated by applying perturbations on the steady states.It is found that high values of the Micropolar and Casson parameters cause the flow to move more slowly.However,when compared to a shrunken surface,a stretched surface produces a greater Micro-rotation flux.展开更多
基金Project supported by Inner Mongolia University of Science and Technology (No.X200829)
文摘On the basis of the perturbation, we present an approach to approximating rational surfaces by the interval Btzier surfaces using energy minimization method. The approach makes the perturbation surfaces have more restrictions than the original surfaces. It could be combined with subdivision method to obtain a piecewise interval polynomial approximation for a rational surface. The applications of this approach are illustrated too.
文摘Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investigated within the framework of linearized water wave theory. The effect of surface tension at the surface below the ice-cover is neglected. There exists only one wave number propagating at just below the ice-cover. A perturbation analysis is employed to solve the boundary value problem governed by Laplace＇s equation by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function and thereby evaluating the reflection and transmission coefficients approximately up to first order. A patch of sinusoidal ripples is considered as an example and the related coefficients are determined.
基金supported by the National Fundamental(973) Research Program of China(Grant No.2013CB430100)the Special Fund for Meteorological Scientific Research in the Public Interest(Grant No.GYHY201506005)the National Natural Science Foundation of China(Grant Nos.41475097,41075079,41275065 and 41475054)
文摘Atmospheric variability is driven not only by internal dynamics, but also by external forcing, such as soil states, SST, snow, sea-ice cover, and so on. To investigate the forecast uncertainties and effects of land surface processes on numerical weather prediction, we added modules to perturb soil moisture and soil temperature into NCEP＇s Global Ensemble Forecast System （GEFS）, and compared the results of a set of experiments involving different configurations of land surface and atmospheric perturbation. It was found that uncertainties in different soil layers varied due to the multiple timescales of interactions between land surface and atmospheric processes. Perturbations of the soil moisture and soil temperature at the land surface changed sensible and latent heat flux obviously, as compared to the less or indirect land surface perturbation experiment from the day-to-day forecasts. Soil state perturbations led to greater variation in surface heat fluxes that transferred to the upper troposphere, thus reflecting interactions and the response to atmospheric external forcing. Various verification scores were calculated in this study. The results indicated that taking the uncertainties of land surface processes into account in GEFS could contribute a slight improvement in forecast skill in terms of resolution and reliability, a noticeable reduction in forecast error, as well as an increase in ensemble spread in an under-dispersive system. This paper provides a preliminary evaluation of the effects of land surface processes on predictability. Further research using more complex and suitable methods is needed to fully explore our understanding in this area.
文摘In this paper, sound scattering from the sea surface in the Persian Gulf region is investigated. Chapman-Harris and Ogden-Erskine empirical relations coupled with perturbation theory are implemented. Based on the Ogden and Erskine＇s experiments, sound scattering from the sea surface has three different regimes in which two mechanisms of surface roughness and subsurface bubble clouds are involved. Ogden-Erskine＇s scattering relation which consists of perturbation theory and Chapman-Harris＇s scattering terms are verified by the experimental data of Critical Sea Tests 7. Subsequently, wind speed in the Persian Gulf is provided based on three data bases of Arzanah station, ERA40, and PERGOS. Accordingly, surface scattering strength in the Persian Gulf region is calculated at different grazing angles, frequencies and provided wind speeds. Based on the resulted values of scattering strength, scattered intensity from the sea surface is also studied. These studies indicate that both scattering strength and scattered intensity generally increase as grazing angle, frequency and wind speed increase.
基金financially supported by the National Natural Science Foundation of China (Grant Nos. U1706230 and51379071)the Key Project of NSFC-Shandong Joint Research Funding POW3C (Grant No. U1906230)the National Science Fund for Distinguished Young Scholars (Grant No. 51425901)
文摘For surface gravity waves propagating over a horizontal bottom that consists of a patch of sinusoidal ripples,strong wave reflection occurs under the Bragg resonance condition.The critical wave frequency,at which the peak reflection coefficient is obtained,has been observed in both physical experiments and direct numerical simulations to be downshifted from the well-known theoretical prediction.It has long been speculated that the downshift may be attributed to higher-order rippled bottom and free-surface boundary effects,but the intrinsic mechanism remains unclear.By a regular perturbation analysis,we derive the theoretical solution of frequency downshift due to third-order nonlinear effects of both bottom and free-surface boundaries.It is found that the bottom nonlinearity plays the dominant role in frequency downshift while the free-surface nonlinearity actually causes frequency upshift.The frequency downshift/upshift has a quadratic dependence in the bottom/free-surface steepness.Polychromatic bottom leads to a larger frequency downshift relative to the monochromatic bottom.In addition,direct numerical simulations based on the high-order spectral method are conducted to validate the present theory.The theoretical solution of frequency downshift compares well with the numerical simulations and available experimental data.
文摘The main goal of this paper is to investigate sound scattering from the sea surface, by Kuo＇s small perturbation method （SPM）, in the Persian Gulf＇s environmental conditions. Accordingly the SPM method is reviewed, then it is demonstrated how it can accurately model sound scattering from the sea surface. Since in Kuo＇s approach, the effects of surface roughness and sub-surface bubble plumes on incident sounds can be studied separately, it is possible to investigate the importance of each mechanism in various scattering regimes. To conduct this study, wind and wave information reported by Arzanah station as well as some numerical atmospheric models for the Persian Gulf are presented and applied to examine sound scattering from the sea surface in the Persian Gulf region. Plots of scattering strength by Kuo＇s SPM method versus grazing angle for various frequencies, wave heights, and wind speeds are presented. The calculated scattering strength by the SPM method for various frequencies and wind speeds are compared against the results of critical sea tests 7 （CST-7）. The favorable agreement achieved for sound scattering in the Persian Gulf region is indicative of the fact that the SPM method can quite accurately model and predict sound scattering from the sea surface.
文摘We present the results of an investigation into the behavior of the unsteady flow of a Casson Micropolar nanofluid over a shrinking/stretching curved surface,together with a heat transfer analysis of the same problem.The body force acting perpendicular to the surface wall is in charge of regulating the fluid flow rate.Curvilinear coordinates are used to account for the considered curved geometry and a set of balance equations for mass,momentum,energy and concentration is obtained accordingly.These are turned into ordinary differential equations using a similarity transformation.We show that these equations have dual solutions for a number of different combinations of various parameters.The stability of such solutions is investigated by applying perturbations on the steady states.It is found that high values of the Micropolar and Casson parameters cause the flow to move more slowly.However,when compared to a shrunken surface,a stretched surface produces a greater Micro-rotation flux.
