Horizontal motions

So far in discussing motion in the atmosphere, we have been emphasizing only horizontal motions. Although of much smaller magnitude than horizontal motions, vertical motions are important both to daily weather formation and to the transport and dispersion of pollutants. 

Persistent vertical motions are linked to the horizontal motions. If there is divergence (spreading) of the horizontal flow, there is sinking (downward vertical motion) of air from above to compensate. Similarly, converging (negative divergence) horizontal air streams cause upward vertical motions,... 

Horizontal motion over topographic features at the Earth s surface. A classic example of this is seen in the cap clouds associated with flow over mountains. 

The horizontal motion of the atmosphere (or wind) is characterized by four spatial scales. These, with their conventional names, are ... 

Horizontal motion of the atmosphere, or wind, is a response of the air to the forces that are present. These include the force due to the pressure gradient, the Coriolis force associated with the rotation of the Earth, and frictional forces acting to retard any motion. If the acceleration of the air mass and frictional effects are small, the horizontal velocity is described by the following expression ... 

Fig. 6. MR wave image of acoustic refraction. Shear waves generated in the upper part of an agar gel phantom (horizontal motion) propagate vertically in the stiff part of the phantom (/i 50 kPa cT 7.5 cm/s) and are refracted by the oblique lower part of soft gel (fi 15 kPa cT 4 cm/s). Note the marked reduction of wavelength in the softer medium. From Ref. 23, reprinted by permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc.

In general, the 3D motion of the spherical pendulum is very complex, but for fixed initial angular displacements, values of the kinetic energy can be found (by trial and error) for which this motion is periodic. The approximation discussed above leads to the approximate description of the horizontal motion in terms of Mathieu functions, for which Flocquet analysis determines periodic solutions in terms of two integers k and n, which can be thought of as quantum numbers. 

So how is the spherical pendulum quantised The answer is that its motion is generally chaotic, except for discrete values of the initial projection speed, for which it is periodic. The precise details of this phenomenon are difficult to get a handle on, because, although the vertical motion is always described by periodic elliptic functions, the horizontal motion is described in terms of Lame functions, which are very difficult to study and for which periodicity is difficult to diagnose. 

As depicted, the luggage moves from left to right after being placed on the tilted entrance conveyor, which then transitions to a horizontal motion for scanning. The larger structure in the center is the CT scanner section. Next comes the exit conveyor that transitions downward for ease in retrieving bags. Conveyors in the entrance tunnel, in the scanner section, and in the exit tunnel all run at the same speed. The two conveyor tunnels at either end each contain several sets of leaded... 

The upper bound of the region of stable steady motion is shown in Fig. 6.7 as a function of (CdRcx ) and /. For large /, secondary motion starts at Rcy = 100, i.e., (Cd Rcj ) = 23.4. At lower /, steady motion persists to higher Rcy the boundary shows a maximum at Rcy = 172, (CdRcj ) = 32.6 for/ = 8 X 10 Three kinds of secondary motion have been observed (S8), although the distinctions between them are not sharp. Immediately above the transition to unsteady motion, a disk shows regular oscillations about a diameter the amplitude of oscillation and of the associated horizontal motion increases with... 

In the real atmosphere horizontal motions along latitude and longitude must also be taken into consideration. Thus, the ozone concentration profile should show a significant derivation near the tropopause due to the downward transport of 03 from the expected profile without vertical eddy diffusion. 

A horizontal air stream entering this zone expands within a chamber and converges towards the outlet (Fig. lb). Particles fed in the chamber with zero velocity accelerate horizontally by the drag force Fd and also fall down. At the end of the acceleration interval the horizontal velocity component vx of all particles almost reaches the are flow velocity u and they do not separate in this direction. Separation occurs due do particles vertical motion across the air stream. Each particle falls at its own terminal settling velocity. Accordingly, due to the horizontal motion they land on the bottom at different chamber locations coarse-close to the inlet, smaller-close to the outlet. Coarse fraction is gathered on the bottom of the chamber, fines do not reach the bottom and are carried away by the air flow through the outlet. 

This equation will be used to obtain a general solution in the case of a particle moving in the absence of a gravitational field, i.e.t for horizontal motion. For a particle moving in a gravitational field (for vertical motion), we shall use three equations which cover the span of the curve given in Figure 3. Thus, for... 

With the eyes closed, gently scrub the lids and eyelashes, in a horizontal motion from left to right, for approximately 20 passes across each lid. 

Let the droplets be constantly created (by nozzles) on the level z = 0 with intensity N, l/(m2sec), each with the horizontal u = uxt) and vertical v = m,0 initial velocity components. After the creation, the droplets move up in the air flow field and interact with it. Because of the latter, their horizontal velocity component changes, u x.z). Having reached the droplet layer top z = h, the droplets of this kind i = 1 disappear , but new droplets, / = 2, appear and continue the same horizontal motion but change their vertical motion by the descending one. The force interaction between the flow and droplets is assumed linear. For simplicity, the droplet initial vertical speed is assumed constant, uz0 = a = const. Figure 3.25,A explains these assumptions. 

Consider a piece of the ocean covered with a monolayer with film pressure 11 = crM - a, where crw and a are the surface tensions of pure water and film, respectively. We further assume that the film is stagnant. Beneath the film, however, there is a horizontal motion (taken to be in the x-direction) with a corresponding boundary layer. Consequently, there is a tangential viscous stress, rvisc, on the film which must be balanced by a gradient in n. 

Upward motion associated with convergence of horizontal motions (or vice versa, sinking due to divergence). This will be evident in the discussion of horizontal motions in Section 10.5. Again, vertical velocities of only cm/s usually are observed. 

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