Review of Environmental fluid mechanics by Hillel Rubin and Joseph Atkinson

Abstract

The book is divided into two approximately equal sections: the first covers the principles of fluid mechanics, and the second deals with applications in environmental fluid mechanics. The book is described on its back cover as a comprehensive reference/test ‘‘detailing the use of physical and numerical models and up-tothe-minute computational approaches for the analysis of environmental processes.’’ It is aimed at upper-level undergraduate and graduate students who have previously taken at least one introductory course in fluid mechanics. The first chapter gives brief descriptions of continuum concepts, fluid properties, dimensional analysis, and a few mathematical preliminaries that include tensor analysis, complexvariable theory, and the classification of second-order partial differential equations. Treatment of the mathematical preliminaries is brief and concise and is likely to be readily accessible only to students who have had a previous introduction to these topics. This is probably a realistic expectation for complex-variable theory and partial differential equations, but the writer suspects that it may be wishful to expect students at this level to have had a previous introduction to topics such as covariant and contravariant tensors, geodesics, and Christoffel symbols. Applications of tensors in the remainder of the text are confined almost exclusively to the use of Cartesian tensors. The second chapter introduces the equations of fluid motion. Eulerian and Lagrangian coordinates, pathlines, streamlines, streaklines, rates of strain, vorticity, circulation, velocities, accelerations, and material derivatives are all discussed. The Reynolds transport theorem and the divergence theorem are used to derive both control volume and partial differential equation forms of the continuity, momentum, and energy equations. The chapter finishes with an unusually nice section on scaling analysis that looks at relative magnitudes of different terms in the governing equations. A good number of both solved and unsolved problems appear at the end of this chapter. Exact solutions of the Navier-Stokes equations are considered in chapter three. Solutions for fully developed laminar flow between flat plates and through pipes, creeping flow around a sphere, and unsteady boundary-layer development near plates that oscillate or start impulsively from rest are either solved in detail or are discussed in general terms. The chapter ends with a brief discussion of finite-difference solutions for creeping flow. A good collection of solved and unsolved problems is also given at the end of this chapter. Potential-flow theory is treated in chapter four. Complex variables and superposition of fundamental solutions are used to obtain the solution for uniform flow past a circular cylinder, and solutions for singularities near infinitely long straight boundaries are obtained by using the method of images. A brief introduction is given to the use of flow nets in seepage problems, and the chapter concludes with an introduction to the use of finite differences for rectangular solution domains. This chapter contains a number of errors. For example, the chapter begins by stating incorrectly that ‘‘viscous layers are shown to be thin when the Reynolds number of the viscous layer is small’’ rather than correctly stating that boundary layers become relatively thin as Reynolds numbers increase. Errors appear in a number of figure drawings, with potential and streamlines failing to meet at right angles in the first figure, incorrect directions shown for some of the velocity components near a stagnation point in the third figure, and incorrect pressure distributions shown for a source and a vortex in the fourth and fifth figures, respectively. The classical result that any object submerged in irrotational flow without separation has zero drag and a lift force given by the product of the fluid mass density, the uniform flow velocity at infinity, and the circulation about the body is derived by using an incorrect form of the Blasius theorem, and some of the functional notation used when discussing finite-difference solutions is confusing. Chapter five contains a fairly broad and comprehensive introduction to turbulence. Some statistical definitions are used to define turbulence scales and to discuss frequency analysis of turbulent flows. The stability of laminar flow is introduced by linearizng the continuity and Navier-Stokes equations to obtain the Orr-Sommerfield equations. A brief qualitative discussion is given of typical results obtained from an eigenvalue analysis of the Orr-Sommerfield equation before embarking on a fairly detailed discussion of turbulence modeling. This latter discussion begins with a derivation of the Reynolds equations for a rotating coordinate system and finishes with a derivation of the equations used in K-« modeling. Boundary-layer theory is discussed in chapter six. The NavierStokes equations are scaled to obtain the differential equations of boundary-layer theory, and the Blasius solution is given for a laminar boundary layer on a flat plate. Then, a control-volume analysis is used to obtain the Pohlhausen-von Karman integral equation, which is solved for both laminar and turbulent boundary layers on a flat plate. The chapter concludes with a brief section on the use of similar control-volume methods for heat and mass diffusion in a motionless fluid. This ends coverage of what the writer terms fundamental fluid mechanics, and it is worth noting that little or no discussion has been included on the important topics of flow separation, secondary flow, lift, and drag. Chapter seven, entitled Surface Water Flows, covers openchannel flow together with an introduction to modeling in lakes and reservoirs. The standard topics of uniform, gradually varied and rapidly varied open-channel flows are given a reasonably complete treatment. The less commonly treated topic of flow in an open channel with lateral inflow or outflow is discussed briefly, and a relatively detailed section discuss velocity distributions for fully developed turbulent flow in wide channels for both smooth and rough bottom boundaries. The chapter ends with a general discussion of modeling heat transport and circulation in lakes and reservoirs in one, two, and three dimensions. This interesting topic is not normally covered in an engineering text at this level, although the discussion of the 1D heat-transport model is difficult