Russell J. Donnelly

Turbulent convection at very high Rayleigh numbers

Turbulent convection occurs when the Rayleigh number (Ra)—which quantifies the relative magnitude of thermal driving to dissipative forces in the fluid motion—becomes sufficiently high. Although many theoretical and experimental studies of turbulent convection exist, the basic properties of heat transport remain unclear. One important question concerns the existence of an asymptotic regime that is supposed to occur at very high Ra. Theory predicts that in such a state the Nusselt number (Nu), representing the global heat transport, should scale as Nu ∝ Raβ with β = 1/2. Here we investigate thermal transport over eleven orders of magnitude of the Rayleigh number (106 ≤ Ra ≤ 10 17), using cryogenic helium gas as the working fluid. Our data, over the entire range of Ra, can be described to the lowest order by a single power-law with scaling exponent β close to 0.31. In particular, we find no evidence for a transition to the Ra1/2 regime. We also study the variation of internal temperature fluctuations with Ra, and probe velocity statistics indirectly.

The Observed Properties of Liquid Helium at the Saturated Vapor Pressure

The equilibrium and transport properties of liquid 4He are deduced from experimental observations at the saturated vapor pressure. In each case, the bibliography lists all known measurements. Quantities reported here include density, thermal expansion coefficient, dielectric constant, superfluid and normal fluid densities, first, second, third, and fourth sound velocities, specific heat, enthalpy, entropy, surface tension, ion mobilities, mutual friction, viscosity and kinematic viscosity, dispersion curve, structure factor, thermal conductivity, latent heat, saturated vapor pressure, thermal diffusivity and Prandtl number of helium I, and displacement length and vortex core parameter in helium II.

Quantized vortex dynamics and superfluid turbulence

to Superfluid Vortices and Turbulence.- Turbulence Experiments.- An Introduction to Experiments on Superfluid Turbulence.- The Experimental Evidence for Vortex Nucleation in 4He.- Applications of Superfluid Helium in Large-Scale Superconducting Systems.- The Temperature Dependent Drag Crisis on a Sphere in Flowing Helium II.- Experiments on Quantized Turbulence at mK Temperatures.- Grid-Generated He II Turbulence in a Finite Channel - Experiment.- Intermittent Switching Between Turbulent and Potential Flow Around a Sphere in He II at mK Temperatures.- Vortex Dynamics.- Vortex Filament Methods for Superfluids.- to HVBK Dynamics.- Magnus Force, Aharonov-Bohm Effect, and Berry Phase in Superfluids.- Using the HVBK Model to Investigate the Couette Flow of Helium II.- Turbulence Theory.- An Introduction to the Theory of Superfluid Turbulence.- Numerical Methods for Coupled Normal-Fluid and Superfluid Flows in Helium II.- From Vortex Reconnections to Quantum Turbulence.- Vortices and Stability in Superfluid Boundary Layers.- Grid Generated He II Turbulence in a Finite Channel-Theoretical Interpretation.- Vortex Tangle Dynamics Without Mutual Friction in Superfluid 4He.- Applications of the Gaussian Model of the Vortex Tangle in the Superfluid Turbulent He II.- Stochastic Dynamics of a Vortex Loop. Thermal Equilibrium.- Stochastic Dynamics of a Vortex Loop. Large-Scale Stirring Force.- Nonequilibrium Vortex Dynamics in Superfluid Phase Transitions and Superfluid Turbulence.- The NLSE and Superfluidity.- The Nonlinear Schrodinger Equation as a Model of Superfluidity.- Vortex Nucleation and Limit Speed for a Flow Passing Nonlinearly Around a Disk in the Nonlinear Schrodinger Equation.- Vortices in Nonlocal Condensate Models of Superfluid Helium.- Ginzburg-Landau Description of Vortex Nucleation in a Rotating Superfluid.- Weak Turbulence Theory for the Gross-Pitaevskii Equation.- Dissipative Vortex Dynamics and Magnus Force.- Transition to Dissipation in Two- and Three-Dimensional Superflows.- Bose-Einstein Condensation.- Motion of Objects Through Dilute Bose-Einstein Condensates.- Stability of a Vortex in a Rotating Trapped Bose-Einstein Condensate*.- Kinetics of Strongly Non-equilibrium Bose-Einstein Condensation.- Quantum Nucleation of Phase Slips in Bose-Einstein Condensates.- Vortex Reconnections and Classical Aspects.- Vortex Reconnection in Normal and Superfluids.- Helicity in Hydro and MHD Reconnection.- Tropicity and Complexity Measures for Vortex Tangles.- The Geometry of Magnetic and Vortex Reconnection.- Current-Sheet Formation near a Hyperbolic Magnetic Neutral Line.- Nonlocality in Turbulence.- Helium 3 and Other Systems.- Quantized Vorticity in Superfluid 3He-A: Structure and Dynamics.- Vortices in Metastable 4He Films.- Quantum Hall E.ect Breakdown Steps and Possible Analogies with Classical and Super.uid Hydrodynamics.- Atomic Bose Condensate with a Spin Structure: The Use of Bloch State.- Quantum Dynamics of Vortex-Antivortex Pairs in a Circular Box.

Friction on quantized vortices in helium II. A review

We present an analysis of recent data on friction and drag on quantized vortices in helium II. From these data, we deduce values of the phenomenological and microscopic coefficients of friction on vortex lines and rings over a wide range of temperatures at the saturated vapor pressure. We demonstrate that the microscopic parameters are unusually sensitive to the input data. We include brief discussions of the vortex core parameter, and present the results of precision fits of a number of thermodynamic and transport properties of He II which are used in mutual friction calculations.

The wind in confined thermal convection

A large-scale circulation velocity, often called the ‘wind’, has been observed in turbulent convection in the Rayleigh–Benard apparatus, which is a closed box with a heated bottom wall. The wind survives even when the dynamical parameter, namely the Rayleigh number, is very large. Over a wide range of time scales greater than its characteristic turnover time, the wind velocity exhibits occasional and irregular reversals without a change in magnitude. We study this feature experimentally in an apparatus of aspect ratio unity, in which the highest attainable Rayleigh number is about 10 16 . A possible physical explanation is attempted.

Power spectral analysis of a dynamical system

Abstract Power spectra for chaotic transitions in three dimensions are presented for a dynamical system first proposed by Rossler. Relations between the spectra and the topology of the corresponding strange attractor are discussed.

The calculated thermodynamic properties of superfluid helium‐4

Comprehensive tables of the primary thermodynamic properties of superfluid helium‐4, such as the specific heat and entropy, are presented as computed from the Landau quasiparticle model, with the aid of inelastic neutron scattering data. The neutron data are presented by continuous functions of temperature pressure, and wave number and certain excitation properties such as number density, normal and superfluid densities are calculated directly from it. A discussion of the methods used in our computations is included, and comparisons of computed and experimental results are made where applicable. Certain inadequacies of present theoretical methods to describe the thermodynamic properties are reported, and the use of an effective spectrum is introduced to offset some of these difficulties. Considerable experimental effort is also needed to improve the present situation.

Friction factors for smooth pipe flow

Friction factor data from two recent pipe flow experiments are combined to provide a comprehensive picture of the friction factor variation for Reynolds numbers from 10 to 36,000,000.

Specific heat and dispersion curve for helium II

The dispersion curve for elementary excitations in He II at low temperatures and at the vapor pressure is evaluated using inelastic neutron scattering data. It is found that this dispersion curve is consistent with recent specific heat measurements of high resolution. We represent the dispersion curve by means of cubic splines, and emphasize the need for further neutron scattering studies at low momentum transfer.

Dynamics of thin vortex rings

As part of a long-range study of vortex rings, their dynamics, interactions with boundaries and with each other, we present the results of experiments on thin core rings generated by a piston gun in water. We characterize the dynamics of these rings by means of the traditional equations for such rings in an inviscid fluid suitably modifying them to be applicable to a viscous fluid. We develop expressions for the radius, core size, circulation and bubble dimensions of these rings. We report the direct measurement of the impulse of a vortex ring by means of a physical pendulum.