The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

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The Structure of Turbulent Shear Flow

We review wall-bounded turbulent flows, particularly high–Reynolds number, zero–pressure gradient boundary layers, and fully developed pipe and channel flows. It is apparent that the approach to an asymptotically high–Reynolds number state is slow, but at a sufficiently high Reynolds number the log law remains a fundamental part of the mean flow description. With regard to the coherent motions, very-large-scale motions or superstructures exist at all Reynolds numbers, but they become increasingly important with Reynolds number in terms of their energy content and their interaction with the smaller scales near the wall. There is accumulating evidence that certain features are flow specific, such as the constants in the log law and the behavior of the very large scales and their interaction with the large scales (consisting of vortex packets). Moreover, the refined attached-eddy hypothesis continues to provide an important theoretical framework for the structure of wall-bounded turbulent flows.

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High–Reynolds Number Wall Turbulence

Localized fluid flow measurements with an He-Ne laser spectrometer

Statistics obtained from seven different direct numerical simulations (DNSs) pertaining to a canonical turbulent boundary layer (TBL) under zero pressure gradient are compiled and compared. The considered data sets include a recent DNS of a TBL with the extended range of Reynolds numbers Reθ = 500–4300. Although all the simulations relate to the same physical flow case, the approaches differ in the applied numerical method, grid resolution and distribution, inflow generation method, boundary conditions and box dimensions. The resulting comparison shows surprisingly large differences not only in both basic integral quantities such as the friction coefficient cf or the shape factor H12, but also in their predictions of mean and fluctuation profiles far into the sublayer. It is thus shown that the numerical simulation of TBLs is, mainly due to the spatial development of the flow, very sensitive to, e.g. proper inflow condition, sufficient settling length and appropriate box dimensions. Thus, a DNS has to be considered as a numerical experiment and should be the subject of the same scrutiny as experimental data. However, if a DNS is set up with the necessary care, it can provide a faithful tool to predict even such notoriously difficult flow cases with great accuracy.

Assessment of direct numerical simulation data of turbulent boundary layers

Direct numerical simulations (DNSs) and experiments of a spatially developing zero-pressure-gradient turbulent boundary layer are presented up to Reynolds number Re-theta=2500, based on momentum th ...

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Turbulent boundary layers up to Reθ=2500 studied through simulation and experiment

A recent assessment of available direct numerical simulation (DNS) data from turbulent boundary layer flows (Schlatter & Orlu, J. Fluid Mech., vol. 659, 2010, pp. 116-126) showed surprisingly l ...

Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects

Simulation and validation of a spatially evolving turbulent boundary layer up to Reθ = 8300

Turbulent flow close to solid walls is dominated by an ensemble of fluctuations of large and small spatial scales. Recent work by Mathis [J. Fluid Mech. 628, 311 (2009); Phys. Fluids 21, 111703 (20 ...

Ramis Örlü

Papers

Assessment of direct numerical simulation data of turbulent boundary layers

Turbulent boundary layers up to Reθ=2500 studied through simulation and experiment

Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects

Simulation and validation of a spatially evolving turbulent boundary layer up to Reθ = 8300

Quantifying the interaction between large and small scales in wall-bounded turbulent flows: A note of caution