1,773 research outputs found
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 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 dimensions using the Dirac constraint formalism; it is shown that its
structure is similar to that of the superparticle in and
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 , and dimensions. With a 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 and a critical layer, where the propagation velocity is equal
to the local mean velocity, that scales with 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 () and
the metric required in the gauge fixing. A contribution arises that has not
been previously encountered; it is of the form . This is possible as in three dimensions
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 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 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, in
powers of can be made in a number of ways. For (the case of interest
when doing one-loop calculations) numerous approaches have been employed to
determine this expansion to very high order; when (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 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 as a quantum mechanical path integral can be assessed. Furthermore, the
exact dependence of 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
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