Effects of Surface Waves

Two surface waves, each of them propagating in opposite directions along the X axis. They will in general have different amplitudes but the same phase velocities that differ greatly from those of the Floquet currents. Thus, the surface waves and the Floqnet cnrrents will interfere with each other, resulting in strong variations of the cnrrent amplitndes as seen in Fig. 1.3c. 

The so-called end currents. These are prevalent close to the edges of the finite array and are usually interpreted as reflections of the two surface waves as they arrive at the edges. 

We emphasize that these surface waves are unique for finite arrays. They will not appear on an infinite array and will consequently not be printed out by, for example, the PMM program that deals strictly with infinite arrays. Nor should they be confused with what is sometimes referred to as edge waves [28], The propagation constant of these equals that of free space, and they die out as you move away from the edges. See also Section 1.5.3. 

Furthermore, the surface waves here are not related to the well-known surface waves that can exist on infinite arrays in a stratified medium next to the elements. These will readily show up in PMM calculations. These are simply grating lobes trapped in the stratified medium and will consequently show up only at higher frequencies, typically above resonance but not necessarily so in a poorly designed array. In contrast, the surface waves associated with finite arrays will typically show up below resonance (20-30%) and only if the interelement spacing is 0.5)t. 

From a practical point of view, the question is of course whether these surface waves can hurt the performance of a periodic structure when used either passively as an FSS or actively as a phased array. And if so, what can be done about it. 

---

Husson, D. (1985). A perturbation theory for the acoustoelastic effect of surface waves. /. Appl. Phys. 57,1562-8. [149]... 

The determination of the effects of surface waves on submerged structures has many practical applications, particularly in an ocean environment. Due to the complexity of the problem, analytic results are limited to idealized flows and geometries. 

D. S. fanning and B. A. Munk, Effect of Surface Waves on the Current of Truncated Periodic Arrays, IEEE Trans. Antennas Propag., Vol. AP-50(9), September 2002, pp. 1254-1265. 

The structure/property relationships in materials subjected to shock-wave deformation is physically very difficult to conduct and complex to interpret due to the dynamic nature of the shock process and the very short time of the test. Due to these imposed constraints, most real-time shock-process measurements are limited to studying the interactions of the transmitted waves arrival at the free surface. To augment these in situ wave-profile measurements, shock-recovery techniques were developed in the late 1950s to assess experimentally the residual effects of shock-wave compression on materials. The object of soft-recovery experiments is to examine the terminal structure/property relationships of a material that has been subjected to a known uniaxial shock history, then returned to an ambient pressure... 

S. Kelling, S. Cerasari, H.H. Rotermund, G. Ertl, and D.A. King, A photoemission electron microscopy (PEEM) study of the effect of surface acoustic waves on catalytic CO oxidation over Pt(110), Chem. Phys. Lett. 293, 325-330 (1998). 

A code has been written to enable the velocities of surface waves in multilayered anisotropic materials, at any orientation and propagation and including piezoelectric effects, to be calculated on a personal computer (Adler et al. 1990). The principle of the calculation is a matrix approach, somewhat along the lines of 10.2 but, because of the additional variables and boundary conditions, and because the wave velocities themselves are being found, it amounts to solving a first-order eight-dimensional vector-matrix equation. A... 

The flow of thin liquid films in channels and columns has also served as the basis of fundamental studies of wave motion (M7), the effects of wall roughness in open-channel flow (R4), the effects of surface-active materials (T9-T12), and the like. 

Semenov (S6) considered generally the effects of a gas drag at the film interface for all the cases listed above for smooth laminar film flow (see Section III, F, 2), and later experimental work confirmed these results (K20, K10, S7) for the case when the film thickness is very small, with no waves present on the film surface, and at moderate gas flow rates. The early treatment by Nusselt (N6, N7) also gave results in agreement with the experimental data obtained under these restricted conditions. Brauer s treatment of the problem (Section III, F, 2) (Bl8) also assumed laminar flow of the film and absence of surface waves. The experimental work of Feind (F2), which refers to countercurrent gas/film flow in a vertical tube, showed that, although such a treatment was useful in predicting the qualitative effects of the gas stream on the film thickness and other properties, the Reynolds number range in which it applied strictly was very limited. 

It is well known that many types of waves and ripples can be damped by interfacial films of surface-active materials, as shown theoretically by Levich (L6, L7). There have been a number of investigations into the effects of surface-active additives on the flow of wavy films (E4, H2, H20, 12, Jl, L15, M7, Sll, S12, T3). In addition, surface-active materials have also been used in various studies of mass and heat transfer to films, and some of these results throw light on the flow behavior of the films, e.g. (H13, Mil, Rl, T9, T10, Til, T12). 

Grimley (G10), 1945 Film flow in tubes and channels (water, water + surfactant), co- and counter-flow of air. Wave observations, onset of rippling, surface velocity, velocity distribution, film thicknesses, effects of surface tension and surfactants. 

Portalski (P3), 1960 Extensive study of film flow on vertical plates, with and without gas flow. Liquids included water, aqueous glycerol solutions, methanol. Data on effects of surface tension changes and surfactants, wave and surface velocities, increase in interfacial area by waves, etc. 

Mayer (M7), 1961 Experimental and theoretical study of wavy flow of water in open channel (slopes up to 5°). Data on growth of turbulent spots, local depths, surface velocity, length of entry zone, wave velocities, heights, frequencies, effect of surface-active materials. 

Yih (Y2), 1963 A general consideration (theoretical) of the stability of film flow down an inclined plane, including the cases of long and short waves and small Nrs,. Results for long waves are in agreement with theory of Benjamin (B5). The effects of surface tension and viscosity on stability are discussed. 

However, this commonly accepted theory is incomplete and applies with much difficulty to systems involving nonvolatile substances. The most relevant example is metals. For a heterogeneous system, only the mechanical effects of sonic waves govern the sonochemical processes. Such an effect as agitation, or cleaning of a solid surface, has a mechanical nature. Thus, ultrasound transforms potassium into its dispersed form. This transformation accelerates electron transfer from the metal to the organic acceptor see Chapter 2. Of course, ultrasonic waves interact with the metal by their cavitational effects. 

Another approach to the rupture of thin liquid films, proposed by Tsekov and Radoev [84,85], is based on stochastic modeling of this critical transition. Autocorrelation functions for steady state [84] and for thinning [85] liquid films were obtained. A method for calculation of the lifetime At and hcr of films was introduced. It accounts for the effect of the spatial correlation of waves. The existence of non-correlated subdomains leads to decrease in At and increase in hcr as a result of the increase in the possibility for film rupture. Coupling of dynamics of surface waves and rate of drainage v leading to stabilisation of thinning films has also been accounted for [86,87]. 

We therefore assume that the major effect of the array is in increased collection of light within the apertures. In the simulation results of this section, we only consider briefly the excitation component to enhanced fluorescence emission. As already established by experiments, the light intensity within periodic arrangements of nanoapertures increases in association with EOT and is a result of aperture coupling effects via surface waves under external excitation. This coupling therefore modulates the response obtained for an isolated aperture. Simulations were performed in the same manner as described before, except for the fact that periodic boundary conditions were used along the sides of the simulaticHi space boundary. 

---