Weakly non-linear waves in rotating fluids
Rotating inviscid incompressible fluids in tubes, investigating axisymmetric nonlinear waves motion in relation to vortex breakdown
Leibovich, S.↗
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Vibration of microgravity environment for rotating fluids in high and low rotating speeds
Time dependent evolutions of the profile of free surface (bubble shapes) for a cylindrical container partially filled with a Newtonian fluid of constant density, rotating about its axis of symmetry, have been studied. Numerical computations of the dynamics of bubble shapes have been carried out with the sinusoidal function vibration of gravity environment in high and low rotating cylinder speeds. The initial condition of bubble profiles was adopted from the steady-state formulations in which the computer algorithms have been developed by Hung and Leslie (1988), and Hung et al. (1988).
Hung, R. J.↗
Effect of gravity level fluctuations for rotating fluids in high and low rotating speeds
Time-dependent evolutions of the profile of the free surface (bubble shapes) for a cylindrical container partially filled with a Newtonian fluid of constant density, rotating about its axis of symmetry, have been studied. Numerical computations of the dynamics of bubble shapes have been carried out with sinusoidal-function vibration of the gravity environment at high and low cylinder speeds.
Hung, R. J.↗
Rotational fluid coupling eliminates hose entanglements
Rotational fluid coupling mechanism circulates a temperature controlled fluid between a stationary heat exchanger and a coolant plate on a rotating platform. The mechanism consists of two concentric cylinders containing one or more flexible tubes which are controlled and positioned in such a way that it eliminates tubing entanglement.
Aubol, P. B.↗
Reorientation of rotating fluid in microgravity environment with and without gravity jitters
In a spacecraft design, the requirements of settled propellant are different for tank pressurization, engine restart, venting, or propellant transfer. The requirement to settle or to position liquid fuel over the outlet end of the spacecraft propellant tank prior main engine restart poses a microgravity fluid behavior problem. In this paper, the dynamical behavior of liquid propellant, fluid reorientation, and propellant resettling have been carried out through the execution of supercomputer CRAY X-MP to simulate the fluid management in a microgravity environment. Results show that the resettlement of fluid can be accomplished more efficiently for fluid in rotating tank than in nonrotating tank, and also better performance for gravity jitters imposed on fluid settlement than without gravity jitters based on the amount of time needed to carry out resettlement period of time between the initiation and termination of geysering.
Hung, R. J.↗
Circularly polarized inertial wave vectors in rotating fluids
The Navier-Stokes equations for a rotating fluid are harmonically analyzed for planar motion in an infinite half-space. All solutions are shown to be a sum of two inertial wave vectors, one circularly polarized to the left (CPL) and the other circularly polarized to the right (CPR). These basic solutions are therefore presented in the same nomenclature and form as that found useful by experimentalists in analyzing flow data (called 'rotary spectra'). The CPL wave acts counter to the Coriolis force and consequently has a slower phase speed and larger damping than the CPR wave. At resonance (forcing frequency = Coriolis frequency) the CPR wave has an infinite phase speed and no damping and is the important component leading to the singular nature of the solutions for certain boundary conditions. All possible resonant singularities are explicitly shown. The unsteady development of these unbounded (limited space structure), cyclic (no time origin or structure) flows is presented to show that with time structure the resonant singularities evolve in a self-similar manner.
Cogley, A. C.↗
Rotating-fluid experiments with an atmospheric general circulation model
In order to determine features of rotating fluid flow that are dependent on the geometry, rotating annulus-type experiments are carried out with a numerical model in spherical coordinates. Rather than constructing and testing a model expressly for this purpose, it is found expedient to modify an existing general circulation model of the atmosphere by removing the model physics and replacing the lower boundary with a uniform surface. A regime diagram derived from these model experiments is presented; its major features are interpreted and contrasted with the major features of rotating annulus regime diagrams. Within the wave regime, a narrow region is found where one or two zonal wave numbers are dominant. The results reveal no upper symmetric regime; wave activity at low rotation rates is thought to be maintained by barotropic rather than baroclinic processes.
Geisler, J. E.↗
Dissipative effects on nonlinear waves in rotating fluids.
Modifications to the existing inviscid theory of long-wave propagation in rotating fluids are studied. A modification to the Korteweg-deVries equation is found to describe weak dissipation in long waves in a swirling fluid. General features of solutions are discussed, and a solution for the damping of solitary waves is presented.
Leibovich, S.↗
Steady accretion of a rotating fluid
The accretion of rotating gas on to a gravitating object is investigated by means of a perturbation to the spherically symmetrical flow. An expression is found for the correction to the accretion rate due to rotation of the gas in terms of the boundary conditions far from the object. In the case of accretion from a cloud with uniform angular velocity, the gas is accreted preferentially from a 'jet' near the axis of rotation. The angular-momentum distribution in the cloud can be altered by the propagation of inertia waves.
Cassen, P.↗
The behavior of surface tension on steady-state rotating fluids in the low gravity environments
The effect of surface tension on steady-state rotating fluids in a low gravity environment is studied. All the values of the physical parameters used in these calculations, except in the low gravity environments, are based on the measurements carried out by Leslie (1985) in the low gravity environment of a free-falling aircraft. The profile of the interface of two fluids is derived from Laplace's equation relating the pressure drop across an interface to the radii of curvature which has been applied to a low gravity rotating bubble that contacts the container boundary. The interface shape depends on the ratio of gravity to surface tension forces, the ratio of centrifugal to surface tension forces, the contact radius of the interface to the boundary, and the contact angle. The shape of the bubble is symmetric about its equator in a zero-gravity environment. This symmetry disappears and gradually shifts to parabolic profiles as the gravity environment becomes non-zero. The location of the maximum radius of the bubble moves upward from the center of the depth toward the top boundary of the cylinder as gravity increases. The contact radius of interface to the boundary r0 at the top side of cylinder increases and r0 at the bottom side of the cylinder decreases as the gravity environment increases from zero to 1 g.
Hung, R. J.↗
Evolution of nonlinear waves in rotating fluids.
Wave equations coverning evolution of long nonlinear axially symmetric wave motion in inviscid rotating fluids
Leibovich, S.↗
Viscous boundary layers in rotating fluids driven by periodic flows
The paper analyzes the boundary layers formed in a rotating fluid by an oscillating flow over an infinite half plate, with particular attention paid to the effects of unsteadiness, the critical latitude effect and the structure of the solution to the boundary layer equations at resonance. The Navier-Stokes boundary layer equations are obtained through an asymptotic expansion with the incorporation of the Rossby and Ekman numbers and are analyzed as the sum of a nonlinear steady solution and a linearized unsteady solution. The solution is predominantly composed of two inertial wave vector components, one circularly polarized to the left and the other circularly polarized to the right. The problem considered here has relevance in oceanography and meteorology, with special reference to the unsteady atmospheric boundary layer.
Bergstrom, R. W.↗
Low gravity experiment for studying a rotating fluid having a free surface
Electrical, mechanical, and operational aspects of a test cell assembly for studying rotating fluids with a free surface are described. Results of a stress analysis prepared to document the structural adequacy for safe use on the KC-135 aircraft are presented along with results of a single load proof test of the most critical load case. Engineering drawings are included.
Holderer, O. C.↗
Effect of surface tension on the dynamical behavior of bubble in rotating fluids under low gravity environment
Time dependent evolutions of the profile of free surface (bubble shapes) for a cylindrical container partially filled with a Newtonian fluid of constant density, rotating about its axis of symmetry, have been studied. Numerical computations of the dynamics of bubble shapes have been carried out with the following situations: (1) linear functions of spin-up and spin-down in low and microgravity environments, (2) linear functions of increasing and decreasing gravity enviroment in high and low rotating cylidner speeds, (3) step functions of spin-up and spin-down in a low gravity environment, and (4) sinusoidal function oscillation of gravity environment in high and low rotating cylinder speeds. The initial condition of bubble profiles was adopted from the steady-state formulations in which the computer algorithms have been developed by Hung and Leslie (1988), and Hung et al. (1988).
Hung, R. J.↗
Time-dependent dynamical behavior of surface tension on rotating fluids under microgravity environment
Time dependent evolutions of the profile of free surface (bubble shapes) for a cylindrical container partially filled with a Newtonian fluid of constant density, rotating about its axis of symmetry, have been studied. Numerical computations of the dynamics of bubble shapes have been carried out with the following situations: (1) linear functions of spin-up and spin-down in low and microgravity environments, (2) step functions of spin-up and spin-down in a low gravity environment, and (3) sinusoidal function oscillation of gravity environment in high and low rotating cylinder speeds.
Hung, R. J.↗
Dynamical behavior of surface tension on rotating fluids in low and microgravity environments
Consideration is given to the time-dependent evolutions of the free surface profile (bubble shapes) of a cylindrical container, partially filled with a Newtonian fluid of constant density, rotating about its axis of symmetry in low and microgravity environments. The dynamics of the bubble shapes are calculated for four cases: linear time-dependent functions of spin-up and spin-down in low and microgravity, linear time-dependent functions of increasing and decreasing gravity at high and low rotating cylinder speeds, time-dependent step functions of spin-up and spin-down in low gravity, and sinusoidal function oscillation of the gravity environment in high and low rotating cylinder speeds. It is shown that the computer algorithms developed by Hung et al. (1988) may be used to simulate the profile of time-dependent bubble shapes under variations of centrifugal, capillary, and gravity forces.
Hung, R. J.↗
Computer modeling of the dynamics of surface tension on rotating fluids in low and microgravity environments
Time-dependent evolutions of the profile of the free surface (bubble shapes) for a cylindrical container partially filled with a Newtonian fluid of constant density, rotating about its axis of symmetry, have been studied. Numerical computations have been carried out with the following situations: (1) linear functions of spin-up and spin-down in low- and microgravity environments, (2) linear functions of increasing and decreasing gravity environments at high- and low-rotating cylinder speeds, and (3) step functions of spin-up and spin-down in a low-gravity environment.
Hung, R. J.↗
Accretion of rotating fluids by barytropes - Numerical results for white-dwarf models
Numerical sequences of rotating axisymmetric nonmagnetic equilibrium models are constructed which represent the evolution of a barytropic star as it accretes material from a rotating medium. Two accretion geometries are considered - one approximating accretion from a rotating cloud and the other, accretion from a Keplerian disk. It is assumed that some process, such as Ekman spin-up or nonequilibrium oscillations, maintains nearly constant angular velocity along cylinders about the rotation axis. Transport of angular momentum in the cylindrically radial direction by viscosity is included. Fluid instabilities and other physical processes leading to enhancement of this transport are discussed. Particular application is made to zero-temperature white-dwarf models, using the degenerate electron equation of state. An initially nonrotating 0.566-solar-mass white dwarf is followed during the accretion of more than one solar mass of material. Applications to degenerate stellar cores, to mass-transfer binary systems containing white dwarfs, such as novae and dwarf novae, to Type I supernovae, and to galactic X-ray sources are considered.
Durisen, R. H.↗