Dissipative effects on a microscopic level are included in the Schrödinger equation. When the decay between different local levels as a result of the coupling to a bath, the Schrödinger equation no longer conserves energy, but the probability of the states is conserved. The procedure is illustrated with several examples that include direct electronic decay and damping of local phonons (vibrational levels). This method significantly reduces the calculational effort compared to conventional density matrix techniques.
In this study, multi‐source data, especially weather radar data, were used in the analysis of structural features and evolution of a squall line‐like rainband (SLLR) of a linear mesoscale convective system (MCS) in the eastern slope of the Taihang Mountains on 12 and 13 August 2018 and reached the following conclusions: (a) The SLLR, located in north of the linear MCS, exhibited a significant horizontal gradient of reflectivity and large vertical extension. The front‐to‐rear flow that appeared between the surface and the stratosphere was lifted upward immediately in front of a cold pool that formed rearward‐tilting updrafts. (b) As the SLLR passed over, surface meteorological quantities changed drastically, coinciding with the heavy precipitation. (c) The SLLR, when propagating northeastward, showed a complex convective development of sequential intensification, weakening, and re‐intensification within a 2.5‐hr period. The temporal intensification was related not only to the development of a low‐level rear‐inflow jet but also to the dynamic interaction between the vertical environmental wind shear and the cold pool. The lifted rear‐inflow jet, which formed over a vertically stacked horizontal vorticity couplet behind the leading edge, provides a reasonable explanation for the intensification of the SLLR, resulting in the reduction of the cold pool circulation and enhancement of the convective updraft. Topographic forcing might play a crucial role in the re‐intensification of the SLLR, which suggests the importance of the cold pool and topography in structural features and convective evolution of the squall line‐like rain bands.
A numerical constraint was developed to improve the global and local conservation for the Yin‐Yang grid system, which has been known as one of the quasi‐uniform grids on a sphere. Two‐dimensional cubic mass distribution within an individual mesh was assumed, to describe the subgrid‐scale structure of local properties and to ensure high‐order‐accuracy mass flux specification for the Yin‐Yang boundary. A three‐point Multi‐moment Constrained finite Volume scheme, in cooperation with a fourth‐order Runge–Kutta scheme, was selected for numerical transport with the help of Boundary Gradient Switching for oscillation suppression. The new scheme was tested with a couple of idealized numerical experiments in advection and shallow‐water models on the Yin‐Yang grid to verify its performance. Numerical results confirmed the exact mass conservation in spherical advection problems, and the numerical convergence rate reached fourth order in both advection and shallow‐water models. Computational stability, shape‐preserving and numerical oscillation‐free properties were also revealed in the nonlinear testing problems.
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