On the interaction of intense acoustic fields and viscous fluid flows.
Intense transverse resonant acoustic field interaction with viscous fluid flows
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Intense transverse resonant acoustic field interaction with viscous fluid flows
Intense transverse resonant acoustic field interaction with viscous fluid flows
Rigid rotating cylindrical shaft vibrations along diameter in viscous fluid using inner and outer expansions method
Flow field around and drag on sphere rising axially through rotating viscous fluid
The general solution is obtained of the equations of motion of a viscous fluid in which the velocity field is inversely proportional to the distance from a certain point. Some particular cases of such motion are investigated.
The stability of the two-dimensional flow induced by the tranverse oscillation of a cylinder in a viscous fluid is investigated in both the linear and weakly nonlinear regime. The major assumption that is made to simplify the problem is that the oscillation frequency is large in which case an unsteady boundary layer is set up on the cylinder. Results are given for cylinders of elliptic cross section and it is found that for any given eccentricity the most dangerous configuration is when the cylinder oscillates parallel to its minor axis. Some discussion of nonlinear effects is also given and for the circular cylinder it is shown that the steady streaming boundary layer of the basic flow is significantly altered by the instability.
The stability of the two-dimensional flow induced by the transverse oscillation of a cylinder in a viscous fluid is investigated in both the linear and weakly nonlinear regime. The major assumption that is made to simplify the problem is that the oscillation frequency is large in which case an unsteady boundary layer is set up on the cylinder. Results are given for cylinders of elliptic cross section and it is found that for any given eccentricity the most dangerous configuration is when the cylinder oscillates parallel to its minor axis. Some discussion of nonlinear effects is also given and for the circular cylinder it is shown that the steady streaming boundary layer of the basic flow is significantly altered by the instability.
Hydrodynamic force experienced by sphere moving slowly through viscous fluid towards plane surface at small gap widths, including inertial effects
In this paper, experiments are described for which inertial effects are negligible. A small aspect-ratio tank filled with a very viscous fluid (Pr = 10 to the 6th) is used to observe the behavior of convection for Rayleigh numbers up to 6.3 x 10 to the 5th. These high values are reached by conducting the experiment in a centrifuge which provides a 130-fold increase in apparent gravity. Rotational effects are small, but cannot be totally dismissed. In this geometry, thermal boundary layer instabilities are indeed observed, and are found to be very similar to their lower Prandtl number counterparts. It is tentatively concluded that once given a certain degree of 'vulnerability' convection can develop 'plume' like instabilities, even when the Prandtl number is infinite. The concept is applied to the earth's mantle and it is speculated that 'plumes' could well be the dominant mode of small-scale convection under the lithospheric plates.
Linear symmetric modes of propagation for viscous compressible liquid in rigid and elastic conduits analyzed using Navier-Stokes equations
The limiting flows of a viscous noncondensable fluid, which are approached by flows with stationary separation zones behind planar symmetrical bodies, with an unlimited increase in the Reynolds number are studied. Quantitative results are obtained in the case of a circulation flow inside of a separation zone.
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Thermal convection in the earth mantle is investigated by means of numerical simulations. The mantle models comprise two horizontal layers of viscous incompressible fluid (with identical or differing properties) separated by a fixed horizontal interface; an isothermal, fixed-heat-flux, or insulating lower boundary; and heat supplied either from below or internally (in the lower layer only, equally in both layers, or primarily in the upper layer). The mathematical formulation of the models is explained, and results for linear stability and finite-amplitude convection are presented in extensive tables and graphs and discussed in detail. Particular attention is given to the presence of thermal coupling without interface distortion in many cases, the predominance of long-wavelength cells in the finite-amplitude models, and the large (50 percent) temperature difference across the interface in all cases.
Linear symmetric modes of propagation for viscous compressible liquid in rigid and elastic conduits analyzed using Navier-Stokes equations
The convective stability of a viscous liquid in spherical layers is investigated taking into consideration rotation, the latitudinal temperature gradient, and shear flow. The results of calculating nonlinear convective motion in spherical layers are examined. A discussion is given of the applicability of the results obtained to studying convection in astrophysical objects.
The dispersion relation is evaluated numerically for Taylor waves in a viscous unstable interface with surface tension. The solution takes account of transverse curvature and the numerical evaluations apply to horizontal cylindrical, as well as to plane, interfaces. The result is verified with frequency and wavelength data obtained during film boiling on horizontal wires. A very general empirical correlation is given, en passant, for the vapor blanket thickness during film boiling.
The study of the breakup of a liquid jet moving in another medium, for example, a jet of fuel from a nozzle, shows that for sufficiently large outflow velocities the jet breaks up into a certain number of drops of different diameters. At still larger outflow velocities, the continuous part of the jet practically vanishes and the jet immediately breaks up at the nozzle into a large number of droplets of varying diameters (the case of "atomization"). The breakup mechanism in this case has a very complicated character and is quite irregular, with the droplets near the nozzle forming a divergent cone.
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