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

There is a special reason for reviewing this book at this time: it is the 50th edition of a compendium that is known and used frequently in most chemical and physical laboratories in many parts of the world. Surely, a publication that has been published for 56 years, withstanding the vagaries of science in this century, must have had something to offer. There is another reason: while the book is a standard fixture in most chemical and physical laboratories, including those in medical centers, it is not as frequently seen in the laboratories of physician's offices (those either in solo or group practice). I believe that the Handbook can be useful in those laboratories. One of the reasons, among others, is that the various basic items of information it offers may be helpful in new tests, either physical or chemical, which are continuously being published. The basic information may relate

Handbook of Chemistry and Physics

https://publications.mpi-cbg.de/Sbalzarini_2005_4820.pdf

Feature point tracking and trajectory analysis for video imaging in cell biology

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

/pdf/the-structure-of-turbulent-shear-flow-2yf3szhaqb.pdf

The Structure of Turbulent Shear Flow

Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

New insights into large eddy simulation

The dynamics of gravity currents are believed to be strongly influenced by dissipation due to turbulence and mixing between the current and the surrounding ambient fluid. This paper describes new theory and experiments on gravity currents produced by lock exchange which suggest that dissipation is unimportant when the Reynolds number is sufficiently high. Although there is mixing, the amount of energy dissipated is small, reducing the current speed by a few percent from the energy-conserving value. Benjamin (J. Fluid Mech. vol. 31, 1968, p. 209) suggests that dissipation is an essential ingredient in gravity current dynamics. We show that dissipation is not important at high Reynolds number, and provide an alternative theory that predicts the current speed and depth based on energy-conserving flow that is in good agreement with experiments. We predict that in a deep ambient the front Froude number is 1, rather than the previously accepted value of √ 2. New experiments are reported for this case that support the new theoretical value. This paper provides an analysis of the motion of a gravity current produced by lock exchange. In a lock exchange experiment, fluids of different densities initially at rest are separated by a vertical barrier – the lock gate – in a tank. When the gate is removed, differences in the hydrostatic pressure cause the denser fluid to flow in one direction along the bottom boundary of the tank, while the lighter fluid flows in the opposite direction along the top boundary of the tank. Figure 1 shows the initial configurations for lock exchange flows: a full-depth release when the depths of heavy and light fluid on both sides of the gate are equal is shown in (a )a nd apartial-depth release when the dense fluid occupies only a fraction of the full depth is shown in (b). Figure 2 shows the flow resulting from a full-depth lock release experiment. In this case the densities on the two sides of the lock gate are very similar (the density ratio γ = ρ1/ρ2 < 1 is close to unity). A dense gravity current travels to the right along the lower boundary and a buoyant current travels to the left along the upper boundary. Visually the flows are very nearly symmetric, and the dense and light fronts travel at almost the same speeds (figure 2b). The currents occupy about half the channel depth in each case, although they may be shallower immediately behind the head where there is mixing. The speeds of the two currents are constant within experimental resolution. Previous similar observations led Benjamin (1968) to develop a theory for the propagation of a steadily advancing current. He considered one half of the flow shown in figure 2(a), say the dense current only. In a frame of reference moving with the current, the front

/pdf/gravity-currents-produced-by-lock-exchange-5dnj5lmlup.pdf

Gravity currents produced by lock exchange

This paper outlines novel techniques for producing qualitative visualisations of density fluctuations and for obtaining quantitative whole-field density measurements in two-dimensional density-stratified flows. These techniques, which utilise image processing technology, are much simpler to set up than the classical schlieren and interferometry methods, and provide useful information in situations where shadowgraph is of little or no value. Moreover, they may be set-up to analyse much larger domains than is feasible with the classical approaches, and do not require high quality optical windows in the experimental apparatus. Ultimately the greatest strength of these techniques is the ability to extract accurate, quantitative measurements of the density field. Application of these techniques is illustrated by an internal wave field produced by an oscillating cylinder. Recent theoretical advances for this classical problem make it the ideal test bed. Results are presented for both a circular and a square cylinder oscillating vertically in a linear stratification. Further aspects of the techniques are illustrated by considering thermal convection from a hand and flow over an obstacle towed through a density stratified fluid.

Whole-field density measurements by ‘synthetic schlieren’

Although the relative importance of airborne transmission of the SARS-CoV-2 virus is controversial, increasing evidence suggests that understanding airflows is important for estimation of the risk of contracting COVID-19. The data available so far indicate that indoor transmission of the virus far outstrips outdoor transmission, possibly due to longer exposure times and the decreased turbulence levels (and therefore dispersion) found indoors. In this paper we discuss the role of building ventilation on the possible pathways of airborne particles and examine the fluid mechanics of the processes involved.

/pdf/effects-of-ventilation-on-the-indoor-spread-of-covid-19-1kaqm52c7y.pdf

Effects of ventilation on the indoor spread of COVID-19

This paper describes an experimental investigation of mixing due to Rayleigh–Taylor instability between two miscible fluids. Attention is focused on the gravitationally driven instability between a layer of salt water and a layer of fresh water with particular emphasis on the internal structure within the mixing zone. Three-dimensional numerical simulations of the same flow are used to give extra insight into the behaviour found in the experiments.The two layers are initially separated by a rigid barrier which is removed at the start of the experiment. The removal process injects vorticity into the flow and creates a small but significant initial disturbance. A novel aspect of the numerical investigation is that the measured velocity field for the start of the experiments has been used to initialize the simulations, achieving substantially improved agreement with experiment when compared with simulations using idealized initial conditions. It is shown that the spatial structure of these initial conditions is more important than their amplitude for the subsequent growth of the mixing region between the two layers. Simple measures of the growth of the instability are shown to be inappropriate due to the spatial structure of the initial conditions which continues to influence the flow throughout its evolution. As a result the mixing zone does not follow the classical quadratic time dependence predicted from similarity considerations. Direct comparison of external measures of the growth show the necessity to capture the gross features of the initial conditions while detailed measures of the internal structure show a rapid loss of memory of the finer details of the initial conditions.Image processing techniques are employed to provide a detailed study of the internal structure and statistics of the concentration field. These measurements demonstrate that, at scales small compared with the confining geometry, the flow rapidly adopts self-similar turbulent behaviour with the influence of the barrier-induced perturbation confined to the larger length scales. Concentration power spectra and the fractal dimension of iso-concentration contours are found to be representative of fully developed turbulence and there is close agreement between the experiments and simulations. Other statistics of the mixing zone show a reasonable level of agreement, the discrepancies mainly being due to experimental noise and the finite resolution of the simulations.

Self-similarity and internal structure of turbulence induced by Rayleigh Taylor instability

We present measurements of the density and velocity fields produced when an oscillating circular cylinder excites internal gravity waves in a stratified fluid. These measurements are obtained using a novel, non-intrusive optical technique suitable for determining the density fluctuation field in temporally evolving flows which are nominally two-dimensional. Although using the same basic principles as conventional methods, the technique uses digital image processing in lieu of large and expensive parabolic mirrors, thus allowing more flexibility and providing high sensitivity: perturbations of the order of 1% of the ambient density gradient may be detected. From the density gradient field and its time derivative it is possible to construct the perturbation fields of density and horizontal and vertical velocity. Thus, in principle, momentum and energy fluxes can be determined.In this paper we examine the structure and amplitude of internal gravity waves generated by a cylinder oscillating vertically at different frequencies and amplitudes, paying particular attention to the role of viscosity in determining the evolution of the waves. In qualitative agreement with theory, it is found that wave motions characterized by a bimodal displacement distribution close to the source are attenuated by viscosity and eventually undergo a transition to a unimodal displacement distribution further from the source. Close quantitative agreement is found when comparing our results with the theoretical ones of Hurley & Keady (1997). This demonstrates that the new experimental technique is capable of making accurate measurements and also lends support to analytic theories. However, theory predicts that the wave beams are narrower than observed, and the amplitude is significantly under-predicted for low-frequency waves. The discrepancy occurs in part because the theory neglects the presence of the viscous boundary layers surrounding the cylinder, and because it does not take into account the effects of wave attenuation resulting from nonlinear wave–wave interactions between the upward and downward propagating waves near the source.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112099005017

Stuart B. Dalziel

Papers

Gravity currents produced by lock exchange

Whole-field density measurements by ‘synthetic schlieren’

Effects of ventilation on the indoor spread of COVID-19

Self-similarity and internal structure of turbulence induced by Rayleigh Taylor instability

Visualization and measurement of internal waves by ‘synthetic schlieren’. Part 1. Vertically oscillating cylinder