The friction factor of two-dimensional rough-boundary turbulent soap film flows

We use momentum transfer arguments to predict the friction factor $f$ 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 $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $f\propto\textrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $\textrm{Re}^{-1/4}$. For large Re, $f \sim r$ 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 $0.588Pr^{-1/2}$ for $Pr\ll Pr^*$ and as $0.982 Pr^{-1/3}$ for $Pr^*\ll\Pr$, with $Pr^*= 0.046$. 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

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