Finescale spiral rainbands associated with Typhoon Rananim （2004） with the band length ranging from 10 to nearly 100 km and band width varying from 5 to 15 km are simulated using the Fifth-Generation NCAR/Penn State...Finescale spiral rainbands associated with Typhoon Rananim （2004） with the band length ranging from 10 to nearly 100 km and band width varying from 5 to 15 km are simulated using the Fifth-Generation NCAR/Penn State Mesoscale Model （MM5）. The finescale rainbands have two types： one intersecting the eyewall and causing damaging wind streaks, and the other distributed azimuthally along the inner edge of the eyewall with a relatively short lifetime. The formation of the high-velocity wind streaks results from the interaction of the azimuthal flow with the banded vertical vorticity structure triggered by tilting of the horizontal vorticity. The vertical advection of azimuthal momentum also leads to acceleration of tangential flow at a relatively high Mtitude. The evolution and structures of the bands are also examined in this study. Further investigation suggests that the boundary inflection points are related tightly to the development of the finescale rainbands, consistent with previous findings using simple symmetric models. In particular; the presence of the level of inflow reversal in the boundary layer is a crucial factor controlling the formation of these bands. The near-surface wavy peaks of vertical vorticity always follow the inflection points in radial flow. The mesoscale vortices and associated convective updrafts in the eyewall are considered to strengthen the activity of finescale bands, and the updrafts can trigger the formation of the bands as they reside in the environment with inflow reversal in the boundary layer.展开更多
We study spatially semidiscrete and fully discrete two-scale composite nite element method for approximations of the nonlinear parabolic equations with homogeneous Dirichlet boundary conditions in a convex polygonal d...We study spatially semidiscrete and fully discrete two-scale composite nite element method for approximations of the nonlinear parabolic equations with homogeneous Dirichlet boundary conditions in a convex polygonal domain in the plane.This new class of nite elements,which is called composite nite elements,was rst introduced by Hackbusch and Sauter[Numer.Math.,75(1997),pp.447-472]for the approximation of partial di erential equations on domains with complicated geometry.The aim of this paper is to introduce an effcient numerical method which gives a lower dimensional approach for solving partial di erential equations by domain discretization method.The composite nite element method introduces two-scale grid for discretization of the domain,the coarse-scale and the ne-scale grid with the degrees of freedom lies on the coarse-scale grid only.While the ne-scale grid is used to resolve the Dirichlet boundary condition,the dimension of the nite element space depends only on the coarse-scale grid.As a consequence,the resulting linear system will have a fewer number of unknowns.A continuous,piecewise linear composite nite element space is employed for the space discretization whereas the time discretization is based on both the backward Euler and the Crank-Nicolson methods.We have derived the error estimates in the L^(∞)(L^(2))-norm for both semidiscrete and fully discrete schemes.Moreover,numerical simulations show that the proposed method is an efficient method to provide a good approximate solution.展开更多
基金supported by the National Basic Research Program of China (2009CB421505)the National Natural Science Foundation of China under Grants Nos.40730948+5 种基金the National Natural Science Foundation of China under Grants Nos.40575030the National Natural Science Foundation of China under Grants Nos.40705024the Shanghai Typhoon Foundation (2009ST09)supported by the National Nature Science Foundation of China under the Grant No.40675060the program of the Ministry of Science and Technology of the People's Republic of China (2006AA09Z151)the program of China Meteorological Administration(GYHY200706031)
文摘Finescale spiral rainbands associated with Typhoon Rananim （2004） with the band length ranging from 10 to nearly 100 km and band width varying from 5 to 15 km are simulated using the Fifth-Generation NCAR/Penn State Mesoscale Model （MM5）. The finescale rainbands have two types： one intersecting the eyewall and causing damaging wind streaks, and the other distributed azimuthally along the inner edge of the eyewall with a relatively short lifetime. The formation of the high-velocity wind streaks results from the interaction of the azimuthal flow with the banded vertical vorticity structure triggered by tilting of the horizontal vorticity. The vertical advection of azimuthal momentum also leads to acceleration of tangential flow at a relatively high Mtitude. The evolution and structures of the bands are also examined in this study. Further investigation suggests that the boundary inflection points are related tightly to the development of the finescale rainbands, consistent with previous findings using simple symmetric models. In particular; the presence of the level of inflow reversal in the boundary layer is a crucial factor controlling the formation of these bands. The near-surface wavy peaks of vertical vorticity always follow the inflection points in radial flow. The mesoscale vortices and associated convective updrafts in the eyewall are considered to strengthen the activity of finescale bands, and the updrafts can trigger the formation of the bands as they reside in the environment with inflow reversal in the boundary layer.
基金The author gratefully acknowledges valuable support provided by the Department of Mathematics,NIT Calicut and the DST,Government of India,for providing support to carry out this work under the scheme TIST(No.SR/FST/MS-I/2019/40).
文摘We study spatially semidiscrete and fully discrete two-scale composite nite element method for approximations of the nonlinear parabolic equations with homogeneous Dirichlet boundary conditions in a convex polygonal domain in the plane.This new class of nite elements,which is called composite nite elements,was rst introduced by Hackbusch and Sauter[Numer.Math.,75(1997),pp.447-472]for the approximation of partial di erential equations on domains with complicated geometry.The aim of this paper is to introduce an effcient numerical method which gives a lower dimensional approach for solving partial di erential equations by domain discretization method.The composite nite element method introduces two-scale grid for discretization of the domain,the coarse-scale and the ne-scale grid with the degrees of freedom lies on the coarse-scale grid only.While the ne-scale grid is used to resolve the Dirichlet boundary condition,the dimension of the nite element space depends only on the coarse-scale grid.As a consequence,the resulting linear system will have a fewer number of unknowns.A continuous,piecewise linear composite nite element space is employed for the space discretization whereas the time discretization is based on both the backward Euler and the Crank-Nicolson methods.We have derived the error estimates in the L^(∞)(L^(2))-norm for both semidiscrete and fully discrete schemes.Moreover,numerical simulations show that the proposed method is an efficient method to provide a good approximate solution.
