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

The TFOS DEWS II Pathophysiology Subcommittee reviewed the mechanisms involved in the initiation and perpetuation of dry eye disease. Its central mechanism is evaporative water loss leading to hyperosmolar tissue damage. Research in human disease and in animal models has shown that this, either directly or by inducing inflammation, causes a loss of both epithelial and goblet cells. The consequent decrease in surface wettability leads to early tear film breakup and amplifies hyperosmolarity via a Vicious Circle. Pain in dry eye is caused by tear hyperosmolarity, loss of lubrication, inflammatory mediators and neurosensory factors, while visual symptoms arise from tear and ocular surface irregularity. Increased friction targets damage to the lids and ocular surface, resulting in characteristic punctate epithelial keratitis, superior limbic keratoconjunctivitis, filamentary keratitis, lid parallel conjunctival folds, and lid wiper epitheliopathy. Hybrid dry eye disease, with features of both aqueous deficiency and increased evaporation, is common and efforts should be made to determine the relative contribution of each form to the total picture. To this end, practical methods are needed to measure tear evaporation in the clinic, and similarly, methods are needed to measure osmolarity at the tissue level across the ocular surface, to better determine the severity of dry eye. Areas for future research include the role of genetic mechanisms in non-Sjogren syndrome dry eye, the targeting of the terminal duct in meibomian gland disease and the influence of gaze dynamics and the closed eye state on tear stability and ocular surface inflammation.

TFOS DEWS II pathophysiology report

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.

/pdf/high-reynolds-number-wall-turbulence-1s7ld2qfbi.pdf

High–Reynolds Number Wall Turbulence

Wall-bounded turbulent flows at high Reynolds numbers have become an increasingly active area of research in recent years. Many challenges remain in theory, scaling, physical understanding, experimental techniques, and numerical simulations. In this paper we distill the salient advances of recent origin, particularly those that challenge textbook orthodoxy. Some of the outstanding questions, such as the extent of the logarithmic overlap layer, the universality or otherwise of the principal model parameters such as the von Karman “constant,” the parametrization of roughness effects, and the scaling of mean flow and Reynolds stresses, are highlighted. Research avenues that may provide answers to these questions, notably the improvement of measuring techniques and the construction of new facilities, are identified. We also highlight aspects where differences of opinion persist, with the expectation that this discussion might mark the beginning of their resolution.

/pdf/wall-bounded-turbulent-flows-at-high-reynolds-numbers-recent-ogu7wzlf0n.pdf

Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues

This review discusses the current understanding of tear-film physiology and mathematical models for some of its dynamics. First, a brief introduction to the tear film and the ocular surface is given. Next, mathematical models for the tear film are discussed, with an emphasis on models that describe the formation and relaxation of the tear film from blinking. Finally, future issues in tear film modeling are presented.

Dynamics of the Tear Film

Elastohydrodynamics of the eyelid wiper

This paper investigates the deposition of the tear film on the cornea of the human eye. The tear film is laid down by the motion of the upper eyelid and then subsequently flows and thins. Of particular interest is the stability of the tear layer and the development of dry patches on the cornea. While there has been significant research on the behaviour of tear films between blinks, this paper focuses on understanding the mechanisms which control the shape and thickness of the deposited film and how this affects the subsequent film behaviour. Numerical and analytical methods are applied to a lubrication model which includes the effects of surface tension, viscosity, gravity and evaporation. The model reveals the importance of the eyelid velocity, motion of the surface lipid layer and the storage of tear film between blinks.

Dynamics of tear film deposition and draining

The Effect of the Lipid Layer on Tear Film Behaviour

We investigate similarity solutions for the outer part of a zero-pressure-gradient turbulent boundary layer in the limit of infinite Reynolds number. Previous work by George (Phil. Trans. R. Soc. vol. 365, 2007 p. 789) has suggested that the only appropriate velocity scale for the outer region is U 1 , the free-stream velocity. This is based on the fact that scaling with U 1 leads to a mathematically valid similarity solution of the momentum equation for the outer region in the asymptotic limit of infinite Reynolds number. Here we show that the classical scaling using the friction velocity also leads to a valid similarity solution for the outer flow in this limit. Therefore on this basis it is not possible to dismiss the friction velocity as a possible scaling as has been suggested by George (2007) and others. We show that both the free-stream velocity and the friction velocity are potentially valid scalings according to this theoretical criterion.

On the asymptotic similarity of the zero-pressure-gradient turbulent boundary layer

Based on lubrication theory, an elastohydrodynamic model of
the human tear film is presented. Using this model we investigate
the effect altering the viscosity of the tears has on the
stresses acting on the cornea during a blink. In order to model
the compliant cornea and eyelid surface, a mattress model is
employed. This model is then coupled with the lubrication
model of the tear film leading to a one-dimensional nonlinear
partial differential equation governing the fluid pressure in the
lubrication film. The differential equation is solved numerically
using a finite-difference scheme. The results indicate that typical
tear additives will lead to an increase in the shear stress
acting on the cornea. This in turn may effect the shedding rates
of corneal epithelial cells. The model is also of use in predicting
the drag force the eyelid exerts on a contact lens and in assessing
how tear additives may effect the movement and rotation of
the contact lens.

https://people.eng.unimelb.edu.au/imarusic/proceedings/16/Jones.pdf

M. B. Jones

Papers

Elastohydrodynamics of the eyelid wiper

Dynamics of tear film deposition and draining

The Effect of the Lipid Layer on Tear Film Behaviour

On the asymptotic similarity of the zero-pressure-gradient turbulent boundary layer

Effect of tear additives on the shear stress and normal stress acting on the ocular surface