Static pressure correction in high Reynolds number fully developed turbulent pipe flow

Measurements are reported of the error in wall static pressure reading due to the finite size of the pressure tapping. The experiments were performed in incompressible turbulent pipe flow over a wide range of Reynolds numbers, and the results indicate that the correction term (as a fraction of the wall stress) continues to increase as the hole Reynolds number $d^+=u_\tau d/\nu$ increases, contrary to previous studies. For small holes relative to the pipe diameter the results follow a single curve, but for larger holes the data diverge from this universal behaviour at a point that depends on the ratio of the hole diameter to the pipe diameter

The Canonical Structure of the Superstring Action

We consider the canonical structure of the Green-Schwarz superstring in $9 + 1$ dimensions using the Dirac constraint formalism; it is shown that its structure is similar to that of the superparticle in $2 + 1$ and $3 + 1$ dimensions. A key feature of this structure is that the primary Fermionic constraints can be divided into two groups using field-independent projection operators; if one of these groups is eliminated through use of a Dirac Bracket (DB) then the second group of primary Fermionic constraints becomes first class. (This is what also happens with the superparticle action.) These primary Fermionic first class constraints can be used to find the generator of a local Fermionic gauge symmetry of the action. We also consider the superstring action in other dimensions of space-time to see if the Fermionic gauge symmetry can be made simpler than it is in $2 + 1$, $3 + 1$ and $9 + 1$ dimensions. With a $3 + 3$ dimensional target space, we find that such a simplification occurs. We finally show how in five dimensions there is no first class Fermionic constraint.Comment: 24 pages, Latex2e; further comments and clarifications adde

A critical layer model for turbulent pipe flow

A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale motions. The model is derived by treating the nonlinearity in the perturbation equation (involving the Reynolds stress) as an unknown forcing, yielding a linear relationship between the velocity field response and this nonlinearity. We do not assume small perturbations. We examine propagating modes, permitting comparison of our results to experimental data, and identify the steady component of the velocity field that varies only in the wall-normal direction as the turbulent mean profile. The "optimal" forcing shape, that gives the largest velocity response, is assumed to lead to modes that will be dominant and hence observed in turbulent pipe flow. An investigation of the most amplified velocity response at a given wavenumber-frequency combination reveals critical layer-like behaviour reminiscent of the neutrally stable solutions of the Orr-Sommerfeld equation in linearly unstable flow. Two distinct regions in the flow where the influence of viscosity becomes important can be identified, namely a wall layer that scales with $R^{+1/2}$ and a critical layer, where the propagation velocity is equal to the local mean velocity, that scales with $R^{+2/3}$ in pipe flow. This framework appears to be consistent with several scaling results in wall turbulence and reveals a mechanism by which the effects of viscosity can extend well beyond the immediate vicinity of the wall.Comment: Submitted to the Journal of Fluid Mechanics and currently under revie

Gauge Dependence in Chern-Simons Theory

We compute the contribution to the modulus of the one-loop effective action in pure non-Abelian Chern-Simons theory in an arbitrary covariant gauge. We find that the results are dependent on both the gauge parameter ($\alpha$) and the metric required in the gauge fixing. A contribution arises that has not been previously encountered; it is of the form $(\alpha / \sqrt{p^2}) \epsilon _{\mu \lambda \nu} p^\lambda$. This is possible as in three dimensions $\alpha$ is dimensionful. A variant of proper time regularization is used to render these integrals well behaved (although no divergences occur when the regularization is turned off at the end of the calculation). Since the original Lagrangian is unaltered in this approach, no symmetries of the classical theory are explicitly broken and $\epsilon_{\mu \lambda \nu}$ is handled unambiguously since the system is three dimensional at all stages of the calculation. The results are shown to be consistent with the so-called Nielsen identities which predict the explicit gauge parameter dependence using an extension of BRS symmetry. We demonstrate that this $\alpha$ dependence may potentially contribute to the vacuum expectation values of products of Wilson loops.Comment: 17 pp (including 3 figures). Uses REVTeX 3.0 and epsfig.sty (available from LANL). Latex thric

On the design of optimal compliant walls for turbulence control

This paper employs the theoretical framework developed by Luhar et al. (J. Fluid Mech., 768, 415-441) to consider the design of compliant walls for turbulent skin friction reduction. Specifically, the effects of simple spring-damper walls are contrasted with the effects of more complex walls incorporating tension, stiffness and anisotropy. In addition, varying mass ratios are tested to provide insight into differences between aerodynamic and hydrodynamic applications. Despite the differing physical responses, all the walls tested exhibit some important common features. First, the effect of the walls (positive or negative) is greatest at conditions close to resonance, with sharp transitions in performance across the resonant frequency or phase speed. Second, compliant walls are predicted to have a more pronounced effect on slower-moving structures because such structures generally have larger wall-pressure signatures. Third, two-dimensional (spanwise constant) structures are particularly susceptible to further amplification. These features are consistent with many previous experiments and simulations, suggesting that mitigating the rise of such two-dimensional structures is essential to designing performance-improving walls. For instance, it is shown that further amplification of such large-scale two-dimensional structures explains why the optimal anisotropic walls identified by Fukagata et al. via DNS (J. Turb., 9, 1-17) only led to drag reduction in very small domains. The above observations are used to develop design and methodology guidelines for future research on compliant walls

Off-Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral

The DeWitt expansion of the matrix element M_{xy} = \left\langle x \right| \exp -[\case{1}{2} (p-A)^2 + V]t \left| y \right\rangle, $(p=-i\partial)$ in powers of $t$ can be made in a number of ways. For $x=y$ (the case of interest when doing one-loop calculations) numerous approaches have been employed to determine this expansion to very high order; when $x \neq y$ (relevant for doing calculations beyond one-loop) there appear to be but two examples of performing the DeWitt expansion. In this paper we compute the off-diagonal elements of the DeWitt expansion coefficients using the Fock-Schwinger gauge. Our technique is based on representing $M_{xy}$ by a quantum mechanical path integral. We also generalize our method to the case of curved space, allowing us to determine the DeWitt expansion of \tilde M_{xy} = \langle x| \exp \case{1}{2} [\case{1}{\sqrt {g}} (\partial_\mu - i A_\mu)g^{\mu\nu}{\sqrt{g}}(\partial_\nu - i A_\nu) ] t| y \rangle by use of normal coordinates. By comparison with results for the DeWitt expansion of this matrix element obtained by the iterative solution of the diffusion equation, the relative merit of different approaches to the representation of $\tilde M_{xy}$ as a quantum mechanical path integral can be assessed. Furthermore, the exact dependence of $\tilde M_{xy}$ on some geometric scalars can be determined. In two appendices, we discuss boundary effects in the one-dimensional quantum mechanical path integral, and the curved space generalization of the Fock-Schwinger gauge.Comment: 16pp, REVTeX. One additional appendix concerning end-point effects for finite proper-time intervals; inclusion of these effects seem to make our results consistent with those from explicit heat-kernel method