Crossing waves

A parameterization of the JONSWAP spectrum has been worked out by Houmb and Overvik (1976). This work gives recommended values of a, y, and f, when the significant wave height 77 and average zero crossing wave period are given (Table 7.6). 

Figure 12.22 Crossing wave patterns in the BZ reaction on the two surfaces of a Nafion membrane, (a) Nafion membrane loaded with ferroin to 16.7% capacity gives strong coupling, (b) Nafion loaded to 38.7% capacity gives weak coupling. (Reprinted with permission from Winston, D. Arora, M. ...

Analyses by the Melnikov Method of Damped Parametrically Excited Cross Waves... 

Fig. 3.2. Neutral Floquet stability diagram for mode 2 cross waves (o = mode 2 cross waves and A = no cross waves).i ...

The velocity potential ip is the field variable, and the free surface y may be expressed in terms of p> by the free surface boundary conditions and the contact line conditions at the vertical sidewalls.h The velocity potential ip and the free surface displacement r] are assumed to be linear combinations of the progressive wavemaker wave and the parametrically excited cross wave given by the following ... 

S. Fadel, Apphcation of the generalized Melnikov method to weakly damped para.-metrically excited cross waves with snrfaee tension, PhD dissertation, Oregon State University, USA (1998). 

There are some other formulas using the parameter of deepwater wave steepness Hq/Lq. They can be useful for predicting the breaker height of regular waves. Nevertheless, they cannot be applied for breaking of random waves, because individual zero-crossing waves in a train of random waves are unrelated to individual waves in deepwaters. Thus, there is little room for the parameter Hq/Lo to function in the breaker index for random waves. 

Variations of zero-crossing wave heights across the surf zone... 

However, the zero-crossing wave height is defined by... 

Tayfun also investigated the effect of spectrum width. A better definition for the zero-crossing wave height than Eq. (7.13) may be given as... 

Zero-crossing wave amplitude in Eq. (7.19) extends the range from 0 to infinity if the number of waves is infinity. When the population of waves is finite, such as data from 20 min measurements every 2h, maximum wave amplitude may be finite. If a time series of wave amplitudes... 

The problem of deriving the pdf of zero-crossing wave periods is very difficult. Rice derived a pdf for the zero-crossing interval. He treated the interval where I t) [Eq. (7.1)] crosses the 0 line upward at t = 0 and crosses the 0 line downward between r and t - - dr. 

The applications of the periodic wave theory for zero-crossing wave properties raise problems. There have been very few studies about the physical properties of zero-crossing waves, of wave period-wavelength/celerity, of wave height/period — water particle velocities, etc. 

Fig. 4. Crossing waves in a layer of BZ reagent exposed to air. (a) Polyacrylamide gel of thickness 1 mm. A plane wave at the top moves across a spiral wave on the bottom, (b) Silica gel layer of thickness 0.6 mm. Long wavelength top waves propagate over a background of short wavelength bottom waves.

Crossing Waves in the BZ RDS with Transversal Oxygen Gradient... 

Fig. 5. Saw-tooth shape of wave fronts due to mutual acceleration of crossing waves propagating in two weakly coupled sublayers (from [51]).

The phenomenon does not depend on the type of gel. Crossing waves (CW) were observed in beaded silica gel [51], in continuous silica gel and in polyacrylamide gel [54]. 

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