2,746 research outputs found
A Model of a Turbulent Boundary Layer With a Non-Zero Pressure Gradient
According to a model of the turbulent boundary layer proposed by the authors,
in the absence of external turbulence the intermediate region between the
viscous sublayer and the external flow consists of two sharply separated
self-similar structures. The velocity distribution in these structures is
described by two different scaling laws. The mean velocity u in the region
adjacent to the viscous sublayer is described by the previously obtained
Reynolds-number-dependent scaling law ,
, ,
. (Here is the dynamic or friction velocity, y is the
distance from the wall, the kinematic viscosity of the fluid, and the
Reynolds number is well defined by the data) In the region
adjacent to the external flow the scaling law is different: . The power for zero-pressure-gradient boundary layers
was found by processing various experimental data and is close (with some
scatter) to 0.2. We show here that for non-zero-pressure-gradient boundary
layers, the power is larger than 0.2 in the case of adverse pressure
gradient and less than 0.2 for favourable pressure gradient. Similarity
analysis suggests that both the coefficient B and the power depend on
and on a new dimensionless parameter P proportional to the
pressure gradient. Recent experimental data of Perry, Maru\v{s}i\'c and Jones
(1)-(4) were analyzed and the results are in agreement with the model we
propose.Comment: 10 pages, 9 figure
The Characteristic Length Scale of the Intermediate Structure in Zero-Pressure-Gradient Boundary Layer Flow
In a turbulent boundary layer over a smooth flat plate with zero pressure
gradient, the intermediate structure between the viscous sublayer and the free
stream consists of two layers: one adjacent to the viscous sublayer and one
adjacent to the free stream. When the level of turbulence in the free stream is
low, the boundary between the two layers is sharp and both have a self-similar
structure described by Reynolds-number-dependent scaling (power) laws. This
structure introduces two length scales: one --- the wall region thickness ---
determined by the sharp boundary between the two intermediate layers, the
second determined by the condition that the velocity distribution in the first
intermediate layer be the one common to all wall-bounded flows, and in
particular coincide with the scaling law previously determined for pipe flows.
Using recent experimental data we determine both these length scales and show
that they are close. Our results disagree with the classical model of the "wake
region".Comment: 11 pages, includes 2 tables and 3 figure
A Note on the Intermediate Region in Turbulent Boundary Layers
We demonstrate that the processing of the experimental data for the average
velocity profiles obtained by J. M. \"Osterlund
(www.mesh.kth.se/jens/zpg/) presented in [1] was incorrect. Properly
processed these data lead to the opposite conclusion: they confirm the
Reynolds-number-dependent scaling law and disprove the conclusion that the flow
in the intermediate (`overlap') region is Reynolds-number-independent.Comment: 8 pages, includes 1 table and 3 figures, broken web link in abstract
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A moving mesh finite element algorithm for fluid flow problems with moving boundaries
A moving mesh finite element method is proposed for the adaptive solution of second- and fourth-order moving boundary problems which exhibit scale invariance. The equations for the mesh movement are based upon the local application of a scale-invariant conservation principle incorporating a monitor function and have been successfully applied to problems in both one and two space dimensions. Examples are provided to show the performance of the proposed algorithm using a monitor function based upon arc-length
Nonlinear Diffusion and Image Contour Enhancement
The theory of degenerate parabolic equations of the forms is used to
analyze the process of contour enhancement in image processing, based on the
evolution model of Sethian and Malladi. The problem is studied in the framework
of nonlinear diffusion equations. It turns out that the standard initial-value
problem solved in this theory does not fit the present application since it it
does not produce image concentration. Due to the degenerate character of the
diffusivity at high gradient values, a new free boundary problem with singular
boundary data can be introduced, and it can be solved by means of a non-trivial
problem transformation. The asymptotic convergence to a sharp contour is
established and rates calculated.Comment: 29 pages, includes 6 figure
On the existence and scaling of structure functions in turbulence according to the data
We sample a velocity field that has an inertial spectrum and a skewness that
matches experimental data. In particular, we compute a self-consistent
correction to the Kolmogorov exponent and find that for our model it is zero.
We find that the higher order structure functions diverge for orders larger
than a certain threshold, as theorized in some recent work. The significance of
the results for the statistical theory of homogeneous turbulence is reviewed.Comment: 15 pages, 5 figures, to appear in PNA
Does Fully-Developed Turbulence Exist? Reynolds Number Independence versus Asymptotic Covariance
By analogy with recent arguments concerning the mean velocity profile of
wall-bounded turbulent shear flows, we suggest that there may exist corrections
to the 2/3 law of Kolmogorov, which are proportional to at
large Re. Such corrections to K41 are the only ones permitted if one insists
that the functional form of statistical averages at large Re be invariant under
a natural redefinition of Re. The family of curves of the observed longitudinal
structure function for different values of Re is bounded by an
envelope. In one generic scenario, close to the envelope, is
of the form assumed by Kolmogorov, with corrections of O((\lnRe)^{-2}). In an
alternative generic scenario, both the Kolmogorov constant and
corrections to Kolmogorov's linear relation for the third order structure
function are proportional to . Recent
experimental data of Praskovsky and Oncley appear to show a definite dependence
of on Re, which if confirmed, would be consistent with the arguments
given here.Comment: 13 Pages. Tex file and Postscript figure included in uufiles
compressed format. Needs macro uiucmac.tex, available from cond-mat archive
or from ftp://gijoe.mrl.uiuc.edu/pu
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