697 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
Momentum and Heat Transfer in a Laminar Boundary Layer with Slip Flow
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77059/1/AIAA-22968-756.pd
Multimodality in Aerodynamic Wing Design Optimization
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143093/1/6.2017-3753.pd
Zipf law in the popularity distribution of chess openings
We perform a quantitative analysis of extensive chess databases and show that
the frequencies of opening moves are distributed according to a power-law with
an exponent that increases linearly with the game depth, whereas the pooled
distribution of all opening weights follows Zipf's law with universal exponent.
We propose a simple stochastic process that is able to capture the observed
playing statistics and show that the Zipf law arises from the self-similar
nature of the game tree of chess. Thus, in the case of hierarchical
fragmentation the scaling is truly universal and independent of a particular
generating mechanism. Our findings are of relevance in general processes with
composite decisions.Comment: 5 pages, 4 figure
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
Roughness-induced critical phenomena in a turbulent flow
I present empirical evidence that turbulent flows are closely analogous to
critical phenomena, from a reanalysis of friction factor measurements in rough
pipes. The data collapse found here corresponds to Widom scaling near critical
points, and implies that a full understanding of turbulence requires explicit
accounting for boundary roughness
On similarity and pseudo-similarity solutions of Falkner-Skan boundary layers
The present work deals with the two-dimensional incompressible,laminar,
steady-state boundary layer equations. First, we determinea family of velocity
distributions outside the boundary layer suchthat these problems may have
similarity solutions. Then, we examenin detail new exact solutions, called
Pseudo--similarity, where the external velocity varies inversely-linear with
the distance along the surface $ (U_e(x) = U_\infty x^{-1}). The present work
deals with the two-dimensional incompressible, laminar, steady-state boundary
layer equations. First, we determine a family of velocity distributions outside
the boundary layer such that these problems may have similarity solutions.
Then, we examenin detail new exact solutions. The analysis shows that solutions
exist only for a lateral suction. For specified conditions, we establish the
existence of an infinite number of solutions, including monotonic solutions and
solutions which oscillate an infinite number of times and tend to a certain
limit. The properties of solutions depend onthe suction parameter. Furthermore,
making use of the fourth--order Runge--Kutta scheme together with the shooting
method, numerical solutions are obtained.Comment: 15 page
Recommended from our members
Enigmatic persistence of dissolved organic matter in the ocean
Marine dissolved organic matter (DOM) contains more carbon than the combined stocks of Earth’s biota. Organisms in the ocean continuously release a myriad of molecules that become food for microheterotrophs, but, for unknown reasons, a residual fraction persists as DOM for millennia. In this Perspective, we discuss and compare two concepts that could explain this persistence. The long-standing ‘intrinsic recalcitrance’ paradigm attributes DOM stability to inherent molecular properties. In the ‘emergent recalcitrance’ concept, DOM is continuously transformed by marine microheterotrophs, with recalcitrance emerging on an ecosystems level. Both concepts are consistent with observations in the modern ocean, but they imply very different responses of the DOM pool to climate-related changes. To better understand DOM persistence, we propose a new overarching research strategy — the ecology of molecules — that integrates the concepts of intrinsic and emergent recalcitrance with the ecological and environmental context
Falkner-Skan Flow Over a Wedge with Slip Boundary Conditions
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76718/1/AIAA-2009-476-210.pd
Hydraulic resistance to overland flow on surfaces with partially submerged vegetation
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/96239/1/wrcr13661.pd
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