Recent progress in the theory of air flow as applied to aeronautics

In summing up it may be said that the hydrodynamic theories are best confirmed by experimental results for bodies with small resistance or drag and can accordingly be used in place of experimental tests

Gottingen Wind Tunnel for Testing Aircraft Models

Given here is a brief description of the Gottingen Wind Tunnel for the testing of aircraft models, preceded by a history of its development. Included are a number of diagrams illustrating, among other things, a sectional elevation of the wind tunnel, the pressure regulator, the entrance cone and method of supporting a model for simple drag tests, a three-component balance, and a propeller testing device, all of which are discussed in the text

Some remarks concerning soaring flight

The publication of the following details is due to the desire of the editor to have the problems of soaring flight treated on the occasion of the Rhone Soaring Flight Contest

Applications of Modern Hydrodynamics to Aeronautics. Part 1: Fundamental Concepts and the Most Important Theorems. Part 2: Applications

A discussion of the principles of hydrodynamics of nonviscous fluids in the case of motion of solid bodies in a fluid is presented. Formulae are derived to demonstrate the transition from the fluid surface to a corresponding 'control surface'. The external forces are compounded of the fluid pressures on the control surface and the forces which are exercised on the fluid by any solid bodies which may be inside of the control surfaces. Illustrations of these formulae as applied to the acquisition of transformations from a known simple flow to new types of flow for other boundaries are given. Theoretical and experimental investigations of models of airship bodies are presented

Induced drag of multiplanes

The most important part of the resistance or drag of a wing system,the induced drag, can be calculated theoretically, when the distribution of lift on the individual wings is known. The calculation is based upon the assumption that the lift on the wings is distributed along the wing in proportion to the ordinates of a semi-ellipse. Formulas and numerical tables are given for calculating the drag. In this connection, the most favorable arrangements of biplanes and triplanes are discussed and the results are further elucidated by means of numerical examples

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 $(\ln\,\Re)^{-1}$ 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 $D_{LL}(r, \Re)$ for different values of Re is bounded by an envelope. In one generic scenario, close to the envelope, $D_{LL}(r, \Re)$ is of the form assumed by Kolmogorov, with corrections of O((\lnRe)^{-2}). In an alternative generic scenario, both the Kolmogorov constant $C_K$ and corrections to Kolmogorov's linear relation for the third order structure function $D_{LLL} (r)$ are proportional to $(\ln\,\Re)^{-1}$. Recent experimental data of Praskovsky and Oncley appear to show a definite dependence of $C_K$ 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

Nonlinear diffusion model for Rayleigh-Taylor mixing

The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusiviy models for the mean temperature profile. It is found that a non-linear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection.Comment: 4 pages, 4 figure, PRL in pres

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

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

Imaging the stick-slip peeling of an adhesive tape under a constant load

Using a high speed camera, we study the peeling dynamics of an adhesive tape under a constant load with a special focus on the so-called stick-slip regime of the peeling. It is the first time that the very fast motion of the peeling point is imaged. The speed of the camera, up to 16000 fps, allows us to observe and quantify the details of the peeling point motion during the stick and slip phases: stick and slip velocities, durations and amplitudes. First, in contrast with previous observations, the stick-slip regime appears to be only transient in the force controlled peeling. Additionally, we discover that the stick and slip phases have similar durations and that at high mean peeling velocity, the slip phase actually lasts longer than the stick phase. Depending on the mean peeling velocity, we also observe that the velocity change between stick and slip phase ranges from a rather sudden to a smooth transition. These new observations can help to discriminate between the various assumptions used in theoretical models for describing the complex peeling of an adhesive tape. The present imaging technique opens the door for an extensive study of the velocity controlled stick-slip peeling of an adhesive tape that will allow to understand the statistical complexity of the stick-slip in a stationary case