Dynamically optimal models of atmospheric motion
A derivation of discrete dynamical equations for the dry atmosphere in the absence of dissipative processes based on the least action (i.e. Hamilton's) principle is presented. This approach can be considered the finite-element method applied to the calculation and minimization of the action. Th...
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| Vydané v: | Nonlinear processes in geophysics Ročník 31; číslo 4; s. 559 - 569 |
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| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
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Gottingen
Copernicus GmbH
05.12.2024
Copernicus Publications |
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| ISSN: | 1607-7946, 1023-5809, 1607-7946 |
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| Abstract | A derivation of discrete dynamical equations for the dry atmosphere in the absence of dissipative processes based on the least action (i.e. Hamilton's) principle is presented. This approach can be considered the finite-element method applied to the calculation and minimization of the action. The algorithm possesses the following characteristic features: For a given set of grid points and a given forward operator (i.e. the mode of interpolation), through the minimization of action, the algorithm ensures maximal closeness (in a broad sense) of the evolution of the discrete system to the motion of the continuous atmosphere (a dynamically optimal algorithm). The grid points can be irregularly spaced, allowing for variable spatial resolution. The spatial resolution can be adjusted locally while executing calculations. By using a set of tetrahedra as finite elements the algorithm ensures a better representation of the topography (piecewise linear rather than staircase). The algorithm automatically calculates the evolution of passive tracers by following the trajectories of the fluid particles, which ensures that all tracer properties required a priori are satisfied. For testing purposes, the algorithm is realized in 2D, and a numerical example representing a convection event is presented. |
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| AbstractList | A derivation of discrete dynamical equations for the dry atmosphere in the absence of dissipative processes based on the least action (i.e. Hamilton's) principle is presented. This approach can be considered the finite-element method applied to the calculation and minimization of the action. The algorithm possesses the following characteristic features:
For a given set of grid points and a given forward operator (i.e. the mode of interpolation), through the minimization of action, the algorithm ensures maximal closeness (in a broad sense) of the evolution of the discrete system to the motion of the continuous atmosphere (a dynamically optimal algorithm).
The grid points can be irregularly spaced, allowing for variable spatial resolution.
The spatial resolution can be adjusted locally while executing calculations.
By using a set of tetrahedra as finite elements the algorithm ensures a better representation of the topography (piecewise linear rather than staircase).
The algorithm automatically calculates the evolution of passive tracers by following the trajectories of the fluid particles, which ensures that all tracer properties required a priori are satisfied. For testing purposes, the algorithm is realized in 2D, and a numerical example representing a convection event is presented. A derivation of discrete dynamical equations for the dry atmosphere in the absence of dissipative processes based on the least action (i.e. Hamilton's) principle is presented. This approach can be considered the finite-element method applied to the calculation and minimization of the action. The algorithm possesses the following characteristic features: For a given set of grid points and a given forward operator (i.e. the mode of interpolation), through the minimization of action, the algorithm ensures maximal closeness (in a broad sense) of the evolution of the discrete system to the motion of the continuous atmosphere (a dynamically optimal algorithm). The grid points can be irregularly spaced, allowing for variable spatial resolution. The spatial resolution can be adjusted locally while executing calculations. By using a set of tetrahedra as finite elements the algorithm ensures a better representation of the topography (piecewise linear rather than staircase). The algorithm automatically calculates the evolution of passive tracers by following the trajectories of the fluid particles, which ensures that all tracer properties required a priori are satisfied. For testing purposes, the algorithm is realized in 2D, and a numerical example representing a convection event is presented. A derivation of discrete dynamical equations for the dry atmosphere in the absence of dissipative processes based on the least action (i.e. Hamilton's) principle is presented. This approach can be considered the finite-element method applied to the calculation and minimization of the action. The algorithm possesses the following characteristic features: For a given set of grid points and a given forward operator (i.e. the mode of interpolation), through the minimization of action, the algorithm ensures maximal closeness (in a broad sense) of the evolution of the discrete system to the motion of the continuous atmosphere (a dynamically optimal algorithm).The grid points can be irregularly spaced, allowing for variable spatial resolution.The spatial resolution can be adjusted locally while executing calculations.By using a set of tetrahedra as finite elements the algorithm ensures a better representation of the topography (piecewise linear rather than staircase).The algorithm automatically calculates the evolution of passive tracers by following the trajectories of the fluid particles, which ensures that all tracer properties required a priori are satisfied. For testing purposes, the algorithm is realized in 2D, and a numerical example representing a convection event is presented. |
| Author | Voronovich, Alexander G. |
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| Cites_doi | 10.1256/smsqj.52409 10.1017/S0022112083001706 10.1146/annurev.fl.20.010188.001301 10.1016/j.jcp.2018.10.038 10.1175/1520-0469(2004)061<2016:PATTCO>2.0.CO;2 10.1256/smsqj.51913 10.1017/S0022112089002934 10.1063/1.1706053 10.1017/S096249290100006X 10.1007/s10208-020-09473-w |
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| SubjectTerms | Algorithms Approximation Atmosphere Atmospheric motion Convection Discrete systems Entropy Evolution Evolutionary algorithms Finite element method Interpolation Mathematical analysis Optimization Ordinary differential equations Spatial resolution Tetrahedra Tracers |
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| Title | Dynamically optimal models of atmospheric motion |
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