759 research outputs found
The friction factor of two-dimensional rough-boundary turbulent soap film flows
We use momentum transfer arguments to predict the friction factor in
two-dimensional turbulent soap-film flows with rough boundaries (an analogue of
three-dimensional pipe flow) as a function of Reynolds number Re and roughness
, considering separately the inverse energy cascade and the forward
enstrophy cascade. At intermediate Re, we predict a Blasius-like friction
factor scaling of in flows dominated by the
enstrophy cascade, distinct from the energy cascade scaling of
. For large Re, in the enstrophy-dominated case.
We use conformal map techniques to perform direct numerical simulations that
are in satisfactory agreement with theory, and exhibit data collapse scaling of
roughness-induced criticality, previously shown to arise in the 3D pipe data of
Nikuradse.Comment: 4 pages, 3 figure
The asymmetric sandwich theorem
We discuss the asymmetric sandwich theorem, a generalization of the
Hahn-Banach theorem. As applications, we derive various results on the
existence of linear functionals that include bivariate, trivariate and
quadrivariate generalizations of the Fenchel duality theorem. Most of the
results are about affine functions defined on convex subsets of vector spaces,
rather than linear functions defined on vector spaces. We consider both results
that use a simple boundedness hypothesis (as in Rockafellar's version of the
Fenchel duality theorem) and also results that use Baire's theorem (as in the
Robinson-Attouch-Brezis version of the Fenchel duality theorem). This paper
also contains some new results about metrizable topological vector spaces that
are not necessarily locally convex.Comment: 17 page
Minimum Induced Drag for Tapered Wings Including Structural Constraints
For a wing in steady level flight, the lift distribution that minimizes induced drag depends on a tradeoff between wingspan and wing-structure weight. In 1933, Prandtl suggested that tapered wings have an advantage over rectangular wings due to this tradeoff. However, Prandtlâs solutions were obtained using assumptions that correspond to rectangular wings. Therefore, his claim was not analytically proven by his 1933 publication. Here, an approach similar to Prandtlâs is taken with more general approximations that apply to wings of arbitrary planform. This more general development is used to study Prandtlâs claim about tapered wings. Closed-form solutions for the optimum wingspan and corresponding induced drag are presented for wings having elliptic and linearly-tapered planforms with constraints of fixed wing loading and maximum stress. It is shown that induced drag is minimized with a triangular planform, which gives a reduction in induced drag of up to 24.44% over the rectangular planform and up to 11.71% over the elliptic planform. Numerical solutions for the lift distributions that minimize induced drag for each planform are also presented. It is shown that the optimum lift distribution produces up to 5.94% less induced drag than the elliptic lift distribution when the triangular planform is used
Local spectroscopy and atomic imaging of tunneling current, forces and dissipation on graphite
Theory predicts that the currents in scanning tunneling microscopy (STM) and
the attractive forces measured in atomic force microscopy (AFM) are directly
related. Atomic images obtained in an attractive AFM mode should therefore be
redundant because they should be \emph{similar} to STM. Here, we show that
while the distance dependence of current and force is similar for graphite,
constant-height AFM- and STM images differ substantially depending on distance
and bias voltage. We perform spectroscopy of the tunneling current, the
frequency shift and the damping signal at high-symmetry lattice sites of the
graphite (0001) surface. The dissipation signal is about twice as sensitive to
distance as the frequency shift, explained by the Prandtl-Tomlinson model of
atomic friction.Comment: 4 pages, 4 figures, accepted at Physical Review Letter
Structural lubricity: Role of dimension and symmetry
When two chemically passivated solids are brought into contact, interfacial
interactions between the solids compete with intrabulk elastic forces. The
relative importance of these interactions, which are length-scale dependent,
will be estimated using scaling arguments. If elastic interactions dominate on
all length scales, solids will move as essentially rigid objects. This would
imply superlow kinetic friction in UHV, provided wear was absent. The results
of the scaling study depend on the symmetry of the surfaces and the
dimensionalities of interface and solids. Some examples are discussed
explicitly such as contacts between disordered three-dimensional solids and
linear bearings realized from multiwall carbon nanotubes.Comment: 7 pages, 1 figur
On the Phenomenology of Hydrodynamic Shear Turbulence
The question of a purely hydrodynamic origin of turbulence in accretion disks
is reexamined, on the basis of a large body of experimental and numerical
evidence on various subcritical (i.e., linearly stable) hydrodynamic flows.
One of the main points of this paper is that the length scale and velocity
fluctuation amplitude which are characteristic of turbulent transport in these
flows scale like , where is the minimal Reynolds number for
the onset of fully developed turbulence. From this scaling, a simple
explanation of the dependence of with relative gap width in subcritical
Couette-Taylor flows is developed. It is also argued that flows in the shearing
sheet limit should be turbulent, and that the lack of turbulence in all such
simulations performed to date is most likely due to a lack of resolution, as a
consequence of the effect of the Coriolis force on the large scale fluctuations
of turbulent flows.
These results imply that accretion flows should be turbulent through
hydrodynamic processes. If this is the case, the Shakura-Sunyaev
parameter is constrained to lie in the range in accretion
disks, depending on unknown features of the mechanism which sustains
turbulence. Whether the hydrodynamic source of turbulence is more efficient
than the MHD one where present is an open question.Comment: 31 pages, 3 figures. Accepted for publication in Ap
Numerical Method for Rapid Aerostructural Design and Optimization
During early phases of wing design, analytic and low-fidelity methods are often used to identify promising design concepts. In many cases, solutions obtained using these methods provide intuition about the design space that is not easily obtained using higher-fidelity methods. This is especially true for aerostructural design. However, many analytic and low-fidelity aerostructural solutions are limited in application to wings with specific planforms and weight distributions. Here, a numerical method for minimizing induced drag with structural constraints is presented that uses approximations that apply to wings with arbitrary planforms and weight distributions. The method is applied to the NASA Ikhana airframe to show how it can be used for rapid aerostructural optimization and design-space exploration. The design space around the optimum solution is visualized, and the sensitivity of the optimum solution to changes in weight distribution, structural properties, wing loading, and taper ratio is shown. The optimum lift distribution and wing-structure weight for the Ikhana airframe are shown to be in good agreement with analytic solutions. Whereas most modern high-fidelity solvers obtain solutions in a matter of hours, all of the solutions shown here can be obtained in a matter of seconds
Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution
Results on the Prandtl-Blasius type kinetic and thermal boundary layer
thicknesses in turbulent Rayleigh-B\'enard convection in a broad range of
Prandtl numbers are presented. By solving the laminar Prandtl-Blasius boundary
layer equations, we calculate the ratio of the thermal and kinetic boundary
layer thicknesses, which depends on the Prandtl number Pr only. It is
approximated as for and as for
, with . Comparison of the Prandtl--Blasius velocity
boundary layer thickness with that evaluated in the direct numerical
simulations by Stevens, Verzicco, and Lohse (J. Fluid Mech. 643, 495 (2010))
gives very good agreement. Based on the Prandtl--Blasius type considerations,
we derive a lower-bound estimate for the minimum number of the computational
mesh nodes, required to conduct accurate numerical simulations of moderately
high (boundary layer dominated) turbulent Rayleigh-B\'enard convection, in the
thermal and kinetic boundary layers close to bottom and top plates. It is shown
that the number of required nodes within each boundary layer depends on Nu and
Pr and grows with the Rayleigh number Ra not slower than \sim\Ra^{0.15}. This
estimate agrees excellently with empirical results, which were based on the
convergence of the Nusselt number in numerical simulations
The apparent roughness of a sand surface blown by wind from an analytical model of saltation
We present an analytical model of aeolian sand transport. The model
quantifies the momentum transfer from the wind to the transported sand by
providing expressions for the thickness of the saltation layer and the apparent
surface roughness. These expressions are derived from basic physical principles
and a small number of assumptions. The model further predicts the sand
transport rate (mass flux) and the impact threshold (the smallest value of the
wind shear velocity at which saltation can be sustained). We show that, in
contrast to previous studies, the present model's predictions are in very good
agreement with a range of experiments, as well as with numerical simulations of
aeolian saltation. Because of its physical basis, we anticipate that our model
will find application in studies of aeolian sand transport on both Earth and
Mars
Mean-field transport in stratified and/or rotating turbulence
We investigate the mean electromotive force in the kinematic framework, that
is, ignoring the back-reaction of the magnetic field on the fluid velocity,
under the assumption of axisymmetric turbulence determined by the presence of
either rotation, density stratification, or both. We use an analogous approach
for the mean passive scalar flux. As an alternative to convection, we consider
forced turbulence in an isothermal layer. When using standard ansatzes, the
mean magnetic transport is then determined by nine, and the mean passive scalar
transport by four coefficients. We give results for all these transport
coefficients. We use the test-field method and the test-scalar method, where
transport coefficients are determined by solving sets of equations with
properly chosen mean magnetic fields or mean scalars. These methods are adapted
to mean fields which may depend on all three space coordinates. We find the
anisotropy of turbulent diffusion to be moderate in spite of rapid rotation or
strong density stratification. Contributions to the mean electromotive force
determined by the symmetric part of the gradient tensor of the mean magnetic
field, which were ignored in several earlier investigations, turn out to be
important. In stratified rotating turbulence, the effect is strongly
anisotropic, suppressed along the rotation axis on large length scales, but
strongly enhanced at intermediate length scales. Also the \OO\times\meanJJ
effect is enhanced at intermediate length scales. The turbulent passive scalar
diffusivity is typically almost twice as large as the turbulent magnetic
diffusivity. Both magnetic and passive scalar diffusion are slightly enhanced
along the rotation axis, but decreased if there is gravity.Comment: 12 pages, 8 figures, A&A, publishe
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