In this paper, we experimentally investigate the pattern transition of two-dimensional Faraday waves at an extremely shallow depth in a Hele-Shaw cell. Several patterns of Faraday waves are observed, which have some s...In this paper, we experimentally investigate the pattern transition of two-dimensional Faraday waves at an extremely shallow depth in a Hele-Shaw cell. Several patterns of Faraday waves are observed, which have some significant differences in wave profile,wave height and wave length. It is found that, in a wide range of the forcing frequency f, there always exists a region of the acceleration amplitude A, in which there exist the so-called hysteretic jumps between different patterns of Faraday waves. All of these experimental observations could enrich our knowledges about the Faraday waves and would be helpful to the further theoretical studies on the related topic in future.展开更多
A steady plane subsonic compressible non-isothermal Couette gas flow is analyzed for moderately high and low Reynolds numbers.The flow channel is formed by two plates in relative motion.Two cases are considered:(a) is...A steady plane subsonic compressible non-isothermal Couette gas flow is analyzed for moderately high and low Reynolds numbers.The flow channel is formed by two plates in relative motion.Two cases are considered:(a) isothermal walls where the temperatures of the plates are equal and constant and(b) with constant but different plate temperatures.The Knudsen number is Kn 0.1,which corresponds to the slip and continuum flow.The flow is defined by continuity,Navier-Stokes and energy continuum equations,along with the velocity slip and the temperature jump first order boundary conditions.An analytical solution for velocity and temperature is obtained by developing a perturbation scheme.The first approximation corresponds to the continuum flow conditions,while the others represent the contribution of the rarefaction effect.In addition,a numerical solution of the problems is given to confirm the accuracy of the analytical results.The exact analytical solution,for constant viscosity and conductivity is found for the isothermal walls case as well.It is shown that it is entirely a substitution to the exact numerical solution for the isothermal walls case.展开更多
基金supported by the National Key Basic Research Program of China(Grant No.2014CB046801)
文摘In this paper, we experimentally investigate the pattern transition of two-dimensional Faraday waves at an extremely shallow depth in a Hele-Shaw cell. Several patterns of Faraday waves are observed, which have some significant differences in wave profile,wave height and wave length. It is found that, in a wide range of the forcing frequency f, there always exists a region of the acceleration amplitude A, in which there exist the so-called hysteretic jumps between different patterns of Faraday waves. All of these experimental observations could enrich our knowledges about the Faraday waves and would be helpful to the further theoretical studies on the related topic in future.
基金supported by the Ministry of Science of the Republic of Serbia (Grant No.174014)
文摘A steady plane subsonic compressible non-isothermal Couette gas flow is analyzed for moderately high and low Reynolds numbers.The flow channel is formed by two plates in relative motion.Two cases are considered:(a) isothermal walls where the temperatures of the plates are equal and constant and(b) with constant but different plate temperatures.The Knudsen number is Kn 0.1,which corresponds to the slip and continuum flow.The flow is defined by continuity,Navier-Stokes and energy continuum equations,along with the velocity slip and the temperature jump first order boundary conditions.An analytical solution for velocity and temperature is obtained by developing a perturbation scheme.The first approximation corresponds to the continuum flow conditions,while the others represent the contribution of the rarefaction effect.In addition,a numerical solution of the problems is given to confirm the accuracy of the analytical results.The exact analytical solution,for constant viscosity and conductivity is found for the isothermal walls case as well.It is shown that it is entirely a substitution to the exact numerical solution for the isothermal walls case.
