Lawrence Talbot

Bio: Lawrence Talbot is an academic researcher. The author has contributed to research in topics: Boundary layer & Boundary layer thickness. The author has an hindex of 1, co-authored 1 publications receiving 1314 citations.

A general classification of three-dimensional flow fields

Abstract: The geometry of solution trajectories for three first‐order coupled linear differential equations can be related and classified using three matrix invariants. This provides a generalized approach to the classification of elementary three‐dimensional flow patterns defined by instantaneous streamlines for flow at and away from no‐slip boundaries for both compressible and incompressible flow. Although the attention of this paper is on the velocity field and its associated deformation tensor, the results are valid for any smooth three‐dimensional vector field. For example, there may be situations where it is appropriate to work in terms of the vorticity field or pressure gradient field. In any case, it is expected that the results presented here will be of use in the interpretation of complex flow field data.

Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope

Abstract: The vibrational characteristics of a cantilever beam are well known to strongly depend on the fluid in which the beam is immersed. In this paper, we present a detailed theoretical analysis of the frequency response of a cantilever beam, that is immersed in a viscous fluid and excited by an arbitrary driving force. Due to its practical importance in application to the atomic force microscope (AFM), we consider in detail the special case of a cantilever beam that is excited by a thermal driving force. This will incorporate the presentation of explicit analytical formulae and numerical results, which will be of value to the users and designers of AFM cantilever beams.

Structural features of turbulent flow over smooth and rough boundaries

Abstract: An experimental study of boundary-layer turbulence in a free surface channel flow is described. Attention is concentrated on the effects of different surface roughness conditions on the turbulence structure in the boundary region. Hydrogen bubble flow tracers and medium high-speed motion photography were used to obtain an instantaneous visual and quantitative description of the flow field. In particular it proved possible to record instantaneous longitudinal and vertical velocity profiles from which distributions of the instantaneous Reynolds stress contribution were computed.Two well-defined intermittent features of the flow structure were visually identified close to the boundary. These consisted of fluid ejection phases, previously reported by Kline et al. (1967) for smooth boundary flow, and fluid inrush phases. Conditional averaging of the instantaneous velocity data yielded quantitative confirmation that ejection phases corresponded with ejection of low momentum fluid outwards from the boundary whilst inrush phases were associated with the transport of high momentum fluid inwards towards the boundary. Inrush and ejection events were present irrespective of the surface roughness condition.Conditional averaging also indicated that both inrush and ejection sequences correlate with an extremely high contribution to Reynolds stress and hence turbulence production close to the boundary. Indeed the present results, taken with those from previous studies, suggest that turbulence production is dominated by the joint contribution from the inrush and ejection events. It is emphasized that these structural features are intermittent, forming important linked elements of a randomly repeating cycle of wall-region turbulence production which is apparently driven by some violent three-dimensional instability mechanism.Whilst the most coherent effects of the observed inrush phases appear to be mainly confined to a region close to the boundary, the influence of the ejection phases is far more extensive. The ejected low momentum fluid elements, drawn from the viscous sublayer and from between the interstices of the roughness elements, travel outwards from the boundary into the body of the flow and give rise to very large positive contributions to Reynolds stress at points remote from the boundary. This effect is sufficiently strong to prompt the suggestion that the ejection process could represent a universal and dominant mode of momentum transport outside the immediate wall region and possibly extending across the entire thickness of the boundary layer.A structural model based on the present observations is seen to exhibit consistency with many commonly visualized features and recorded average properties of turbulent boundary-layer flows in general.

Handbook of Nonlinear Partial Differential Equations

Abstract: SOME NOTATIONS AND REMARKS PARABOLIC EQUATIONS WITH ONE SPACE VARIABLE Equations with Power-Law Nonlinearities Equations with Exponential Nonlinearities Equations with Hyperbolic Nonlinearities Equations with Logarithmic Nonlinearities Equations with Trigonometric Nonlinearities Equations Involving Arbitrary Functions Nonlinear Schrodinger Equations and Related Equations PARABOLIC EQUATIONS WITH TWO OR MORE SPACE VARIABLES Equations with Two Space Variables Involving Power-Law Nonlinearities Equations with Two Space Variables Involving Exponential Nonlinearities Other Equations with Two Space Variables Involving Arbitrary Parameters Equations Involving Arbitrary Functions Equations with Three or More Space Variables Nonlinear Schrodinger Equations HYPERBOLIC EQUATIONS WITH ONE SPACE VARIABLE Equations with Power-Law Nonlinearities Equations with Exponential Nonlinearities Other Equations Involving Arbitrary Parameters Equations Involving Arbitrary Functions Equations of the Form wxy=F(x,y,w, wx, wy ) HYPERBOLIC EQUATIONS WITH TWO OR THREE SPACE VARIABLES Equations with Two Space Variables Involving Power-Law Nonlinearities Equations with Two Space Variables Involving Exponential Nonlinearities Nonlinear Telegraph Equations with Two Space Variables Equations with Two Space Variables Involving Arbitrary Functions Equations with Three Space Variables Involving Arbitrary Parameters Equations with Three Space Variables Involving Arbitrary Functions ELLIPTIC EQUATIONS WITH TWO SPACE VARIABLES Equations with Power-Law Nonlinearities Equations with Exponential Nonlinearities Equations Involving Other Nonlinearities Equations Involving Arbitrary Functions ELLIPTIC EQUATIONS WITH THREE OR MORE SPACE VARIABLES Equations with Three Space Variables Involving Power-Law Nonlinearities Equations with Three Space Variables Involving Exponential Nonlinearities Three-Dimensional Equations Involving Arbitrary Functions Equations with n Independent Variables EQUATIONS INVOLVING MIXED DERIVATIVES AND SOME OTHER EQUATIONS Equations Linear in the Mixed Derivative Equations Quadratic in the Highest Derivatives Bellman Type Equations and Related Equations SECOND-ORDER EQUATIONS OF GENERAL FORM Equations Involving the First Derivative in t Equations Involving Two or More Second Derivatives THIRD-ORDER EQUATIONS Equations Involving the First Derivative in t Equations Involving the Second Derivative in t Hydrodynamic Boundary Layer Equations Equations of Motion of Ideal Fluid (Euler Equations) Other Third-Order Nonlinear Equations FOURTH-ORDER EQUATIONS Equations Involving the First Derivative in t Equations Involving the Second Derivative in t Equations Involving Mixed Derivatives EQUATIONS OF HIGHER ORDERS Equations Involving the First Derivative in t and Linear in the Highest Derivative General Form Equations Involving the First Derivative in t Equations Involving the Second Derivative in t Other Equations SUPPLEMENTS: EXACT METHODS FOR SOLVING NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS Classification of Second-Order Semilinear Partial Differential Equations in Two Independent Variables Transformations of Equations of Mathematical Physics Traveling-Wave Solutions and Self-Similar Solutions. Similarity Methods Method of Generalized Separation of Variables Method of Functional Separation of Variables Generalized Similarity Reductions of Nonlinear Equations Group Analysis Methods Differential Constraints Method Painleve Test for Nonlinear Equations of Mathematical Physics Inverse Scattering Method Conservation Laws Hyperbolic Systems of Quasilinear Equations REFERENCES INDEX

The Overall Convective Heat Transfer from Smooth Circular Cylinders

Abstract: Publisher Summary Accurate knowledge of the overall convective heat transfer from circular cylinders is of importance in a number of fields, such as boiler design, hotwire anemometry, and the rating of electrical conductors. The wide dispersion in the published experimental data for the heat transfer from smooth circular cylinders by natural and forced convection is attributed to various factors associated with the experiments. The error due to heat conduction to the supports is particularly important with natural convection, especially where the heat loss and the temperature rise of the cylinder are calculated from the voltage drop across it. A common cause of error is the use of too small a space ratio, so that the temperature and velocity fields are distorted. To reduce this error to less than l%, the space ratio D c /D for natural convection or D T /D for forced convection should exceed 100. The error caused by blockage with wind tunnel measurements can be calculated depending on the type of tunnel. One of the greatest sources of error with forced convection is the failure to allow for the effect of stream turbulence.