The role of coherent structures in the production and dissipation of turbulence in a boundary layer is characterized, summarizing the results of recent investigations. Coherent motion is defined as a three-dimensional region of flow where at least one fundamental variable exhibits significant correlation with itself or with another variable over a space or time range significantly larger than the smallest local scales of the flow. Sections are then devoted to flow-visualization experiments, statistical analyses, numerical simulation techniques, the history of coherent-structure studies, vortices and vortical structures, conceptual models, and predictive models. Diagrams and graphs are provided.

Coherent Motions in the Turbulent Boundary Layer

Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem, but the results of such investigations agree poorly in many cases with experiments. Nevertheless, linear effects play a central role in hydrodynamic instability. A reconciliation of these findings with the traditional analysis is presented based on the "pseudospectra" of the linearized problem, which imply that small perturbations to the smooth flow may be amplified by factors on the order of 105 by a linear mechanism even though all the eigenmodes decay monotonically. The methods suggested here apply also to other problems in the mathematical sciences that involve nonorthogonal eigenfunctions.

https://people.maths.ox.ac.uk/trefethen/publication/PDF/1993_57.pdf

Hydrodynamic Stability Without Eigenvalues

▪ Abstract We review the direct numerical simulation (DNS) of turbulent flows. We stress that DNS is a research tool, and not a brute-force solution to the Navier-Stokes equations for engineering problems. The wide range of scales in turbulent flows requires that care be taken in their numerical solution. We discuss related numerical issues such as boundary conditions and spatial and temporal discretization. Significant insight into turbulence physics has been gained from DNS of certain idealized flows that cannot be easily attained in the laboratory. We discuss some examples. Further, we illustrate the complementary nature of experiments and computations in turbulence research. Examples are provided where DNS data has been used to evaluate measurement accuracy. Finally, we consider how DNS has impacted turbulence modeling and provided further insight into the structure of turbulent boundary layers.

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DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research

The micromachining technology that emerged in the late 1980s can provide micron-sized sensors and actuators. These micro transducers are able to be integrated with signal conditioning and processing circuitry to form micro-electromechanical-systems (MEMS) that can perform real-time distributed control. This capability opens up a new territory for flow control research. On the other hand, surface effects dominate the fluid flowing through these miniature mechanical devices because of the large surface-to-volume ratio in micron-scale configurations. We need to reexamine the surface forces in the momentum equation. Owing to their smallness, gas flows experience large Knudsen numbers, and therefore boundary conditions need to be modified. Besides being an enabling technology, MEMS also provide many challenges for fundamental flow-science research.

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Micro-electro-mechanical-systems (mems) and fluid flows

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Evidence of very long meandering features in the logarithmic region of turbulent boundary layers

The fluctuating wall‐shear stress was measured with various types of hot‐wire and hot‐film sensors in turbulent boundary‐layer and channel flows. The rms level of the streamwise wall‐shear stress fluctuations was found to be 40% of the mean value, which was substantiated by measurements of the streamwise velocity fluctuations in the viscous sublayer. Heat transfer to the fluid via the probe substrate was found to give significant differences between the static and dynamic response for standard flush‐mounted hot‐film probes with air or oil as the flow medium, whereas measurements in water were shown to be essentially unaffected by this problem.

The fluctuating wall‐shear stress and the velocity field in the viscous sublayer

The bursting frequency in turbulent boundary layers has been measured over the Reynolds-number range 103 < U∞/ν < 104. When scaled with the variables appropriate for the wall region, the non-dimensional frequency was constant independent of Reynolds number. A strong effect of the sensor size was noted on the measured bursting frequency. Only sensors having a spatial scale less than twenty viscous lengthscales were free from spatial-averaging effects and yielded consistent results. The spatial-resolution problem was apparently the reason for erroneous results reported in the past.

Scaling of the bursting frequency in turbulent boundary layers

A microfabricated floating-element shear-stress sensor for measurements in turbulent boundary-layers is reported. Using surface micromachining of polyimide, a 500- mu m*500- mu m probe has been fabricated incorporating a differential-capacitor readout circuit. A model for the sensor response is described and is used for the design of an element to measure shear stresses of 1 Pa in air. The sensor is packaged for calibration in laminar flow, and electrical results obtained match the expected response. >

Design and calibration of a microfabricated floating-element shear-stress sensor

Knowledge of the wall shear stress is of both fundamental and practical importance The mean stress is indicative of the overall state of the flow over a given surface while the fluctuating stress is a “footprint” of the individual processes that transfer momentum to the wall The measurement techniques can be divided into two main categories: direct and indirect The indirect techniques can be further divided into momentum balance methods and correlation methods

The Measurement of Wall Shear Stress

The coupling between high-amplitude wall-pressure peaks and flow structures, especially in the near-wall region, was studied for a zero-pressure-gradient turbulent-boundary-layer flow and for the flow in the interior of artificially generated turbulent spots. By use of an ‘enhanced’ conditional averaging technique it was shown that buffer region shear-layer structures are to a high degree responsible for the generation of large positive wall-pressure peaks. The relation was proved to be bi-directional in that strong shear layers were shown to accompany positive pressure peaks and correspondingly that large pressure peaks were associated with shear-layer structures detected in the buffer region. This also indicates a link between the wall-pressure peaks and turbulence-producing mechanisms. The pressure-peak amplitude was found to scale linearly with the velocity amplitude of the generating flow structure, indicating that a dominating role here is played by the so-called turbulence – mean shear interaction. The large negative wall-pressure peaks were found to be associated primarily with sweep-type motions. All essential features of the relation between wall-pressure peaks and flow structures in artificially generated spots in a laminar boundary layer were found to be identical to those in the equilibrium turbulent boundary layer.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112087000326

Joseph H. Haritonidis

Papers

The fluctuating wall‐shear stress and the velocity field in the viscous sublayer

Scaling of the bursting frequency in turbulent boundary layers

Design and calibration of a microfabricated floating-element shear-stress sensor

The Measurement of Wall Shear Stress

On the generation of high-amplitude wall-pressure peaks in turbulent boundary layers and spots