We present numerical computations of a new wind-wave coupling theory that is governed by a system of nonlinear advance-delay differential equations (NLADDE). NLADDE are functional differential equations for which the ...We present numerical computations of a new wind-wave coupling theory that is governed by a system of nonlinear advance-delay differential equations (NLADDE). NLADDE are functional differential equations for which the derivative of an unknown function depends nonlinearly on the past (delayed), present, and future (advanced) values of the unknown function (if time is the independent variable). A practical numerical method for solving NLADDE is implemented, based on a collocation method. The method is tested for two problems with known analytic solutions and is shown to be numerically convergent. Numerical solutions to the coupled wind and wave problem reveal estimates of the wave height spectrum, the distribution of breaking waves (both depend on wave scale), as well as the vertical air-side profiles of turbulent stress and wind speed.展开更多
Meso-scale structures existing in the form of particle-rich clusters, streamers or strands in circulating fluidized beds, and of ascending bubble plumes and descending liquid-rich vortices in bubble columns and slurry...Meso-scale structures existing in the form of particle-rich clusters, streamers or strands in circulating fluidized beds, and of ascending bubble plumes and descending liquid-rich vortices in bubble columns and slurry-bed reactors, as commonly observed, have played an important role in the macro-scale behavior of particle-fluid systems. These meso-scale structures span a wide range of length and time scales, and their origin, evolution and influence are still far from being well understood.展开更多
The linear stability analysis of the fiber suspension Taylor-Couette flow against axisymmetric and non-axisymmetric disturbances is investigated. A generalized complex eigenvalue problem generated from the linearized ...The linear stability analysis of the fiber suspension Taylor-Couette flow against axisymmetric and non-axisymmetric disturbances is investigated. A generalized complex eigenvalue problem generated from the linearized set of the three-dimensional governing system equations around the basic Couette azimuthal solution are solved numerically with the Chebyshev spectral method. In a wide range of radius ratios and the magnitudes of counter rotating, critical bifurcation thresholds from the axisymmetric Couette flow to the flow with different azimuthal wave numbers are obtained. The complex dispersion relations of the linearized stability equation system for vortex patterns with different azimuthal wave number are calculated for real axial wave numbers for axially extended vortex structures.展开更多
基金supported by the U.S. National Science Foundation (Grant OCE- 0526177)the U.S. Office of Naval Research (Grant N00014-06-10729)supported by a WHOI/NOAA Cooperative Institute for Climate and Ocean Research Postdoctoral Scholarship
文摘We present numerical computations of a new wind-wave coupling theory that is governed by a system of nonlinear advance-delay differential equations (NLADDE). NLADDE are functional differential equations for which the derivative of an unknown function depends nonlinearly on the past (delayed), present, and future (advanced) values of the unknown function (if time is the independent variable). A practical numerical method for solving NLADDE is implemented, based on a collocation method. The method is tested for two problems with known analytic solutions and is shown to be numerically convergent. Numerical solutions to the coupled wind and wave problem reveal estimates of the wave height spectrum, the distribution of breaking waves (both depend on wave scale), as well as the vertical air-side profiles of turbulent stress and wind speed.
文摘Meso-scale structures existing in the form of particle-rich clusters, streamers or strands in circulating fluidized beds, and of ascending bubble plumes and descending liquid-rich vortices in bubble columns and slurry-bed reactors, as commonly observed, have played an important role in the macro-scale behavior of particle-fluid systems. These meso-scale structures span a wide range of length and time scales, and their origin, evolution and influence are still far from being well understood.
基金the Major Programof the National Natural Science Foundation of China with Grant No10632070
文摘The linear stability analysis of the fiber suspension Taylor-Couette flow against axisymmetric and non-axisymmetric disturbances is investigated. A generalized complex eigenvalue problem generated from the linearized set of the three-dimensional governing system equations around the basic Couette azimuthal solution are solved numerically with the Chebyshev spectral method. In a wide range of radius ratios and the magnitudes of counter rotating, critical bifurcation thresholds from the axisymmetric Couette flow to the flow with different azimuthal wave numbers are obtained. The complex dispersion relations of the linearized stability equation system for vortex patterns with different azimuthal wave number are calculated for real axial wave numbers for axially extended vortex structures.
