This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-(3+1)- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmet...This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-(3+1)- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmetry algebra, symmetry group and group-invariant solutions are analysed. Otherwise, some exact explicit solutions are obtained from the corresponding (2+1)-dimensional equation, the inviscid barotropic nondivergent vorticy equation. To show the properties and characters of these solutions, some plots as well as their possible physical meanings of the atmospheric circulation are given out.展开更多
By means of the reductive perturbation method, three types of generalized (2+l)-dimensional Kadomtsev- Petviashvili (KP) equations are derived from the baroclinic potential vorticity (BPV) equation, including t...By means of the reductive perturbation method, three types of generalized (2+l)-dimensional Kadomtsev- Petviashvili (KP) equations are derived from the baroclinic potential vorticity (BPV) equation, including the modified KP (mKP) equation, standard KP equation and cylindrical KP (cKP) equation. Then some solutions of generalized cKP and KP equations with certain conditions are given directly and a relationship between the generalized mKP equation and the mKP equation is established by the symmetry group direct method proposed by Lou et al. From the relationship and the solutions of the mKP equation, some solutions of the generalized mKP equation can be obtained. Furthermore, some approximate solutions of the baroclinic potential vorticity equation are derived from three types of generalized KP equations.展开更多
Vortex double layers (VDLs) and vortex projectiles (VPs) are the essential coherent structures which emerge in the shock excited (s/f/s) planar parallel "curtain" simulations of a 2D shock tube with PPM. The...Vortex double layers (VDLs) and vortex projectiles (VPs) are the essential coherent structures which emerge in the shock excited (s/f/s) planar parallel "curtain" simulations of a 2D shock tube with PPM. These opposite signed layers, formed by shock induced baroclinic deposition of vorticity, "ind" and are strongly affected by secondary reflected shocks and vortex interactions. In our visiometric mode of working, we quantify several of these processes and introduce time epochs to discuss the emerging phenomena and normalizations to scale (collapse) the data at M =1.5 and 2.0. This versatile configuration, easily obtained in the laboratory, allows us to study the formation, evolution and reacceleration of VPs and stratified turbulence and mixing.展开更多
Starting from the primary equations and using the method of multiple timescale, theauthor derives three stages of baroclinic atm ospheric motion, i.e. the stage of geostrophicadaptation the stage of quasi-geostrophic ...Starting from the primary equations and using the method of multiple timescale, theauthor derives three stages of baroclinic atm ospheric motion, i.e. the stage of geostrophicadaptation the stage of quasi-geostrophic potential vorticity adaptation and the balanced state.The potential vorticity adaptation comes into being through the process in which long wavesdisperse unbalanced energy. It is demonstrated by means of energy variation that under non-linear condition, the quasi-geostrophic evolution in which the potential vorticity conserves in-evitably leads to a quasi-balanced state. In this balanced state isolines of energy, stream lines andisohypses run parallel with each other. The first order approximation of this balanced stateis the so-called balance equation. Thus in nonlinear atmosphere this balanced state is moregeneral than the quasi-geostrophic balance. This result is significant for mid-range and long-range weather evolution.展开更多
The adjoint sensitivity related to explosive cyclogenesis in a conditionally unstable atmosphere is investigated in this study.The PSU/NCAR limited-area,nonhydrostatic primitive equation numerical model MM5 and its ad...The adjoint sensitivity related to explosive cyclogenesis in a conditionally unstable atmosphere is investigated in this study.The PSU/NCAR limited-area,nonhydrostatic primitive equation numerical model MM5 and its adjoint system are employed for numerical simulation and adjoint computation,respectively.To ensure the explosive development of a baroclinic wave,the forecast model is initialized with an idealized condition including an idealized two-dimensional baroclinic jet with a balanced three-dimensional moderateamplitude disturbance,derived from a potential vorticity inversion technique.Firstly,the validity period of the tangent linear model for this idealized baroclinic wave case is discussed,considering different initial moisture distributions and a dry condition.Secondly,the 48-h forecast surface pressure center and the vertical component of the relative vorticity of the cyclone are selected as the response functions for adjoint computation in a dry and moist environment,respectively.The preliminary results show that the validity of the tangent linear assumption for this idealized baroclinic wave case can extend to 48 h with intense moist convection,and the validity period can last even longer in the dry adjoint integration.Adjoint sensitivity analysis indicates that the rapid development of the idealized baroclinic wave is sensitive to the initial wind and temperature perturbations around the steering level in the upstream.Moreover,the moist adjoint sensitivity can capture a secondary high sensitivity center in the upper troposphere,which cannot be depicted in the dry adjoint run.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10735030,90718041 and 40975038)Shanghai Leading Academic Discipline Project(Grant No.B412)Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT0734)
文摘This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-(3+1)- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmetry algebra, symmetry group and group-invariant solutions are analysed. Otherwise, some exact explicit solutions are obtained from the corresponding (2+1)-dimensional equation, the inviscid barotropic nondivergent vorticy equation. To show the properties and characters of these solutions, some plots as well as their possible physical meanings of the atmospheric circulation are given out.
基金supported by National Natural Science Foundation of China (Grant Nos.10735030 and 40775042)Ningbo Natural Science Foundation (Grant No. 2008A610017)+1 种基金National Basic Research Program of China (973 Program) (Grant Nos. 2005CB422301 and 2007CB814800)K.C. Wong Magna Fund in Ningbo University
文摘By means of the reductive perturbation method, three types of generalized (2+l)-dimensional Kadomtsev- Petviashvili (KP) equations are derived from the baroclinic potential vorticity (BPV) equation, including the modified KP (mKP) equation, standard KP equation and cylindrical KP (cKP) equation. Then some solutions of generalized cKP and KP equations with certain conditions are given directly and a relationship between the generalized mKP equation and the mKP equation is established by the symmetry group direct method proposed by Lou et al. From the relationship and the solutions of the mKP equation, some solutions of the generalized mKP equation can be obtained. Furthermore, some approximate solutions of the baroclinic potential vorticity equation are derived from three types of generalized KP equations.
文摘Vortex double layers (VDLs) and vortex projectiles (VPs) are the essential coherent structures which emerge in the shock excited (s/f/s) planar parallel "curtain" simulations of a 2D shock tube with PPM. These opposite signed layers, formed by shock induced baroclinic deposition of vorticity, "ind" and are strongly affected by secondary reflected shocks and vortex interactions. In our visiometric mode of working, we quantify several of these processes and introduce time epochs to discuss the emerging phenomena and normalizations to scale (collapse) the data at M =1.5 and 2.0. This versatile configuration, easily obtained in the laboratory, allows us to study the formation, evolution and reacceleration of VPs and stratified turbulence and mixing.
文摘Starting from the primary equations and using the method of multiple timescale, theauthor derives three stages of baroclinic atm ospheric motion, i.e. the stage of geostrophicadaptation the stage of quasi-geostrophic potential vorticity adaptation and the balanced state.The potential vorticity adaptation comes into being through the process in which long wavesdisperse unbalanced energy. It is demonstrated by means of energy variation that under non-linear condition, the quasi-geostrophic evolution in which the potential vorticity conserves in-evitably leads to a quasi-balanced state. In this balanced state isolines of energy, stream lines andisohypses run parallel with each other. The first order approximation of this balanced stateis the so-called balance equation. Thus in nonlinear atmosphere this balanced state is moregeneral than the quasi-geostrophic balance. This result is significant for mid-range and long-range weather evolution.
基金Supported by the National(Key)Basic Research and Development(973)Program of China(2012CB417201)China Meteorological Administration Special Public Welfare Research Fund(GYHY201006004)National Natural Science Foundation of China(41275055 and 41275059)
文摘The adjoint sensitivity related to explosive cyclogenesis in a conditionally unstable atmosphere is investigated in this study.The PSU/NCAR limited-area,nonhydrostatic primitive equation numerical model MM5 and its adjoint system are employed for numerical simulation and adjoint computation,respectively.To ensure the explosive development of a baroclinic wave,the forecast model is initialized with an idealized condition including an idealized two-dimensional baroclinic jet with a balanced three-dimensional moderateamplitude disturbance,derived from a potential vorticity inversion technique.Firstly,the validity period of the tangent linear model for this idealized baroclinic wave case is discussed,considering different initial moisture distributions and a dry condition.Secondly,the 48-h forecast surface pressure center and the vertical component of the relative vorticity of the cyclone are selected as the response functions for adjoint computation in a dry and moist environment,respectively.The preliminary results show that the validity of the tangent linear assumption for this idealized baroclinic wave case can extend to 48 h with intense moist convection,and the validity period can last even longer in the dry adjoint integration.Adjoint sensitivity analysis indicates that the rapid development of the idealized baroclinic wave is sensitive to the initial wind and temperature perturbations around the steering level in the upstream.Moreover,the moist adjoint sensitivity can capture a secondary high sensitivity center in the upper troposphere,which cannot be depicted in the dry adjoint run.