Measurement of angular momentum transport in turbulent flow between independently rotating cylinders

We present measurements of the angular momentum flux (torque) in Taylor-Couette flow of water between independently rotating cylinders for all regions of the \(\Omega_1, \Omega_2\) parameter space at high Reynolds numbers, where $\Omega_1$ \(\Omega_2\) is the inner (outer) cylinder angular velocity. We find that the Rossby number Ro = \(\Omega_1 - \Omega_2\)/\Omega_2 fully determines the state and torque $G$ as compared to G(Ro = \infty) \equiv \Gi. The ratio G/\Gi is a linear function of $Ro^{-1}$ in four sections of the parameter space. For flows with radially-increasing angular momentum, our measured torques greatly exceed those of previous experiments [Ji \textit{et al.}, Nature, \textbf{444}, 343 (2006)], but agree with the analysis of Richard and Zahn [Astron. Astrophys., \textbf{347}, 734 (1999)].Comment: 4 pages, 4 figures, to appear in Physical Review Letter

Collective patterns arising out of spatio-temporal chaos

We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under a periodic boundary condition. Thus the spatial inhomogeneity of the statistical state arises through a spontaneous symmetry breaking. The transition from a state of homogeneous spatio-temporal chaos to one exhibiting spatial order is explained by introducing a collective viscosity which relates the averaged pattern with a correlation of the fluctuations.Comment: 11 pages (Revtex) + 5 figures (postscript

Boolean Chaos

We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultra-wide-band, extending from dc to beyond 2 GHz. The observed behavior is reproduced qualitatively using an autonomously updating Boolean model with signal propagation times that depend on the recent history of the gates and filtering of pulses of short duration, whose presence is confirmed experimentally. Electronic Boolean chaos may find application as an ultra-wide-band source of radio wavesComment: 10 pages and 4 figur

Variational bound on energy dissipation in turbulent shear flow

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in plane Couette flow, bridging the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits structure, namely a pronounced minimum at intermediate Reynolds numbers, and recovers the Busse bound in the asymptotic regime. The most notable feature is a bifurcation of the minimizing wavenumbers, giving rise to simple scaling of the optimized variational parameters, and of the upper bound, with the Reynolds number.Comment: 4 pages, RevTeX, 5 postscript figures are available as one .tar.gz file from [email protected]

Characterization of reconnecting vortices in superfluid helium

When two vortices cross, each of them breaks into two parts and exchanges part of itself for part of the other. This process, called vortex reconnection, occurs in classical as well as superfluids, and in magnetized plasmas and superconductors. We present the first experimental observations of reconnection between quantized vortices in superfluid helium. We do so by imaging micron-sized solid hydrogen particles trapped on quantized vortex cores (Bewley GP, Lathrop DP, Sreenivasan KR, 2006, Nature, 441:588), and by inferring the occurrence of reconnection from the motions of groups of recoiling particles. We show the distance separating particles on the just-reconnected vortex lines grows as a power law in time. The average value of the scaling exponent is approximately 1/2, consistent with the scale-invariant evolution of the vortices

Variational bound on energy dissipation in plane Couette flow

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in turbulent plane Couette flow. Using the compound matrix technique in order to reformulate this principle's spectral constraint, we derive a system of equations that is amenable to numerical treatment in the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits a minimum at intermediate Reynolds numbers, and reproduces the Busse bound in the asymptotic regime. As a consequence of a bifurcation of the minimizing wavenumbers, there exist two length scales that determine the optimal upper bound: the effective width of the variational profile's boundary segments, and the extension of their flat interior part.Comment: 22 pages, RevTeX, 11 postscript figures are available as one uuencoded .tar.gz file from [email protected]

Velocity Statistics Distinguish Quantum Turbulence from Classical Turbulence

By analyzing trajectories of solid hydrogen tracers, we find that the distributions of velocity in decaying quantum turbulence in superfluid $^4$He are strongly non-Gaussian with $1/v^3$ power-law tails. These features differ from the near-Gaussian statistics of homogenous and isotropic turbulence of classical fluids. We examine the dynamics of many events of reconnection between quantized vortices and show by simple scaling arguments that they produce the observed power-law tails.Comment: 4 pages, 4 figure

Microwave Gaseous Discharges

Contains reports on three research projects

Perfect-fluid cylinders and walls - sources for the Levi-Civita space-time

The diagonal metric tensor whose components are functions of one spatial coordinate is considered. Einstein's field equations for a perfect-fluid source are reduced to quadratures once a generating function, equal to the product of two of the metric components, is chosen. The solutions are either static fluid cylinders or walls depending on whether or not one of the spatial coordinates is periodic. Cylinder and wall sources are generated and matched to the vacuum (Levi--Civita) space--time. A match to a cylinder source is achieved for -\frac{1}{2}<\si<\frac{1}{2}, where \si is the mass per unit length in the Newtonian limit \si\to 0, and a match to a wall source is possible for |\si|>\frac{1}{2}, this case being without a Newtonian limit; the positive (negative) values of \si correspond to a positive (negative) fluid density. The range of \si for which a source has previously been matched to the Levi--Civita metric is 0\leq\si<\frac{1}{2} for a cylinder source.Comment: 22 pages, LaTeX, one included figure. Revised version: three (non-perfect-fluid) interior solutions are added, one of which falsifies the original conjecture in Sec. 4, and the circular geodesics of the Levi-Civita space-time are discussed in a footnot