The present paper discusses a class of nonlinear diffusion-convection equations with source. The method that we use is the conditional symmetry method. It is shown that the equation admits certain conditional symmetri...The present paper discusses a class of nonlinear diffusion-convection equations with source. The method that we use is the conditional symmetry method. It is shown that the equation admits certain conditional symmetries for coefficient functions of the equations. As a consequence, solutions to the resulting equations are obtained.展开更多
The peristaltic transport of viscous fluid in an asymmetric channel is concentrated. The channel walls exhibit convective boundary conditions. Both cases of hydrodynamic and magnetohydrodynamic(MHD) fluids are conside...The peristaltic transport of viscous fluid in an asymmetric channel is concentrated. The channel walls exhibit convective boundary conditions. Both cases of hydrodynamic and magnetohydrodynamic(MHD) fluids are considered. Mathematical analysis has been presented in a wave frame of reference. The resulting problems are non-dimensionalized. Long wavelength and low Reynolds number approximations are employed. Joule heating effect on the thermal equation is retained. Analytic solutions for stream function and temperature are constructed. Numerical integration is carried out for pressure rise per wavelength. Effects of influential flow parameters have been pointed out through graphs.展开更多
We used a two-dimensional quasi-geostrophic barotropic model simulation to study effects of an initial brows-like meso-scale vortex on tropical cyclone (TC) track. Our results show that the impact of each of the three...We used a two-dimensional quasi-geostrophic barotropic model simulation to study effects of an initial brows-like meso-scale vortex on tropical cyclone (TC) track. Our results show that the impact of each of the three foundational factors (the environ- mental current, the asymmetric structure and the asymmetric convection system) on TC track varies with time and the im- portance of each of the factors is different for the different TC motion time period. They show two kinds of the effects. One is a direct way. The asymmetric outer wind structure and the positive longitudinal wind speed averaged in radial-band (100-300) km in the period of (0-11) h are caused by the introduction of the initial brows-like meso-scale vortex, which results in TC track to turn to the north from the northwest directly. The other is an indirect influence. First, initial TC axisymmetric circula- tion becomes a non-axisyrnmetric circulation after the addition of the meso-scale vortex. The initial non-axisymmetric circula- tion experiences an axisymmetrizational process in the period of (0-11) h. Second, axisymmetrizationed TC horizontal size is enlarged after t=-12 h. Third, both the TC asymmetric structure and the TC energy dispersion induced-anticyclone are intensi- fied, which quickens the TC motion and results in the track to turn to the north indirectly. The TC motion is characterized by the unusual track under the direct and the indirect effect. The formation of the unusual track should be attributed to the com- mon effects of three factors, including the environmental flow, the TC asymmetric structure and the asymmetric convection system.展开更多
The NCEP/NCAR R1 reanalysis data are employed to investigate the impact of forced and inertial instability in the lower troposphere over the Arabian Sea on the onset process of Indian summer monsoon(ISM),and to reveal...The NCEP/NCAR R1 reanalysis data are employed to investigate the impact of forced and inertial instability in the lower troposphere over the Arabian Sea on the onset process of Indian summer monsoon(ISM),and to reveal the important role of zonal advection of zonal geostrophic momentum played in the forced unstable convection.Results show that during the ISM onset the zero absolute vorticity contour(??=0)shifts northward due to the strong cross-equatorial pressure gradient in the lower troposphere over southern Arabian Sea.Thus a region with negative absolute vorticity is generated near the equator in the northern hemisphere,manifesting the evident free inertial instability.When a southerly passes through this region,under the influence of friction a lower convergence that facilitates the convection flourishing at the lower latitudes appears to the north of zero absolute vorticity contour.However,owing to such a traditional inertial instability,the convection is confined near the equator which does not have direct influence on the ISM onset.On the contrary in the region to the north of the zero absolute vorticity contour and to the south of the low pressure center near the surface,although the atmosphere there is inertially stable,the lower westerly jet can develop and bring on the apparent zonal advection of zonal geostrophic momentum.Both theoretical study and diagnosing analysis present that such a zonal advection of geostrophic momentum is closely associated with the zonal asymmetric distribution of meridional land-sea thermal contrast,which induces a convergence center near and further north of the westerly jet in the lower troposphere over the southwestern coast of the Indian Peninsula,providing a favorable lower circulation for the ISM onset.It illustrates that the development of convection over the Arabian Sea in late spring and early summer is not only due to the frictional inertial instability but also strongly affected by the zonal asymmetric distribution of land-sea thermal contrast.Moreover,before the ISM onset due to the eastward development of the South Asian High(SAH)in the upper troposphere,high potential vorticity is transported to the region over the Arabian Sea.Then a local trumpet-shaped stream field is generated to cause the evident upper divergence-pumping effect which favors the ISM onset.When the upper divergence is vertically coupled with the lower convergence resulted from the aforementioned forced unstable convection development near the southwestern coast of Indian Peninsula,the atmospheric baroclinic unstable development is stimulated and the ISM onset is triggered.展开更多
The flow field distribution in centrifugal compressor is significantly affected by the non-axisymmetric geometry structure of the volute.The experimental and numerical simulation methods were adopted in this work to s...The flow field distribution in centrifugal compressor is significantly affected by the non-axisymmetric geometry structure of the volute.The experimental and numerical simulation methods were adopted in this work to study the compressor flow field distribution with different flow conditions.The results show that the pressure distribution in volute is characterized by the circumferential non-uniform phenomenon and the pressure fluctuation on the high static pressure zone propagates reversely to upstream,which results in the non-axisymmetric flow inside the compressor.The non-uniform level of pressure distribution in large flow condition is higher than that in small flow condition,its effect on the upstream flow field is also stronger.Additionally,the non-uniform circumferential pressure distribution in volute brings the non-axisymmetric flow at impeller outlet.In different flow conditions,the circumferential variation of the absolute flow angle at impeller outlet is also different.Meanwhile,the non-axisymmetric flow characteristics in internal impeller can be also reflected by the distribution of the mass flow.The high static pressure region of the volute corresponds to the decrease of mass flow in upstream blade channel,while the low static pressure zone of the volute corresponds to the increase of the mass flow.In small flow condition,the mass flow difference in the blade channel is bigger than that in the large flow condition.展开更多
In some rocket nozzle flows, the existence of the transition from FSS to RSS and the occurrence of asymmetric flow are known in previous researches. As a result, the transition causes excessive side-loads that may dam...In some rocket nozzle flows, the existence of the transition from FSS to RSS and the occurrence of asymmetric flow are known in previous researches. As a result, the transition causes excessive side-loads that may damage the nozzle. Thus, it is important to investigate the method in order to control the asymmetric flow separation. In the present study, the relationship between the asymmetric separation and the rate of change of the pressure ratio with time was investigated from the point of view of the transition from FSS to RSS in the supersonic nozzle experimentally. Further, change of the flow separation by using step and cavity, and the possibility of the control was demonstrated. As a result, it was shown that the method using a cavity was effective for the control of the separation pattern.展开更多
We prove the convergence of an adaptive mixed finite element method(AMFEM) for(nonsymmetric) convection-diffusion-reaction equations. The convergence result holds for the cases where convection or reaction is not pres...We prove the convergence of an adaptive mixed finite element method(AMFEM) for(nonsymmetric) convection-diffusion-reaction equations. The convergence result holds for the cases where convection or reaction is not present in convection- or reaction-dominated problems. A novel technique of analysis is developed by using the superconvergence of the scalar displacement variable instead of the quasi-orthogonality for the stress and displacement variables, and without marking the oscillation dependent on discrete solutions and data. We show that AMFEM is a contraction of the error of the stress and displacement variables plus some quantity. Numerical experiments confirm the theoretical results.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10371098 and the Program for New Century Excellent Talents in Universities under Grant No. NCET-04-0968.
文摘The present paper discusses a class of nonlinear diffusion-convection equations with source. The method that we use is the conditional symmetry method. It is shown that the equation admits certain conditional symmetries for coefficient functions of the equations. As a consequence, solutions to the resulting equations are obtained.
基金support from Higher Education Commission (HEC) of Pakistan through Ph.D Indigeous Scheme.
文摘The peristaltic transport of viscous fluid in an asymmetric channel is concentrated. The channel walls exhibit convective boundary conditions. Both cases of hydrodynamic and magnetohydrodynamic(MHD) fluids are considered. Mathematical analysis has been presented in a wave frame of reference. The resulting problems are non-dimensionalized. Long wavelength and low Reynolds number approximations are employed. Joule heating effect on the thermal equation is retained. Analytic solutions for stream function and temperature are constructed. Numerical integration is carried out for pressure rise per wavelength. Effects of influential flow parameters have been pointed out through graphs.
基金supported by,National Natural Science Foundation of China (Grant Nos.40775038,40875031,40975036 and 40730948)Wuxi Research Center for Environment Science and Technology
文摘We used a two-dimensional quasi-geostrophic barotropic model simulation to study effects of an initial brows-like meso-scale vortex on tropical cyclone (TC) track. Our results show that the impact of each of the three foundational factors (the environ- mental current, the asymmetric structure and the asymmetric convection system) on TC track varies with time and the im- portance of each of the factors is different for the different TC motion time period. They show two kinds of the effects. One is a direct way. The asymmetric outer wind structure and the positive longitudinal wind speed averaged in radial-band (100-300) km in the period of (0-11) h are caused by the introduction of the initial brows-like meso-scale vortex, which results in TC track to turn to the north from the northwest directly. The other is an indirect influence. First, initial TC axisymmetric circula- tion becomes a non-axisyrnmetric circulation after the addition of the meso-scale vortex. The initial non-axisymmetric circula- tion experiences an axisymmetrizational process in the period of (0-11) h. Second, axisymmetrizationed TC horizontal size is enlarged after t=-12 h. Third, both the TC asymmetric structure and the TC energy dispersion induced-anticyclone are intensi- fied, which quickens the TC motion and results in the track to turn to the north indirectly. The TC motion is characterized by the unusual track under the direct and the indirect effect. The formation of the unusual track should be attributed to the com- mon effects of three factors, including the environmental flow, the TC asymmetric structure and the asymmetric convection system.
基金supported jointly by the CAS Programme (Grant No. XDA11010402)the National Basic Research Program of China (Grant Nos. 2010CB950403, 2012CB417203)+1 种基金the National Natural Science Foundation of China (Grant No. 41275088)the Project founded by China Postdoctoral Science Foundation.
文摘The NCEP/NCAR R1 reanalysis data are employed to investigate the impact of forced and inertial instability in the lower troposphere over the Arabian Sea on the onset process of Indian summer monsoon(ISM),and to reveal the important role of zonal advection of zonal geostrophic momentum played in the forced unstable convection.Results show that during the ISM onset the zero absolute vorticity contour(??=0)shifts northward due to the strong cross-equatorial pressure gradient in the lower troposphere over southern Arabian Sea.Thus a region with negative absolute vorticity is generated near the equator in the northern hemisphere,manifesting the evident free inertial instability.When a southerly passes through this region,under the influence of friction a lower convergence that facilitates the convection flourishing at the lower latitudes appears to the north of zero absolute vorticity contour.However,owing to such a traditional inertial instability,the convection is confined near the equator which does not have direct influence on the ISM onset.On the contrary in the region to the north of the zero absolute vorticity contour and to the south of the low pressure center near the surface,although the atmosphere there is inertially stable,the lower westerly jet can develop and bring on the apparent zonal advection of zonal geostrophic momentum.Both theoretical study and diagnosing analysis present that such a zonal advection of geostrophic momentum is closely associated with the zonal asymmetric distribution of meridional land-sea thermal contrast,which induces a convergence center near and further north of the westerly jet in the lower troposphere over the southwestern coast of the Indian Peninsula,providing a favorable lower circulation for the ISM onset.It illustrates that the development of convection over the Arabian Sea in late spring and early summer is not only due to the frictional inertial instability but also strongly affected by the zonal asymmetric distribution of land-sea thermal contrast.Moreover,before the ISM onset due to the eastward development of the South Asian High(SAH)in the upper troposphere,high potential vorticity is transported to the region over the Arabian Sea.Then a local trumpet-shaped stream field is generated to cause the evident upper divergence-pumping effect which favors the ISM onset.When the upper divergence is vertically coupled with the lower convergence resulted from the aforementioned forced unstable convection development near the southwestern coast of Indian Peninsula,the atmospheric baroclinic unstable development is stimulated and the ISM onset is triggered.
基金sponsored by the National Natural Science Foundation of China(No.51276017)
文摘The flow field distribution in centrifugal compressor is significantly affected by the non-axisymmetric geometry structure of the volute.The experimental and numerical simulation methods were adopted in this work to study the compressor flow field distribution with different flow conditions.The results show that the pressure distribution in volute is characterized by the circumferential non-uniform phenomenon and the pressure fluctuation on the high static pressure zone propagates reversely to upstream,which results in the non-axisymmetric flow inside the compressor.The non-uniform level of pressure distribution in large flow condition is higher than that in small flow condition,its effect on the upstream flow field is also stronger.Additionally,the non-uniform circumferential pressure distribution in volute brings the non-axisymmetric flow at impeller outlet.In different flow conditions,the circumferential variation of the absolute flow angle at impeller outlet is also different.Meanwhile,the non-axisymmetric flow characteristics in internal impeller can be also reflected by the distribution of the mass flow.The high static pressure region of the volute corresponds to the decrease of mass flow in upstream blade channel,while the low static pressure zone of the volute corresponds to the increase of the mass flow.In small flow condition,the mass flow difference in the blade channel is bigger than that in the large flow condition.
文摘In some rocket nozzle flows, the existence of the transition from FSS to RSS and the occurrence of asymmetric flow are known in previous researches. As a result, the transition causes excessive side-loads that may damage the nozzle. Thus, it is important to investigate the method in order to control the asymmetric flow separation. In the present study, the relationship between the asymmetric separation and the rate of change of the pressure ratio with time was investigated from the point of view of the transition from FSS to RSS in the supersonic nozzle experimentally. Further, change of the flow separation by using step and cavity, and the possibility of the control was demonstrated. As a result, it was shown that the method using a cavity was effective for the control of the separation pattern.
基金supported by Education Science Foundation of Chongqing(Grant No.KJ120420)National Natural Science Foundation of China(Grant No.11171239)+1 种基金Major Research Plan of National Natural Science Foundation of China(Grant No.91430105)Open Fund of Key Laboratory of Mountain Hazards and Earth Surface Processes,Chinese Academy Sciences
文摘We prove the convergence of an adaptive mixed finite element method(AMFEM) for(nonsymmetric) convection-diffusion-reaction equations. The convergence result holds for the cases where convection or reaction is not present in convection- or reaction-dominated problems. A novel technique of analysis is developed by using the superconvergence of the scalar displacement variable instead of the quasi-orthogonality for the stress and displacement variables, and without marking the oscillation dependent on discrete solutions and data. We show that AMFEM is a contraction of the error of the stress and displacement variables plus some quantity. Numerical experiments confirm the theoretical results.
