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Three-dimensional dynamical model in Java Display PDF 417 in Java Three-dimensional dynamical model

13.3 Three-dimensional dynamical model generate, create pdf-417 2d barcode none in java projects Android 1=2 Qv;sfc FQv cd u2 v2 z Qv;dz=2 ;. 13:74 . where the subsc ripts sfc and dz/2 refer to the surface value and the grid point above the surface; the value of the drag coefficient cd 1.1 10 3 4 10 5 (u2 v2)1/2 (see Moss and Rosenthal 1975 as suggested by Rotunno and Emanuel 1987). More complicated, and perhaps better, formulas based on observed fluxes are included in many models (see Stull 1988 for listings of these equations).

13.3 Three-dimensional dynamical model 13.3.

1 Theoretical formulation of a three-dimensional dynamical model The example used here is the Straka Atmospheric Model (SAM) (Straka and Mansell 2005), which is a non-hydrostatic model based on the compressible Navier Stokes equations for fluid flow. A terrain-following coordinate system is employed. In addition, a three-dimension map factor is used for grid stretching.

The model can be applied to flows of air on scales of fractions of meters to hundreds of meters or more. Other physical processes are taken into account such as radiation and microphysics. The latter of these are a primary topic of this book.

Parameterizations for other processes can be found in Stensrud (2007). 13.3.

2 Analytical equations for the orthogonal Cartesian dynamical model To begin with, the equations for compressible fluid flow can be written as ]ui 1 ] ruj ui ui ]uj 1 ]p 1 ]tij Eijk uj f di3 g 13:75 ]t r ]xj r ]xi r ]xi r ]xj where the product rule has been used on the advective term to write it in flux form. The orthogonal Cartesian velocity components ui = (1, 2, 3) are the velocity components in the x-, y-, and z-directions, g = 9.8 m s 2 is gravitational acceleration, r is the density, and p is the pressure.

In addition, f 2 O sin f , and f 0 2O cos f , where O is the angular frequency of the Earth, which is 7.29 10 5 s 1, and f is the latitude. The subgrid stress tensor is given as tij r Km Dij and the eddy-mixing coefficient for momentum Km is defined later.

The deformation tensor Dij is defined as   ]ui ]uj 2 ]uk : 13:76 Dij dij ]xj ]xi 3 ]xk. Model dynamics and finite differences The continuity equation can be written as ] ruj ]r ]t ]xj and the ideal gas equation is P rRd Tv : Lastly, the Poisson equation will be used,  R=cp p0 y v Tv ; p. 13:77 . 13:78 . 13:79 . where p0 is a r eference pressure that is 100 000 Pa, cp = 1004 J kg 1 K 1, and cv = 717 J kg 1 K 1. This fully compressible system permits both acoustic and gravity wave solutions. Since the thermodynamic quantities vary more rapidly in the vertical than the horizontal direction, they may be written as a sum of a base-state variable which is a function of z only and a perturbation from the base state, 8 > p p z p0 < r r z r0 : 13:80 > : 0 y y z y Also, the base state is hydrostatic, ]p ]z rg: 13:81 .

Now (13.80) is pdf417 2d barcode for Java substituted into (13.75), using a binomial expansion and neglecting higher-order terms and making use of (13.

81) results in ]ui 1 ] ruj ui ui ]uj 1 ]p0 1 ]tij r0 Eijk uj f di3 g 13:82 ]t r ]xj r ]xj r ]xi r ]xi r and the moist Poisson equation holds for the mean state,   p p0 R=c : yv Tv p. 13:83 . Now (13.79) is Java pdf417 used, the natural logarithm taken, and using (13.80), the mean terms are subtracted, resulting in r0 y0v r yv cv p0 : cp p 13:84 .

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