68 research outputs found
Transition to turbulence in slowly divergent pipe flow
The results of a combined experimental and numerical study of the flow in
slowly diverging pipes are presented. Interestingly, an axisymmetric conical
recirculation cell has been observed. The conditions for its existence and the
length of the cell are simulated for a range of diverging angles and expansion
ratios. There is a critical velocity for the appearance of this state. When the
flow rate increases further, a subcritical transition for localized turbulence
arises. The transition and relaminarization experiments described here quantify
the extent of turbulence. The findings suggest that the transition scenario in
slowly diverging pipes is a combination of stages similar to those observed in
sudden expansions and in straight circular pipe flow.Comment: 8 pages, 5 figure
Helicity cascades in rotating turbulence
The effect of helicity (velocity-vorticity correlations) is studied in direct
numerical simulations of rotating turbulence down to Rossby numbers of 0.02.
The results suggest that the presence of net helicity plays an important role
in the dynamics of the flow. In particular, at small Rossby number, the energy
cascades to large scales, as expected, but helicity then can dominate the
cascade to small scales. A phenomenological interpretation in terms of a direct
cascade of helicity slowed down by wave-eddy interactions leads to the
prediction of new inertial indices for the small-scale energy and helicity
spectra.Comment: 7 pages, 8 figure
Orthogonal, solenoidal, three-dimensional vector fields for no-slip boundary conditions
Viscous fluid dynamical calculations require no-slip boundary conditions.
Numerical calculations of turbulence, as well as theoretical turbulence closure
techniques, often depend upon a spectral decomposition of the flow fields.
However, such calculations have been limited to two-dimensional situations.
Here we present a method that yields orthogonal decompositions of
incompressible, three-dimensional flow fields and apply it to periodic
cylindrical and spherical no-slip boundaries.Comment: 16 pages, 2 three-part figure
Laminar Craya-Curtet jets
This Brief Communication investigates laminar Craya-Curtet flows, formed when a jet with moderately large Reynolds number discharges into a coaxial ducted flow of much larger radius. It is seen that the Craya-Curtet number, C=(J/sub c//J/sub j/)/sup 1/2/, defined as the square root of the ratio of the momentum flux of the coflowing stream to that of the central jet, arises as the single governing parameter when the boundary-layer approximation is used to describe the resulting steady slender jet. The numerical integrations show that for C above a critical value C/sub c/ the resulting streamlines remain aligned with the axis, while for C<C/sub c/ the entrainment demands of the jet cannot be satisfied by the coflow, and a toroidal recirculation region forms. The critical Craya-Curtet number is determined for both uniform and parabolic coflow, yielding C/sub c/=0.65 and C/sub c/=0.77, respectively. The streamlines determined numerically are compared with those obtained experimentally by flow visualizations, yielding good agreement in the resulting flow structure and also in the value of C/sub c
The decay of Batchelor and Saffman rotating turbulence
The decay rate of isotropic and homogeneous turbulence is known to be
affected by the large-scale spectrum of the initial perturbations, associated
with at least two cannonical self-preserving solutions of the von
K\'arm\'an-Howarth equation: the so-called Batchelor and Saffman spectra. The
effect of long-range correlations in the decay of anisotropic flows is less
clear, and recently it has been proposed that the decay rate of rotating
turbulence may be independent of the large-scale spectrum of the initial
perturbations. We analyze numerical simulations of freely decaying rotating
turbulence with initial energy spectra (Batchelor turbulence) and
(Saffman turbulence) and show that, while a self-similar decay
cannot be identified for the total energy, the decay is indeed affected by
long-range correlations. The decay of two-dimensional and three-dimensional
modes follows distinct power laws in each case, which are consistent with
predictions derived from the anisotropic von K\'arm\'an-Howarth equation, and
with conservation of anisotropic integral quantities by the flow evolution
Anisotropy and non-universality in scaling laws of the large scale energy spectrum in rotating turbulence
Rapidly rotating turbulent flow is characterized by the emergence of columnar
structures that are representative of quasi-two dimensional behavior of the
flow. It is known that when energy is injected into the fluid at an
intermediate scale , it cascades towards smaller as well as larger scales.
In this paper we analyze the flow in the \textit{inverse cascade} range at a
small but fixed Rossby number, {}. Several
{numerical simulations with} helical and non-helical forcing functions are
considered in periodic boxes with unit aspect ratio. In order to resolve the
inverse cascade range with {reasonably} large Reynolds number, the analysis is
based on large eddy simulations which include the effect of helicity on eddy
viscosity and eddy noise. Thus, we model the small scales and resolve
explicitly the large scales. We show that the large-scale energy spectrum has
at least two solutions: one that is consistent with
Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of
energy in two-dimensional (2D) turbulence with a {}
scaling, and the other that corresponds to a steeper {}
spectrum in which the three-dimensional (3D) modes release a substantial
fraction of their energy per unit time to 2D modes. {The spectrum that} emerges
{depends on} the anisotropy of the forcing function{,} the former solution
prevailing for forcings in which more energy is injected into 2D modes while
the latter prevails for isotropic forcing. {In the case of anisotropic forcing,
whence the energy} goes from the 2D to the 3D modes at low wavenumbers,
large-scale shear is created resulting in another time scale ,
associated with shear, {thereby producing} a spectrum for the
{total energy} with the 2D modes still following a {}
scaling
Scaling dependence on the fluid viscosity ratio in the selective withdrawal transition
In the selective withdrawal experiment fluid is withdrawn through a tube with
its tip suspended a distance S above a two-fluid interface. At sufficiently low
withdrawal rates, Q, the interface forms a steady state hump and only the upper
fluid is withdrawn. When Q is increased (or S decreased), the interface
undergoes a transition so that the lower fluid is entrained with the upper one,
forming a thin steady-state spout. Near this transition the hump curvature
becomes very large and displays power-law scaling behavior. This scaling allows
for steady-state hump profiles at different flow rates and tube heights to be
scaled onto a single similarity profile. I show that the scaling behavior is
independent of the viscosity ratio.Comment: 33 Pages, 61 figures, 1 tabl
Variance anisotropy in compressible 3-D MHD
All Rights Reserved.We employ spectral method numerical simulations to examine the dynamical development of anisotropy of the variance, or polarization, of the magnetic and velocity field in compressible magnetohydrodynamic (MHD) turbulence. Both variance anisotropy and spectral anisotropy emerge under influence of a large-scale mean magnetic field B0; these are distinct effects, although sometimes related. Here we examine the appearance of variance parallel to B0, when starting from a highly anisotropic state. The discussion is based on a turbulence theoretic approach rather than a wave perspective. We find that parallel variance emerges over several characteristic nonlinear times, often attaining a quasi-steady level that depends on plasma beta. Consistency with solar wind observations seems to occur when the initial state is dominated by quasi-two-dimensional fluctuations
Stereo-PIV measurements of spatio-temporal turbulence correlations in an axisymmetric jet
Stereoscopic three-component particle image velocimetry (3C-PIV) measurements
have been made in a turbulent round jet to investigate the spatio-temporal correlations
that are the origin of aerodynamic noise. Restricting attention to subsonic, isothermal
jets, measurements were taken in a water flow experiment where, for the same
Reynolds number and nozzle size, the shortest time scale of the dynamically important
turbulent structures is more than an order of magnitude greater that in equivalent
airflow experiments, greatly facilitating time-resolved PIV measurements. Results
obtained (for a jet nozzle diameter and velocity of 40 mm and 1 m s\u1000001, giving
Re D 4 104) show that, on the basis of both single-point statistics and two-point
quantities (correlation functions, integral length scales) the present incompressible
flow data are in excellent agreement with published compressible, subsonic airflow
measurements. The 3C-PIV data are first compared to higher-spatial-resolution 2C-PIV
data and observed to be in good agreement, although some deterioration in quality
for higher-order correlations caused by high-frequency noise in the 3C-PIV data is
noted. A filter method to correct for this is proposed, based on proper orthogonal
decomposition (POD) of the 3C-PIV data. The corrected data are then used to
construct correlation maps at the second- and fourth-order level for all velocity
components. The present data are in accordance with existing hot-wire measurements,
but provide significantly more detailed information on correlation components than has
previously been available. The measured relative magnitudes of various components of
the two-point fourth-order turbulence correlation coefficient (Rij;kl) – the fundamental
building block for free shear flow aerodynamic noise sources – are presented and
represent a valuable source of validation data for acoustic source modelling. The
relationship between fourth-order and second-order velocity correlations is also
examined, based on an assumption of a quasi-Gaussian nearly normal p.d.f. for
the velocity fluctuations. The present results indicate that this approximation shows
reasonable agreement for the measured relative magnitudes of several correlation
components; however, areas of discrepancy are identified, indicating the need for
work on alternative models such as the shell turbulence concept of Afsar (Eur. J.
Mech. (B/Fluids), vol. 31, 2012, pp. 129–139)
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