Acoustic streaming reversal by a finite amplitude sound wave in a non‐Newtonian fluid

An attempt has been made to develop a method for dealing with solutions of problems connected with the production of waves by spherical concentrations of compressed air. Starting from the general equations for three-dimensional spherically symmetrical flow in a homogeneous compressible medium having constant entropy everywhere, a process has been devised to apply step-by-step calculations over small intervals of time to investigate the general features of such a motion. A complete solution has been worked out in one particular case for a not very intense initial distribution of pressure, and various indirect checks have indicated that the results are reasonably accurate. These results show m any features of definite interest. As distinct from plane or spherical sound wave theory, it is found that a train of waves passes away from the centre of disturbance, the amplitudes and wave lengths falling off from wave to wave. Furthermore, as distinct from finite amplitude plane wave theory which shows that any wave must eventually become a shock wave, the waves obtained in the finite amplitude spherical wave case show no indication of becoming shock waves, and indeed show towards the closing stages of the calculation a similarity to sound wave propagation. The method is applicable to any spherically symmetrical motion up to such a time as the formation of a shock wave takes place and then fails owing to the assumption of constant entropy.

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On the Development of Transverse Ridges on Rock Glaciers

Journal of Glaciology ◽

10.1017/s002214300000931x ◽

1989 ◽

Vol 35 (121) ◽

pp. 383-391 ◽

Cited By ~ 23

Author(s):

Deborah S. Loewenherz ◽

Christopher J. Lawrence ◽

Richard L. Weaver

Keyword(s):

Stability Analysis ◽

Newtonian Fluid ◽

Lower Layer ◽

Elastic Solid ◽

Surface Region ◽

Finite Amplitude ◽

Climatic Conditions ◽

Rock Glacier ◽

Rock Glaciers ◽

The Stability

AbstractThe stability of a low Reynolds number flow on an inclined plane is investigated with respect to modelling the initiation of transverse wave-like ridges which commonly occur on the surfaces of rock-glacier forms. In accordance with field observations indicating the presence of stratification in rock glaciers, two models of rock-glacier structure are considered, each stratified and possessing a lower layer which is treated as a Newtonian fluid. An upper, less compliant layer is treated, alternatively, as a Newtonian fluid of viscosity greater than that of the lower layer, or as an elastic solid under longitudinal compression induced by a decrease in the slope of the underlying incline. A linear stability analysis is used to examine the behaviour of each of the proposed models, and both are found to generate instabilities at wavelengths comparable to those associated with transverse surficial ridges on rock glaciers. The growth rates of a flow disturbance predicted by the viscous-stratified model appear to be too slow to account fully for the development of wave forms of finite amplitude, suggesting that other mechanisms are involved in the amplification of an initial disturbance. The results of the stability analysis of the elastic lamina model indicate that finite surficial ridges may develop on rock glaciers as a product of a buckling instability in the surface region if there is a decrease in the slope of the underlying incline. Both of the analyses illustrate that transverse ridges can occur on the surface of a rock glacier in the absence of any variations in debris supply to the system. The results further imply that the use of these features in the paleoreconstruction of Holocene climatic conditions must entail an assessment of the relative roles of external climatically driven forcingversusinternal Theologically derived instability.

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