Bicubic Numerical Model: Ideal Parallel Simulations of Lamb Wave and Tornado Disturbance in the Atmosphere
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Abstract:
A new numerical model with a new algorithm of the Coons bicubic curved surface fitting by means of “bicubic curved surface fitting-time step integration-bicubic curved-surface fitting...” is presented. Obviously, this model can give a nonlinear description to atmospheric motion and can get the solution (approximate numerical solution) of a nonlinear partial differential equation system by the numerical analysis method. Actually, with the cubic spline function, BiNM is a Coons bicubic curvedsurface fitting model for many physical fields of the atmospheric motion in the x, y, or z directions (but the timedimension is not considered here). It can make the fitting of the synoptic system by a continuous regular polyhedrons composed with N pieces of Hermite bicubic patches in mathematical RN space. By this kind of fitting, the atmospheric physical field P, as well as its differential PX and PXX, and P's integral in the X (X = x, y, z) space can be all obtained at any time. It is indicated that, by the differential quotient instead of linear difference, BiNM can describe multiscale and nonlinear atmospheric motions and forecast (simulate) them by time integration for their governing equations. A Bicubic Numerical Model (BiNM) with the Z coordinate system and high resolution (22 m grid spacing in horizontal and 52 layers in vertical) is used. An ideal predefined disturbance of mospheric acoustic waves (Lamb waves) is simulated by using the primary atmospheric equations of motion and the Eulerian time integration scheme; meanwhile, the same gravity wave as an ideal tornado disturbance is also simulated by assuming that the free atmosphere be incompressible, such that the acoustic wave is eliminated in the simulation, showing that tornados are not acoustic waves but gravity waves in the atmosphere. It is also found that: (1) the simulated Lamb wave would propagate in horizontal direction at a speed similar to the speed of acoustic waves in the atmosphere and last for only a few seconds at its original place, in which energy dispersion is much more quickly than tornado disturbance; (2) like gravity wave in the atmosphere, the simulated tornado disturbance can last for more than one minute at its original place, and its inner (outer) part is all the while a convergence (divergence) circle from its bottom up, having a cold core and showing stationary wave features. The tornado disturbance can develop from the input of water vapor into the disturbance and the releasing of condensation latent heat. Under the incompressible flow assumption, a wetadiabatic energy balance equation is derived, which theoretically proved that condensation latent heat can help the development of a tornado.
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Supported by:Beijing E-Tiller Technology Development Co., Ltd.
Supported by:Beijing E-Tiller Technology Development Co., Ltd.