Wave forces

In the absence of factors dictating a specific choice, velocity waves are a good overall choice because (1) it is numerically easier to perform digital integration to get displacement than it is to differentiate displacement to get velocity, (2) slope waves are immediately computable from velocity waves. Slope waves are important because they are proportional to force waves. 

Consider first the series junction of N waveguides containing transverse force and velocity waves. At a series junction, there is a common velocity while the forces sum. For definiteness, we may think of A ideal strings intersecting at a single point, and the intersection point can be attached to a lumped load impedance Rj (s), as depicted in Fig. 10.11 for TV= 4. The presence of the lumped load means we need to look at the wave variables in the frequency domain, i.e., V(s) = C v for velocity waves and F(s) = C / for force waves, where jC denotes the Laplace transform. In the discrete-time case, we use the z transform instead, but otherwise the story is identical. 

Flutter, 177 Force waves, 432 Formant, 302, 322 speech, 245 Forward masking auditory, 246 Fourier transform, 285 Frame size (Layer 1, 2), 76 Frequency domain smearing, 9, 13 Frequency modulation, 178, 315 Frequency response envelope, 95, 100, 119, 123... 

The digitized traveling force-wave components become... 

Fig. 19 (a) The bifurcation diagram for spatially periodic solutions at a forcing wave number q = 0.5 and modulation amplitudes a = 0 dotted), a = 0.01 dashed), and a = 0.03 solid), (b)—(d) The three solutions yrs (x) over one period corresponding to the different branches of the bifurcation diagram for a = 0.03 and = 1. Figure from [122]. Reprinted with permission by Springer... 

Adhesion, as in adhesive tape, is the tendency of different materials to stick together. Adhesion is a major factor responsible for surface waves in bodies of water. Although the physics is a complex trade-off involving many forces, waves begin by water sticking to the wind blowing past. The idea of pouring oil on troubled waters, often used as a metaphor for a... 

The continental United States has three marine shores the Pacific coast, the Atlantic coast, and the coast of the Gulf of Mexico. Including the shorelines of the Great Lakes, U.S. coasts total more than 95,000 miles (152,855 km). All three marine coastlines are exposed to many of the same natural forces. Waves and tides continually bathe their shores while winds and precipitation rebuild their substrates. In addition, the shores in all locations are occasionally exposed to the powerful forces of storms. 

Typical mass balance methods to measure the air-sea gas transfer have one major drawback the response time is of the order of hours to days, making a parameterisation with parameters such as wind forcing, wave field, or surface chemical enrichments nearly impossible. The controlled flux technique uses heat as a proxy tracer for gases to measure the air-sea gas transfer rate locally and with a temporal resolution of less than a minute. This method offers an entirely new approach to measure the air-sea gas fluxes in conjunction with investigation of the wave field, surface chemical enrichments and the surface micro turbulence at the water surface. The principle of this technique is very simple a heat flux is forced onto the water surface and the skin-bulk temperature difference across the thermal sublayer is measured. 

Ratio of inertial to gravitational force Wave and surface behavior (mixed natural and forced convection)... 

Four types of waves have been distinguished, that is, forced, swell, surf and forerunners. Forced waves are those formed by the wind in the generating area they are usually irregular. On moving out of the area of generation, the waves become long and regular. They are then referred to as swell or free waves. As these waves approach a shoreline, they feel the bottom, which... 

Numerical models have been developed for calculating the probable maximum seiche in the form of the amplitude of oscillation as a function of time at any point within a bay of arbitrary shape. These models usually require as input a specification of the overall geometry (bathymetry and coastal topography) and of the forcing wave system. They also require as input the time dependence of the excitation (tsunami wave, surge wave, wind wave etc.) at the open boundary or source location. The amplitude time history of the seiches for the location of the plant should then be calculated. Hydraulic model studies and/or field results should be used to validate the calculation model selected. 

When the influence of surface tension cannot be neglected it is necessary to generalize the result (5.85) for the velocity of propagation of the waves in order to account for surface forces. Waves in which surface tension forces cannot be neglected are called capillary waves. Consider a plane wave with amplitude A moving along the jc-axis, in Cartesian coordinates, having a profile of the form,... 

Froude number, Fr gL L characteristic length dimension of system inertial force gravitational force Wave tind surface behavior pouring streams... 

Cancun beaches is shown in Fig. 20.36(a), in which the raised limestone platform extends 200 m offshore and supports a relatively thin sand layer on top (1.0—1.5 m maximum thickness). This natural raised structure forces waves to break some distance offshore and results in an area with calm seawater and white sand beaches, making for ideal conditions for water sports and safe relaxation. A large frontal dune stmcture had existed at the rear of the beaches, but with the development of large seaside resorts since the mid-1970s, this frontal dune structure was destroyed and thus it cannot contribute sand to the beaches to compensate for sand loss resulting from littoral processes. Furthermore, waves from storm activity contribute to continual sand loss from the beaches. 

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