The numerical computation of turbulent flows

Fundamental Principles Laminar Boundary Layer Flow Laminar Duct Flow External Natural Convection Internal Natural Convection Transition to Turbulence Turbulent Boundary Layer Flow Turbulent Duct Flow Free Turbulent Flows Convection with Change of Phase Mass Transfer Convection in Porous Media.

/pdf/convection-heat-transfer-47drgw6czo.pdf

Convection Heat Transfer

A theoretical framework is proposed for the analysis of adhesion between cells or of cells to surfaces when the adhesion is mediated by reversible bonds between specific molecules such as antigen and antibody, lectin and carbohydrate, or enzyme and substrate. From a knowledge of the reaction rates for reactants in solution and of their diffusion constants both in solution and on membranes, it is possible to estimate reaction rates for membrane-bound reactants. Two models are developed for predicting the rate of bond formation between cells and are compared with experiments. The force required to separate two cells is shown to be greater than the expected electrical forces between cells, and of the same order of magnitude as the forces required to pull gangliosides and perhaps some integral membrane proteins out of the cell membrane.

https://science.sciencemag.org/content/sci/200/4342/618.full.pdf

Models for the specific adhesion of cells to cells

It is shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to the streamline through the centre, experiences a lift force 81·2μVa2k½/v½ + smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamlines moving in the direction opposite to V. Here, a denotes the radius of the sphere, κ the magnitude of the velocity gradient, and μ and v the viscosity and kinematic viscosity, respectively. The relevance of the result to the observations by Segree & Silberberg (1962) of small spheres in Poiseuille flow is discussed briefly. Comments are also made about the problem of a sphere in a parabolic velocity profile and the functional dependence of the lift upon the parameters is obtained.

/pdf/the-lift-on-a-small-sphere-in-a-slow-shear-flow-1ltpy7jdp5.pdf

The lift on a small sphere in a slow shear flow

A comprehensive and critical review of closure approximations for two-equation turbulence models has been made. Particular attention has focused on the scale-determining equation in an attempt to find the optimum choice of dependent variable and closure approximations. Using a combination of singular perturbation methods and numerical computations, this paper demonstrates that: 1) conventional A:-e and A>w formulations generally are inaccurate for boundary layers in adverse pressure gradient; 2) using "wall functions'' tends to mask the shortcomings of such models; and 3) a more suitable choice of dependent variables exists that is much more accurate for adverse pressure gradient. Based on the analysis, a two-equation turbulence model is postulated that is shown to be quite accurate for attached boundary layers in adverse pressure gradient, compressible boundary layers, and free shear flows. With no viscous damping of the model's closure coefficients and without the aid of wall functions, the model equations can be integrated through the viscous sublayer. Surface boundary conditions are presented that permit accurate predictions for flow over rough surfaces and for flows with surface mass addition.

Reassessment of the scale-determining equation for advanced turbulence models

The behavior of steady, periodic, deep-water gravity waves on a linear shear current is investigated. A weakly nonlinear approximation for the small amplitude waves is constructed via a variational principle. A local analysis of those large amplitude waves with sharp crests, called extreme waves, is also provided. To construct solutions for all waveheights (especially the limiting ones) a convenient mathematical formulation which involves only the wave profile and some constants of the motion is derived and then solved by numerical means. It is found that for some shear currents the highest waves are not necessarily the extreme waves. Furthermore a certain non-uniqueness in the sense of a fold is shown to exist and a new type of limiting wave is discovered.

/pdf/steady-deep-water-waves-on-a-linear-shear-current-151lv0patm.pdf

Steady Deep‐Water Waves on a Linear Shear Current

We apply some general results for Hamiltonian systems, depending on the notion of signature of eigenvalues, to determine the circumstances under which collisions of imaginary eigenvalue for the linearized problem about a travelling water wave of permanent form are avoided or lead to loss of stability, up to non-degeneracy assumptions A new superharmonic instability is predicted and verified

Stability of Water Waves

Remarks are made about the status of research on the role of vorticity in fluid dynamics and some unsolved problems of current interest are described.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112081001511

Dynamics of vorticity

Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves

This paper considers axial motion in a rapidly rotating fluid of small viscosity. It is shown that solutions for the structure of vertical free shear layers must be allowed to be singular at the points where they receive fluid from a rising or spinning axisymmetric body. The possible types of singularities are elucidated by the use of similarity solutions and an hypothesis is introduced to limit their strength. Three particular cases of axially bounded motion are considered in detail; the split disk, the rising disk and the rising sphere. The hypothesis is shown to lead to a unique solution for the Stewartson layers. For the rising body, a Wiener-Hopf problem, which is independent of the body shape, must be solved for the central part of the Stewartson layers.

Philip Geoffrey Saffman

Papers

Steady Deep‐Water Waves on a Linear Shear Current

Stability of Water Waves

Dynamics of vorticity

Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves

The Structure of Free Vertical Shear Layers in a Rotating Fluid and the Motion Produced by a Slowly Rising Body