Abstract: A new physical model of liquid He^4 based on the hypothesis that rotons behave like tiny quantized circular vortex rings is presented. It is shown that the energy of a state will not only depend on the distribution in numbers of rotons with various momenta, but also on the arrangements and orientations of the rotons. The λ-transition then can be interpreted to reveal two aspects: T_λ is both the lowest temperature at which all helium atoms partake in excitation, and the point of the initiation of the general destruction of order, i.e. the general randomization of the orientation of the rotons. Other implications from the theory are also discussed.

ID: CaltechAUTHORS:20150713-145026468

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Abstract: Based on the new interpretation that rotons behave like tiny quantized vortex rings, a theory is constructed to give a complete picture of ultrasonic cavitation in liquid helium. The problem of nuclei of cavitation is approached from a new direction. Questions like the λ-peak of the audible threshold, the distinction among audible, incipient visible and desinent visible cavitation thresholds in He II, the lack of such distinction in He I, the reduction of audible threshold by rotation in He II and the absence of such reduction in He I, are satisfactorily explained. The relevance of the present theory to cavitation in ordinary liquids is briefly discussed.

ID: CaltechAUTHORS:20150713-160435368

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Abstract: The normal shock, hydraulic jump, and vortex breakdown have a common feature: they are all marked by a transition from a supercritical to a subcritical flow state. These phenomena are due to the nonlinearity of the flow, and it will be shown that viscosity also plays an essential role. This paper demonstrates explicitly how viscosity enters into these flows, The treatment of normal shock served a starting illustration. Then an equation governing the phenomenon of hydraulic jump is derived with the inclusion of the effect of viscosity. It is explicitly shown that supercritical flow is not stable and has to go through a transition to a conjugate subcritical flow state downstream. Similar treatment is also applied to vortex breakdown with largely similar results.

ID: CaltechAUTHORS:HSIrpt85-39

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Abstract: A brief critical survey on the hydrodynamic formulations of the superfluid helium is given first. For the irreversible process, three major formulations, i.e. those due to Gorter-Mellink, Lin, and Hall-Vinen, Bekarevitch-Khalatnikov, are described, discussed and compared. Then some results of analyses based on the Gorter-Mellink formulation are presented. The paper concludes with some interesting findings resulting from the assumption that rotons are vortex rings.

ID: CaltechAUTHORS:20150713-151026611

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Abstract: An analysis is made of the stability of two fluid layers in the gravity field. The upper layer is incompressible, inviscid and of infinite extent. The lower layer is incompressible, viscous and bounded below by a rigid plane. Both fluids are moving in the same direction parallel to the interface. It is found that the controlling mechanism for instability is of the Rayleigh-Taylor type which is inherent in inviscid flows. The main effect of viscosity is to diminish the rate of growth of the disturbances while the presence of linear shear flow in the lower layer has a tendency to stabilize the system.

ID: CaltechAUTHORS:20141014-160812802

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Abstract: A stability analysis is made for the laminar flow of a layer of a viscous and electrically conducting fluid down an inclined plane in a transverse magnetic field. It is found that the effect of the magnetic field, revealed through the Hartmann number, is to stabilize the flow. A simpler and physically clearer approximate treatment of the same problem based on the principle of local balance is also given. The results agree quite satisfactorily with the exact analysis.

ID: CaltechAUTHORS:20140603-144216060

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Abstract: A complete analysis of acoustic absorption by a spherical gas bubble is developed by the application of the classical Rayleigh method. The absorption considered is that due to the viscosity and heat conduction of the gas bubble. Specific results are presented for the S-wave scatter and absorption for the case of an air bubble in water, and the absorption effects of viscosity and heat conduction alone are calculated explicitly. The results found here are of similar magnitude to those found by Pfriem and Spitzer who used an approximate procedure.

ID: CaltechAUTHORS:HydroLabRpt85-19

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Abstract: In the first portion of this paper a review is given of the theory of the propagation of sound in a homogeneous gas taking into account the effect of heat conduction. This consideration is preliminary to the treatment in the second portion of the paper of the propagation of sound in a liquid with a homogeneous and isotropic distribution of gas bubbles. Again the effect of heat conduction is included. If f is the ratio of gas volume in the mixture to liquid volume, it is shown for the range of values of f of general interest that the acoustic condensations and rarefactions of the gaseous portion of the medium are essentially isothermal. It is also found that the attenuation of an acoustic disturbance by heat conduction is quite small.

ID: CaltechAUTHORS:20150713-152651809

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Abstract: The problem considered is the behavior of a gas bubble in a liquid saturated with dissolved gas when oscillating pressures are imposed on the system. This situation is encountered in experiments on cavitation and in the propagation of sonic and ultrasonic waves in liquids. Since gas diffuses into the bubble during the expansion half-cycle in which the pressure drops below its mean value, and diffuses out of the bubble during the compression half-cycle in which the pressure rises above its mean value, there is no net transfer of mass into or out of the bubble in first order. There is, however, in second order a net inflow of gas into the bubble which is called rectified diffusion. The equations which determine the system include the equation of state of the gas in the bubble, the equation of motion for the bubble boundary in the liquid, and the equation for the diffusion of dissolved gas in the liquid. In the solution presented here, the acoustic approximation is made; that is, the amplitude of the pressure oscillation is taken to be small. It is also assumed that the gas in the bubble remains isothermal throughout the oscillations; this assumption is valid provided the oscillation frequency is not too high. Under these conditions one finds for the mean rate of gas flow into the bubble the expression (dm/dt) = (8π/3)D C_∞ R_0 (ΔP/P_0)^2 where D is the diffusivity of the dissolved gas in the liquid, C_∞ is the equilibrium dissolved gas concentration for the mean ambient pressure P_0, R_0 is the mean radius of the bubble, and ΔP is the amplitude of the acoustic pressure oscillations. It may be remarked that the most important contribution to the rectification effect comes from the convection contribution to the diffusion process.

ID: CaltechAUTHORS:20150713-141317248

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