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Journal articles on the topic 'Falkner-Skan'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Calvert, Velinda, and Mohsen Razzaghi. "Solutions of the Blasius and MHD Falkner-Skan boundary-layer equations by modified rational Bernoulli functions." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 8 (2017): 1687–705. http://dx.doi.org/10.1108/hff-05-2016-0190.

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Purpose This paper aims to propose a new numerical method for the solution of the Blasius and magnetohydrodynamic (MHD) Falkner-Skan boundary-layer equations. The Blasius and MHD Falkner-Skan equations are third-order nonlinear boundary value problems on the semi-infinite domain. Design/methodology/approach The approach is based upon modified rational Bernoulli functions. The operational matrices of derivative and product of modified rational Bernoulli functions are presented. These matrices together with the collocation method are then utilized to reduce the solution of the Blasius and MHD Falkner-Skan boundary-layer equations to the solution of a system of algebraic equations. Findings The method is computationally very attractive and gives very accurate results. Originality/value Many problems in science and engineering are set in unbounded domains. One approach to solve these problems is based on rational functions. In this work, a new rational function is used to find solutions of the Blasius and MHD Falkner-Skan boundary-layer equations.

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2

Awais, Muhammad, A. Aqsa, Saeed Awan, Saeed Rehman, and Muhammad Raja. "Hydromagnetic Falkner-Skan fluid rheology with heat transfer properties." Thermal Science 24, no. 1 Part A (2020): 339–46. http://dx.doi.org/10.2298/tsci180509312a.

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This article addresses the effects of heat transfer on magnetohydrodynamic Falkner-Skan wedge flow of a Jeffery fluid. The continuity, momentum and energy balance equations yield the relevant PDE which are transforms to ODE by exploitation of similarity variables. Strength of optimal homotopy series solutions is practiced to solved analytically the transformed ODE model of hydromagnetic Falkner-Skan fluid rheology with heat transfer scenarios. The graphical and numerical illustrations of the result are presented for different interesting flow parameters. Numerical values of Nusselt number are tabulated. It is observed that for the Falkner-Skan rheology, the applied magnetic field acts as a controlling agnet which controls the fluids velocity up to the desired value whereas Debrorah number enhances the fluid velocity.

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3

Lan, K. Q., and G. C. Yang. "Positive Solutions of the Falkner–Skan Equation Arising in the Boundary Layer Theory." Canadian Mathematical Bulletin 51, no. 3 (2008): 386–98. http://dx.doi.org/10.4153/cmb-2008-039-7.

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AbstractThe well-known Falkner–Skan equation is one of the most important equations in laminar boundary layer theory and is used to describe the steady two-dimensional flow of a slightly viscous incompressible fluid past wedge shaped bodies of angles related to λπ/2, where λ ∈ ℝ is a parameter involved in the equation. It is known that there exists λ* < 0 such that the equation with suitable boundary conditions has at least one positive solution for each λ ≥ λ* and has no positive solutions for λ < λ*. The known numerical result shows λ* = –0.1988. In this paper, λ* ∈ [–0.4,–0.12] is proved analytically by establishing a singular integral equation which is equivalent to the Falkner–Skan equation. The equivalence result provides new techniques to study properties and existence of solutions of the Falkner–Skan equation.

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4

Eerdun, Buhe, Qiqige Eerdun, Bala Huhe, Chaolu Temuer, and Jing-Yu Wang. "Variational iteration method with He's polynomials for MHD Falkner-Skan flow over permeable wall based on Lie symmetry method." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 6 (2014): 1348–62. http://dx.doi.org/10.1108/hff-02-2013-0072.

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Purpose – The purpose of this paper is to consider a steady two-dimensional magneto-hydrodynamic (MHD) Falkner-Skan boundary layer flow of an incompressible viscous electrically fluid over a permeable wall in the presence of a magnetic field. Design/methodology/approach – The governing equations of MHD Falkner-Skan flow are transformed into an initial values problem of an ordinary differential equation using the Lie symmetry method which are then solved by He's variational iteration method with He's polynomials. Findings – The approximate solution is compared with the known solution using the diagonal Pad’e approximants and the geometrical behavior for the values of various parameters. The results reveal the reliability and validity of the present work, and this combinational method can be applied to other nonlinear boundary layer flow problems. Originality/value – In this paper, an approximate analytical solution of the MHD Falkner-Skan flow problem is obtained by combining the Lie symmetry method with the variational iteration method and He's polynomials.

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5

Jiwari, Ram, Vikas Kumar, Ram Karan, and Ali Saleh Alshomrani. "Haar wavelet quasilinearization approach for MHD Falkner–Skan flow over permeable wall via Lie group method." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 6 (2017): 1332–50. http://dx.doi.org/10.1108/hff-04-2016-0145.

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Purpose This paper aims to deal with two-dimensional magneto-hydrodynamic (MHD) Falkner–Skan boundary layer flow of an incompressible viscous electrically conducting fluid over a permeable wall in the presence of a magnetic field. Design/methodology/approach Using the Lie group approach, the Lie algebra of infinitesimal generators of equivalence transformations is constructed for the equation under consideration. Using these suitable similarity transformations, the governing partial differential equations are reduced to linear and nonlinear ordinary differential equations (ODEs). Further, Haar wavelet approach is applied to the reduced ODE under the subalgebra 4.1 for constructing numerical solutions of the flow problem. Findings A new type of solutions was obtained of the MHD Falkner–Skan boundary layer flow problem using the Haar wavelet quasilinearization approach via Lie symmetric analysis. Originality/value To find a solution for the MHD Falkner–Skan boundary layer flow problem using the Haar wavelet quasilinearization approach via Lie symmetric analysis is a new approach for fluid problems.

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6

Ullah, H., S. Islam, M. Idrees, and M. Arif. "Solution of Boundary Layer Problems with Heat Transfer by Optimal Homotopy Asymptotic Method." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/324869.

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Application of Optimal Homotopy Asymptotic Method (OHAM), a new analytic approximate technique for treatment of Falkner-Skan equations with heat transfer, has been applied in this work. To see the efficiency of the method, we consider Falkner-Skan equations with heat transfer. It provides us with a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature as finite difference (N. S. Asaithambi, 1997) and shooting method (Cebeci and Keller, 1971). The obtained solutions show that OHAM is effective, simpler, easier, and explicit.

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7

Belden, E. R., Z. A. Dickman, S. J. Weinstein, A. D. Archibee, E. Burroughs, and N. S. Barlow. "Asymptotic Approximant for the Falkner–Skan Boundary Layer Equation." Quarterly Journal of Mechanics and Applied Mathematics 73, no. 1 (2020): 36–50. http://dx.doi.org/10.1093/qjmam/hbz021.

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Summary We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., Q. J. Mech. Appl. Math. 70 (2017) 21–48.) yields accurate analytic closed-form solutions to the Falkner–Skan boundary layer equation for flow over a wedge having angle $\beta\pi/2$ to the horizontal. A wide range of wedge angles satisfying $\beta\in[-0.198837735, 1]$ are considered, and the previously established non-unique solutions for $\beta&lt;0$ having positive and negative shear rates along the wedge are accurately represented. The approximant is used to determine the singularities in the complex plane that prescribe the radius of convergence of the power series solution to the Falkner–Skan equation. An attractive feature of the approximant is that it may be constructed quickly by recursion compared with traditional Padé approximants that require a matrix inversion. The accuracy of the approximant is verified by numerical solutions, and benchmark numerical values are obtained that characterize the asymptotic behavior of the Falkner–Skan solution at large distances from the wedge.

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8

Asaithambi, Asai. "A series solution of the Falkner–Skan equation using the crocco–wang transformation." International Journal of Modern Physics C 28, no. 11 (2017): 1750139. http://dx.doi.org/10.1142/s012918311750139x.

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A direct series solution for the Falkner–Skan equation is obtained by first transforming the problem using the Crocco–Wang transformation. The transformation converts the third-order problem to a second-order two-point boundary value problem. The method first constructs a series involving the unknown skin-friction coefficient [Formula: see text]. Then, [Formula: see text] is determined by using the secant method or Newton’s method. The derivative needed for Newton’s method is also computed using a series derived from the transformed differential equation. The method is validated by solving the Falkner–Skan equation for several cases reported previously in the literature.

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9

Hendi, Fatheah A., and Majid Hussain. "Analytic Solution for MHD Falkner-Skan Flow over a Porous Surface." Journal of Applied Mathematics 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/123185.

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10

Afzal, Noor. "Improved series solutions of Falkner-Skan equation." AIAA Journal 23, no. 6 (1985): 969–71. http://dx.doi.org/10.2514/3.9020.

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11

Bretteville, Jacques, and Sylvie Saintlos. "Théories multicouches pour l'écoulement de Falkner–Skan." Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics 329, no. 1 (2001): 19–25. http://dx.doi.org/10.1016/s1620-7742(00)01283-6.

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12

Padé, Offer. "On the solution of Falkner–Skan equations." Journal of Mathematical Analysis and Applications 285, no. 1 (2003): 264–74. http://dx.doi.org/10.1016/s0022-247x(03)00402-5.

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13

Marinca, Vasile, Remus-Daniel Ene, and Bogdan Marinca. "Analytic Approximate Solution for Falkner-Skan Equation." Scientific World Journal 2014 (2014): 1–22. http://dx.doi.org/10.1155/2014/617453.

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This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. Our method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. The obtained results reveal that this procedure is very effective, simple, and accurate. A very good agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration.

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14

Brodie, P., and W. H. H. Banks. "Further properties of the Falkner-Skan equation." Acta Mechanica 65, no. 1-4 (1987): 205–11. http://dx.doi.org/10.1007/bf01176882.

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15

Merkin, J. H. "Mixed convection in a Falkner–Skan system." Journal of Engineering Mathematics 100, no. 1 (2016): 167–85. http://dx.doi.org/10.1007/s10665-015-9840-8.

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16

Elgazery, Nasser S. "Numerical solution for the Falkner–Skan equation." Chaos, Solitons & Fractals 35, no. 4 (2008): 738–46. http://dx.doi.org/10.1016/j.chaos.2006.05.040.

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17

Malik, M., J. Mathew, and J. Dey. "Mechanism of instability of Falkner-Skan flows." Acta Mechanica 164, no. 1-2 (2003): 75–89. http://dx.doi.org/10.1007/s00707-003-0016-7.

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18

Auteri, F., and L. Quartapelle. "Galerkin-Laguerre Spectral Solution of Self-Similar Boundary Layer Problems." Communications in Computational Physics 12, no. 5 (2012): 1329–58. http://dx.doi.org/10.4208/cicp.130411.230911a.

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AbstractIn this work the Laguerre basis for the biharmonic equation introduced by Jie Shen is employed in the spectral solution of self-similar problems of the boundary layer theory. An original Petrov-Galerkin formulation of the Falkner-Skan equation is presented which is based on a judiciously chosen special basis function to capture the asymptotic behaviour of the unknown. A spectral method of remarkable simplicity is obtained for computing Falkner-Skan-Cooke boundary layer flows. The accuracy and efficiency of the Laguerre spectral approximation is illustrated by determining the linear stability of nonseparated and separated flows according to the Orr-Sommerfeld equation. The pentadiagonal matrices representing the derivative operators are explicitly provided in an Appendix to aid an immediate implementation of the spectral solution algorithms.

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19

Asaithambi, Asai. "On Solving the Nonlinear Falkner–Skan Boundary-Value Problem: A Review." Fluids 6, no. 4 (2021): 153. http://dx.doi.org/10.3390/fluids6040153.

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This article is a review of ongoing research on analytical, numerical, and mixed methods for the solution of the third-order nonlinear Falkner–Skan boundary-value problem, which models the non-dimensional velocity distribution in the laminar boundary layer.

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20

Sripathy, B., P. Vijayaraju, and G. Hariharan. "Wavelet based Numerical Solution for Falkner-Skan Equation." Asian Journal of Research in Social Sciences and Humanities 7, no. 3 (2017): 361. http://dx.doi.org/10.5958/2249-7315.2017.00175.7.

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21

Saintlos, Sylvie, and Jacques Bretteville. "Approximation uniformément valable pour l'écoulement de Falkner–Skan." Comptes Rendus Mécanique 330, no. 10 (2002): 673–82. http://dx.doi.org/10.1016/s1631-0721(02)01507-3.

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22

El-Gindy, T. M., H. M. El Hawary, and H. S. Hussien. "An optimization technique for the falkner-skan equation." Optimization 35, no. 4 (1995): 357–66. http://dx.doi.org/10.1080/02331939508844155.

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23

Andersson, H. I., and T. Ytrehus. "Falkner-Skan Solution for Gravity-Driven Film Flow." Journal of Applied Mechanics 52, no. 4 (1985): 783–86. http://dx.doi.org/10.1115/1.3169146.

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It is demonstrated that the development of a viscous film flow down along a vertical wall can be described by the classical Falkner-Skan equation from aerodynamic boundary layer theory for the particular parameter-value m = 1/2. This leads to a well-known exact solution for the velocity field, as long as the viscous boundary layer can be considered not to interact with the free surface of the film. An exact reference solution for developing film flow is thus made available, against which approxiate solutions may be tested for accuracy.

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24

Sánchez-Álvarez, José J., María Higuera, and José M. Vega. "Optimal streaks in a Falkner–Skan boundary layer." Physics of Fluids 23, no. 2 (2011): 024104. http://dx.doi.org/10.1063/1.3553465.

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25

Lipatov, I. I., and K. T. Ngo. "Solution of Falkner—Skan Equations for Hypersonic Flows." Fluid Dynamics 55, no. 4 (2020): 525–33. http://dx.doi.org/10.1134/s0015462820040072.

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26

Olagunju, David O. "The Falkner–Skan flow of a viscoelastic fluid." International Journal of Non-Linear Mechanics 41, no. 6-7 (2006): 825–29. http://dx.doi.org/10.1016/j.ijnonlinmec.2006.04.008.

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27

Astin, P., and G. Wilks. "Jet profile solutions of the Falkner-Skan equation." ZAMP Zeitschrift f�r angewandte Mathematik und Physik 47, no. 5 (1996): 790–98. http://dx.doi.org/10.1007/bf00915275.

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28

Zhang, Liang, Liwu Fan, Zitao Yu, and Renwei Mei. "Correlating convection heat transfer for Falkner-Skan flow." International Journal of Heat and Mass Transfer 131 (March 2019): 101–8. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2018.11.046.

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29

Abdulhameed, M., Habibi Saleh, Ishak Hashim, and Rozaini Roslan. "Radiation Effects on Two-Dimensional MHD Falkner-Skan Wedge Flow." Applied Mechanics and Materials 773-774 (July 2015): 368–72. http://dx.doi.org/10.4028/www.scientific.net/amm.773-774.368.

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Radiation effects on two-dimensional MHD Falkner-Skan boundary layer wedge have been studied. Analytical solution of nonlinear boundary-layer equations is obtained by modified homotopy perturbation method. It is observed that the magnetic field tends to decelerate fluid flow whereas radiations and thermal diffusion tend to increase fluid temperature.

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30

Guan, Jiang, and Yue Kai. "Asymptotic Analysis to Two Nonlinear Equations in Fluid Mechanics by Homotopy Renormalisation Method." Zeitschrift für Naturforschung A 71, no. 9 (2016): 863–68. http://dx.doi.org/10.1515/zna-2016-0210.

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AbstractBy the homotopy renormalisation method, the global approximate solutions to Falkner-Skan equation and Von Kármá’s problem of a rotating disk in an infinite viscous fluid are obtained. The homotopy renormalisation method is simple and powerful for finding global approximate solutions to nonlinear perturbed differential equations arising in mathematical physics.

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31

Khan, Masood, and Azeem Shahzad. "Falkner–Skan Boundary Layer Flow of a Sisko Fluid." Zeitschrift für Naturforschung A 67, no. 8-9 (2012): 469–78. http://dx.doi.org/10.5560/zna.2012-0049.

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In this paper, we investigate the steady boundary layer flow of a non-Newtonian fluid, represented by a Sisko fluid, over a wedge in a moving fluid. The equations of motion are derived for boundary layer flow of an incompressible Sisko fluid using appropriate similarity variables. The governing equations are reduced to a single third-order highly nonlinear ordinary differential equation in the dimensionless stream function, which is then solved analytically using the homotopy analysis method. Some important parameters have been discussed by this study, which include the power law index n, the material parameter A, the wedge shape factor b, and the skin friction coefficient Cf. A comprehensive study is made between the results of the Sisko and the power-law fluids.

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32

AL-JAWARY, Majeed. "Reliable Iterative Methods for Solving the Falkner-Skan Equation." GAZI UNIVERSITY JOURNAL OF SCIENCE 33, no. 1 (2020): 168–86. http://dx.doi.org/10.35378/gujs.457840.

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33

Wortman, A. "Comment on "Improved Series Solutions of Falkner-Skan Equation"." AIAA Journal 24, no. 5 (1986): 863. http://dx.doi.org/10.2514/3.48673.

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34

Sher, I., and A. Yakhot. "New Approach to Solution of the Falkner-Skan Equation." AIAA Journal 39, no. 5 (2001): 965–67. http://dx.doi.org/10.2514/2.1403.

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35

Asaithambi, Asai. "A finite-difference method for the Falkner-Skan equation." Applied Mathematics and Computation 92, no. 2-3 (1998): 135–41. http://dx.doi.org/10.1016/s0096-3003(97)10042-x.

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36

Shishkina, Olga, Susanne Horn, and Sebastian Wagner. "Falkner–Skan boundary layer approximation in Rayleigh–Bénard convection." Journal of Fluid Mechanics 730 (August 1, 2013): 442–63. http://dx.doi.org/10.1017/jfm.2013.347.

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AbstractTo approximate the velocity and temperature within the boundary layers in turbulent thermal convection at moderate Rayleigh numbers, we consider the Falkner–Skan ansatz, which is a generalization of the Prandtl–Blasius one to a non-zero-pressure-gradient case. This ansatz takes into account the influence of the angle of attack $\beta $ of the large-scale circulation of a fluid inside a convection cell against the heated/cooled horizontal plate. With respect to turbulent Rayleigh–Bénard convection, we derive several theoretical estimates, among them the limiting cases of the temperature profiles for all angles $\beta $, for infinite and for infinitesimal Prandtl numbers $\mathit{Pr}$. Dependences on $\mathit{Pr}$ and $\beta $ of the ratio of the thermal to viscous boundary layers are obtained from the numerical solutions of the boundary layers equations. For particular cases of $\beta $, accurate approximations are developed as functions on $\mathit{Pr}$. The theoretical results are corroborated by our direct numerical simulations for $\mathit{Pr}= 0. 786$ (air) and $\mathit{Pr}= 4. 38$ (water). The angle of attack $\beta $ is estimated based on the information on the locations within the plane of the large-scale circulation where the time-averaged wall shear stress vanishes. For the fluids considered it is found that $\beta \approx 0. 7\mathrm{\pi} $ and the theoretical predictions based on the Falkner–Skan approximation for this $\beta $ leads to better agreement with the DNS results, compared with the Prandtl–Blasius approximation for $\beta = \mathrm{\pi} $.

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37

Yun, Beong In. "New Approximate Analytical Solutions of the Falkner-Skan Equation." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/170802.

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We propose an iterative method for solving the Falkner-Skan equation. The method provides approximate analytical solutions which consist of coefficients of the previous iterate solution. By some examples, we show that the presented method with a small number of iterations is competitive with the existing method such as Adomian decomposition method. Furthermore, to improve the accuracy of the proposed method, we suggest an efficient correction method. In practice, for some examples one can observe that the correction method results in highly improved approximate solutions.

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38

Korpela, Seppo A. "On Large Prandtl Number Convection in Falkner-Skan Flow." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 71, no. 2 (1991): 121–23. http://dx.doi.org/10.1002/zamm.19910710215.

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39

Zaturska, M. B., and W. H. H. Banks. "A new solution branch of the Falkner-Skan equation." Acta Mechanica 152, no. 1-4 (2001): 197–201. http://dx.doi.org/10.1007/bf01176954.

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40

Zhang, Jiawei, and Binghe Chen. "An iterative method for solving the Falkner–Skan equation." Applied Mathematics and Computation 210, no. 1 (2009): 215–22. http://dx.doi.org/10.1016/j.amc.2008.12.079.

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41

Khoshrouye Ghiasi, Emran, and Reza Saleh. "Non-Dimensional Optimization of Magnetohydrodynamic Falkner–Skan Fluid Flow." INAE Letters 3, no. 3 (2018): 143–47. http://dx.doi.org/10.1007/s41403-018-0043-2.

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42

Molla, Mohammad Riazuddin. "An Analytic Treatment of the Falkner-Skan Boundary Layer Equation." Dhaka University Journal of Science 61, no. 1 (2013): 139–44. http://dx.doi.org/10.3329/dujs.v61i1.15115.

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The existence and uniqueness of a positive solution of a singular nonlinear boundary value problem formulated from the Falkner-Skan boundary layer equation, are studied. The constructive method such as the method of upper and lower solutions is used to show the existence and uniqueness of a positive solution. Dhaka Univ. J. Sci. 61(1): 139-144, 2013 (January) DOI: http://dx.doi.org/10.3329/dujs.v61i1.15115

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43

Pattnaik, Jyotsnarani, Dash C., and Ojha L. "MHD Falkner-skan Flow through Porous Medium Over Permeable Surface." Modelling, Measurement and Control B 86, no. 2 (2017): 380–95. http://dx.doi.org/10.18280/mmc_b.860205.

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44

Han, S. "Finite Difference Solution of the Falkner—Skan Wedge Flow Equation." International Journal of Mechanical Engineering Education 41, no. 1 (2013): 1–7. http://dx.doi.org/10.7227/ijmee.41.1.1.

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45

Martin, Michael J., and Iain D. Boyd. "Falkner-Skan Flow over a Wedge with Slip Boundary Conditions." Journal of Thermophysics and Heat Transfer 24, no. 2 (2010): 263–70. http://dx.doi.org/10.2514/1.43316.

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46

Cullen, Andrew Craig, and Simon Clarke. "A fast, spectrally accurate solver for the Falkner--Skan equation." ANZIAM Journal 58 (October 10, 2017): 57. http://dx.doi.org/10.21914/anziamj.v58i0.11746.

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47

Harris, Simon D., Derek B. Ingham, and Ioan Pop. "Impulsive Falkner‐Skan flow with constant wall heat flux: revisited." International Journal of Numerical Methods for Heat & Fluid Flow 19, no. 8 (2009): 1008–37. http://dx.doi.org/10.1108/09615530910994478.

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48

Hastings, S. P., and W. C. Troy. "Oscillating Solutions of the Falkner–Skan Equation for Negative $\beta $." SIAM Journal on Mathematical Analysis 18, no. 2 (1987): 422–29. http://dx.doi.org/10.1137/0518032.

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49

Temimi, Helmi, and Mohamed Ben-Romdhane. "Numerical Solution of Falkner-Skan Equation by Iterative Transformation Method." Mathematical Modelling and Analysis 23, no. 1 (2018): 139–51. http://dx.doi.org/10.3846/mma.2018.009.

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In this paper, we study the nonlinear boundary-layer equation of Falkner- Skan defned on a semi-infnite domain. An iterative finite difference (IFD) scheme is proposed to numerically solve such nonlinear ordinary differential equation. A computational iterative scheme is developed based on Newton-Kantorovich quasilinearization. At every iteration, the obtained linearized differential equation is numerically solved using the standard finite difference method. Numerical experiments show the accuracy and efficiency of the method compared to existing solvers. The computation is performed for different parameter values, including the special case of Blasius problem.

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50

Matsson, O. John E. "Görtler vortices in Falkner–Skan flows with suction and blowing." International Journal for Numerical Methods in Fluids 56, no. 3 (2007): 257–77. http://dx.doi.org/10.1002/fld.1516.

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