Vertical propagation

Mason, W. and Wheeler, R.V., The propagation of flame in mixtures of methane and air. Part 11. Vertical propagation, Journal of the Chemical Society Transactions, 117, 1227-1237, 1920. 

In summary, from the direct observation of the vertical propagation of femtosecond-terawatt laser pulses in the atmosphere, it is demonstrated that not only the filaments, but also the whole beam, have a non-linear behaviour [18]. The overall beam is partially recollimated near to the non-linear focus. Also, filamentation can occur at 2 km altitude, which is essential for remote atmospheric applications of filamentation. 

Vertical Propagation of Flame.4—In tins case the effect of convection currents becomes increasingly pronounced. The tube in which the flame travels becomes a chimney, and, with bottom ignition, the speed of the flame is enhanced by that of the draught. With top ignition the flame tends to bum at the mouth of the tube until all the combustible mixture has risen to the top. 

The infrared radiation scheme includes the effects of water vapor, carbon dioxide, ozone, and clouds. Gravity wave drag parametrization is based on a simplified linear theory for vertically propagating gravity waves generated in a statically stable flow over mesoscale orographic. GEM physics package version 4.2 was used in the current study. 

Matsuno, T., Vertical propagation of stationary planetary waves in the Northern hemisphere. J Atmos Sci 21, 871, 1970. 

Tj = Tv is the wavelength of the vertically propagating primary wave through the backfill. 

Empirical curves based, at present, on engineering judgment, transform the water content in each story to interior damage ratio. Also an empirical scheme for vertical propagation of interior damage was implemented (to be further refined in the ftdure). So the... 

Eliassen-Palm flux A measure of the pseudomomentum associated with vertically propagating atmospheric waves. Its divergence gives the acceleration of the zonal-mean zonal wind by atmospheric waves. 

Vertically propagating Kelvin and mixed Rossby-gravity modes have been identified in the stratosphere the evidence in the troposphere is less clear. Internal oceanic Kelvin waves are considered by many oceanographers to be the piimaiy mechanism for the eastward transport of heat along the equator associated with the significant in-terarmual phenomenon known as the El Nino/Southem oscillation (ENSO), which affects weather and chmate globally. 

The system of equations of horizontal motion [Eqs. (9) and (10)], hydrostatic equilibrium [Eq. (16)], mass continuity [Eq. (12)], thermodynamics [Eq. (8)], and the ideal gas law [Eq. (7)] is called the hydrostatic prediction model, or primitive equations. The hydrostatic assumption modifies the basic atmospheric prediction system in such a way as to eliminate the vertical propagation of sound waves. 

A very important aspect of SFSI is the difference between free field motions and the motions that are changed (affected) but the presence of the structure. Figure 5 shows comparison of free field short period motions (obtained by vertical propagation of earthquake motions through the model without the presence of bridge structure and piles) and the ones recorded at the base of column of the left bent in stiff and soft soils. 

Everything so far has treated the CSR as being caused by vertically propagating shear waves, a 1-D situation. This is obviously of uncertain relevance for soil-structure response situations such as quay walls. A reasonable view is that analysis where 2-D effects may be important will require finite element simulations with simple to advanced soil models. Discussion of these models is beyond the scope of this manual. However, the recommended site characterization presented in Section 8.6.6 does include the data needs for these types of analysis. 

In FD solutions, the derivatives in differential equations are approximated with finite differences computed over a discrete grid. Consider the case of a vertically propagating, planar SH wave in a horizontally layered medium. The plane strain approximation reduces the wave Eq. 3 to one dimension ... 

In the above example of a vertically propagating SH wave, consider the interface generated by a horizontally layered sedimentary deposit resting on top of a denser, higher-velocity bedrock. 

Many computer programs are available to estimate free-field shear distortions SHAKE (Schnabel et al. 1972), FLUSH (Lysmer et al. 1975), D-MOD (Matasovic 1993), and DEEPSOIL (Hashash et al. 2011 Hashash and Park 2001), among others. One-dimensional site response analyses can be used to characterize the change in the propagating ground motions on variable soil profiles, but these analyses only take into consideration vertically propagating shear waves. However, these are the waves that... 

Most pseudo-static SSI analyses focus on the interaction of vertically propagating shear waves with the transverse section of a tunnel. These analysis approaches are described next. 

Nonlinear soil behavior can be approximated by an equivalent linear characterization of soil dynamic properties. The method makes use of the exact continuum solution of wave propagation in horizontally layered viscoelastic materials subjected to vertically propagating transient motions (e.g., Roesset 1977). It models the nonlinear variation of soil shear modulus and... 

Kanai et al. (1959) discovered from earthquake observations that a horizontal component in site response can be explained by multi-reflection of SH-waves propagating vertically in soil layers. Horizontal displacement of the vertically propagating SH-wave is expressed as... 

The variables T and are the spatially and temporally varying deviations of temperature and geopotential from T iz) and 4>o(z) respectively, and J = Q pCp is called the thermotidal heating. If J is specified, along with boundary conditions, the tidal equations (9.2.34)-(9.2.38) can be solved for m, v, w, 4>, and T. At the lower boundary, the component of the velocity field normal to the surface must vanish. As z 00 solutions with an exponential behavior are required to remain finite for vertically propagating solutions, the energy flux is required to be directed upward. 

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