06 Feb 2024
 | 06 Feb 2024

Dynamically-optimal models of atmospheric motion

Alexander Voronovich

Abstract. A derivation of a dynamical core 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: (1) For a given set of grid points and a given forward operator the algorithm ensures through the minimization of action maximal closeness (in a broad sense) of the evolution of the discrete system to the motion of the continuous atmosphere (a dynamically-optimal algorithm); (2) The grid points can be irregularly spaced allowing for variable spatial resolution; (3) The spatial resolution can be adjusted locally while executing calculations; (4) By using a set of tetrahedra as finite elements the algorithm ensures a better representation of the topography (piecewise linear rather than staircase); (5) The algorithm automatically calculates the evolution of passive tracers by following the trajectories of the fluid particles, which ensures that all a priori required tracer properties 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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Alexander Voronovich

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2024-303', Anonymous Referee #1, 27 Feb 2024
    • AC1: 'Reply on RC1', Alexander Voronovich, 29 Feb 2024
  • RC2: 'Comment on egusphere-2024-303', Anonymous Referee #2, 08 May 2024
  • RC3: 'Comment on egusphere-2024-303', Anonymous Referee #3, 21 May 2024
Alexander Voronovich
Alexander Voronovich


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Short summary
The paper presents in a novel way of obtaining the ordinary differential equations representing evolution of a continuous atmosphere that is based on the least action (i.e., Hamilton’s) principle. The equations represent dynamics of the atmosphere unambiguously and in a certain sense most accurately. The algorithm possesses characteristic features which are beneficial for a dynamical core; in particular, the algorithm allows changing spatial resolution in the course of calculations.