Invented Forces in Supercell Models

Abstract

This paper examines methods used in supercell models to maintain a steady, sheared, horizontally uniform environment with a three-force balance in the planetary boundary layer (PBL) and a two-force balance above it. Steady environments are maintained while ignoring the thermal-wind balance that permits large shear above the PBL. The Taylor-Proudman theorem indicates that wind profiles above the PBL must be unidirectional for balanced environments. In principle, supercell models that do not accommodate thermal advection should not support balanced steady environments with veering horizontally uniform winds.Recent methods add a permanent, pervasive, horizontal external force that varies only with height. By adding two more degrees of freedom, this force circumvents the Taylor-Proudman theorem and enables a static, horizontally uniform environment for any wind profile. It succeeds by adding spurious energy in lieu of flow towards low pressure to offset frictional loss of kinetic energy. However, the artificial force has downsides. It decouples the environmental horizontal equation of motion from the hydrostatic equation and the thermodynamics from the dynamics. It cancels environmental friction and the part of the Coriolis force that acts on the environmental wind. Within the storm, its curl can speciously generate significant horizontal vorticity near the ground. Inaccuracies arise in circulations around material circuits because of modifications by the artificial force and resulting miscalculations of parcel trajectories. Doubt is cast on conclusions about tornadogenesis drawn from recent simulations that contain an invented force.

Mathematical Modeling of Structure and Dynamics of Concentrated Tornado-like Vortices: A Review

“…In [111,112], it is proposed to use a certain fictitious force that creates false (artificial) horizontal vorticity. However, [113] notes that in meteorology, the laws of mass, energy, momentum, angular momentum, and entropy conservation must be inviolable. In [113], it is shown that rapid tornado genesis in modeling can be associated with a combination of the following factors: (1) excessively strong convective initiation in a very unstable atmosphere, which leads to too-strong low-level updraft at the beginning of the supercell's life; (2) the use of a lower boundary condition of semi-slip; (3) the absence of perturbations to excite significant turbulence, which leads to too-strong friction force and too-large shear in a toothin layer near the ground [114]; and (4) the use of omnipresent, all-pervading external force to maintain a stable horizontally homogeneous medium-this force introduces additional degrees of freedom that allow the restrictions of the Taylor-Proudman theorem to be bypassed but leads to changes in the dynamics within the storm.…”

“…In [111,112], it is proposed to use a certain fictitious force that creates false (artificial) horizontal vorticity. However, [113] notes that in meteorology, the laws of mass, energy, Examples of the formation of vortices in high-temperature substances and under the action of a strong magnetic field, as well as under conditions of fast plasma processes, are possible [115][116][117][118].…”