Wave front break

If a wave passes a small obstacle, a wave front break occurs when Lf < 2Rc, with subsequent shrinking of open wave ends and widening of the break... 

Wave Front Breaks and Emergence of Spiral Waves at Local Gradients of Parameters... 

Fig. 3. Wave front break and emergence of a single spiral wave at a steep gradient of excitability created in the BZ RDS by local decrease of acidity (from [2]).

The objective in these gauges is to measure the time-resolved material (particle) velocity in a specimen subjected to shock loading. In many cases, especially at lower impact pressures, the impact shock is unstable and breaks up into two or more shocks, or partially or wholly degrades into a longer risetime stress wave as opposed to a single shock wave. Time-resolved particle velocity gauges are one means by which the actual profile of the propagating wave front can be accurately measured. 

The distortion which brings about the breaking carries a portion of the material forward and because of the intense pressure generated behind the wave, the reciprocal movement of the medium is prevented. The forward movement of the medium and the prevention of counter-movement serve to increase the speed of the wave front. This effect explains the fact that the rate of detonation increases more rapidly with increase of density in an insensitive than in a sensitive explosive. The insensitive material must be distorted and moved forward to a greater extent than the sensitive material before rupture occurs... 

When an airplane exceeds the speed of sound, we say that it breaks the sound barrier. In so doing, it generates a sonic wave or pressure wave-front. When steam and gas flow into the converging section of the jet diffuser shown in Fig. 16.1, the same thing happens. The gradually converging sides of the diffuser increase the velocity of the steam and gas, as the vapor enters the diffuser throat up to, and even above, the speed of sound. This creates a pressure wavefront, or sonic boost. This sonic boost, will multiply the pressure of the flowing steam and gas by a factor of perhaps 3 or 4. 

Spiral (coil) waves can be generated by striking lightly the Petri dish so as to break the wave front (ring) then the disrupted ends of the wave front wind around a common centre forming spiral structures (Fig. 94). 

A single spiral wave, which constitutes the initial condition for all experiments, is created in the center of the gel disk by breaking a wave front with an intense light spot. The location of the spiral wave tip is defined online as the intersection point of contour lines (0.6 x amplitude) extracted from two digitized images taken with time interval 2.0 s. The tip trajectory, the control signal and the wave activity at an arbitrary detection point can be visualized online by the computer. 

During exhaustion of the resin bed, the selectivity sequence manifests itself as zones of sulfate-rich, arsenate-rich, bicarbonate-rich, etc. bands with the sul-fate-rich zone located at the beginning of the column and the next-preferred ion after it and so on. In the beginning of an exhaustion cycle, the resin-bed profile is similar to Figure 6a in composition. As the exhaustion progresses, the respective anion bands are displaced in the direction of the outlet where they break through into the effluent as wave fronts. The first wave front to break through... 

In a small glass beaker add % ml of solution 2 to 6 ml of solution 1. Then add 1 ml of solution 3 and wait a few minutes for the solution to become clear. Then add 1 ml of. 025M (standard) Ferroin. Mix well, pour into a 90 mm petri dish and cover it. The solution is uniformly red, but in a few minutes blue dots will appear and spread out in rings. Shortly the dish will be full of target patterns. Spiral waves can be produced by gently tipping the dish so as to break some of the blue wave fronts. Free ends wrap around into spiral structures. 

The highest void fraction occurs at the wave front, and the void fraction is decreased rapidly in time. The temporal variation of the void fraction depends on the air supply from the surface, advection, and buoyancy, and these effects are difficult to discriminate from each other. Although the process is complex, the normahzed temporal characteristics show a universal behavior. Similar laboratory experiments were observed by several researchers. Furthermore, Cox and Shin found the self-similar exponential decay of the temporal series of void fraction normalized by the averaged value in different types of breaking waves. In addition, they reported that the maximum void fraction in the time series was three to four times higher than its average value. 

Recently, the breakup of free spiral waves has been observed in the numerical simulations of reaction-diffusion models [42-46]. This effect is principally of the same nature as breaking (or spontaneous depinning) of a pinned spiral wave. The main question is here what induces breaking of the wave front at a certain distance from the free tip. In some of the stimulations (e.g. [42-45]), the breakup is preceded by the onset of meandering which might actually produce the inhomogeneities of the residual inhibitor concentration that force the wave to break. 

Fig. 4. Evolution of a spiral wave which results from the integration of Equation (1) with initial conditions similar to (8). (a) Breaking of the wave front emitted by the spiral due to the Eckhaus instability, (b) Proliferation of defects in the system. The latter are pushed out of the system by the front of the spiral. The parameters of Equation (1) are fi — -a = 0.8 and the size of the system is L = 170.

In experiments, Zhabotinsky and Zaikin [2] observed that a break of the wave front results in formation of a spiral wave when a circular chemical wave encounters a region with a nonuniform negative gradient of excitability (Figure 3). 

In uniform systems spiral waves usually appear as a pair when a break of a wave front creates two open ends of the front [2, 3] in nonuniform systems single spirals emerge frequently [44]. Only one open end of the wave front can form a spiral under some asymmetric spatial distributions of parameters (Figure 3). Single spirals can emerge at nonuniformities situated near a boundary of the system. In other cases, one spiral from a pair can be brought by gradient-induced drift to the medium boundary where it perishes. 

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