690 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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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
Self-Similar Solutions to a Density-Dependent Reaction-Diffusion Model
In this paper, we investigated a density-dependent reaction-diffusion
equation, . This equation is known as the
extension of the Fisher or Kolmogoroff-Petrovsky-Piscounoff equation which is
widely used in the population dynamics, combustion theory and plasma physics.
By employing the suitable transformation, this equation was mapped to the
anomalous diffusion equation where the nonlinear reaction term was eliminated.
Due to its simpler form, some exact self-similar solutions with the compact
support have been obtained. The solutions, evolving from an initial state,
converge to the usual traveling wave at a certain transition time. Hence, it is
quite clear the connection between the self-similar solution and the traveling
wave solution from these results. Moreover, the solutions were found in the
manner that either propagates to the right or propagates to the left.
Furthermore, the two solutions form a symmetric solution, expanding in both
directions. The application on the spatiotemporal pattern formation in
biological population has been mainly focused.Comment: 5 pages, 2 figures, accepted by Phys. Rev.
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