Dilational waves

Conical Sheets. Conical sheets are deemed to be shorter than flat sheets because the radius of the curvature may have a destabilizing effect on fluctuations.Fraser et al.[116] indicated that dilational waves in a sheet may be neglected because the degree of instability of these waves is always less than that of sinuous waves. 

In planar waves the amplitude A(r) = Aq is a constant. All particles situated within a plane normal to the wave vector move at the same time. Longitudinal waves are planar waves where the displacements are parallel to the wave vector (v and c are colinear). Longitudinal waves can propagate in every material media. These are compression or dilatation waves. In transverse waves, v and c are orthogonal. Transverse waves do not propagate in fluids. 

Droplet formation occurs primarily through the surface tension and viscosity dominated breakup of these liquid threads due to symmetric (or dilational) waves as described by Rayleigh (6) for inviscid liquids and by Weber (J) for viscous fluids. Figure 3 shows the double pulsed image of the droplet formation process for No. 2 and SRC-II fuel sprays under identical atomizer conditions. These two photographs illustrate typical differences seen between these two fuels. 

The wave equation which describes the propagation of dilatational waves can be expressed as... 

Two models have been presented which are based on the Lagrangian and Eulerian difference schemes respectively. These models were able to calculate in detail the interaction of acoustic waves with inclusions in discontinuous fluids. The Lagrangian model was able to consider the transfer of normal to shear stresses at fluid discontinuities. The Eulerian model is limited to the study of dilatation waves but its computational efficiency enables it to... 

The model depends on the assumption that a nerve impulse is a propagating disturbance in the form of surface dilation wave note that... 

The equation of dilational wave motion for the solid phase is written as ... 

Response by dilatational waves and transversally reflected several times Response dominated by flexural and shear waves... 

Lucassen-Reynders and Lucassen (Lucassen 1968, Lucassen-Reynders and Lucassen 1969) have derived the dispersion relation for a liquid surface in the presence of a surface film. They showed that periodic disturbance of such a film-covered surface results in a surface tension that varies from point to point on the surface because of the fluctuations in surface concentration. Consequently, in addition to a transverse stress being developed, a finite tangential surface stress is also present. The solution to this dispersion equation has two roots, one of which corresponds to the capillary waves (transverse motion) and one of which corresponds to longitudinal or dilational waves derived from the transverse stress. The dispersion relation (D( o)) obtained for a film at the interface between two media is... 

Dilatational wave velocity 1439 m/sec 4 node axisymmetric finite elements ... 

Although this dilational wave is intrinsically dissipative, the damping rate is asymptotically smaller, OdMa] /" ), than its frequency. Up to some extent the flow field accompanying the di-... 

In the particular case of waves originated in overstability or (linear) oscillatory instability, I have shown how two types of surface waves, transverse and longitudinal (or, better, capillary-gravity and dilational, respectively) can be excited by the Marangoni effect and how they are related to each other thus leading to their combined (symbiotic-like) survival and to resonance effects. I have also given comments about the excitation of internal waves in the layer heated above and hence stably stratified and how in turn these waves are, in particular, related to the surface dilational waves. 

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