C. Pozrikidis: TCFD Errata

Errata

Introduction to Theoretical and Computational Fluid Dynamics

C. Pozrikidis
Oxford University Press, 1997

page 1, line 17 up.
The "zero" on the right-hand side of the equation should be set in bold.
page 3, full paragraph 3.
Keiko Nomura pointed out that the following statement is false:
"Thus slender particles resembling needles and rectangular parcels maintain their initial orientation."
This statement is indeed inaccurate. The correct statement is:
"The average rate of rotation of two perpendicular slender particles centered at a point, is equal to zero. As a consequence, the rate of rotation of slender partciles passing through a point, averaged over all possible orientations, is equal to zero; and by extension, the rate of rotation of rectangular parcels averaged over all orientations, also vanishes. "
An illuminating discussion of the relationship between the vorticity and the rate of rotation of infinitesimal or finite fluid parcels is given by: J. A. Shercliff, 1975, A note on vorticity, J. Inst. Maths. Applics. ,16, 259-262.
page 5, equation (1.1.18).
Thanks to Mohammed Elhakimi
The argument x on the right-hand side should be y.
page16, caption of figure1.4.1.
The pair "(eta, xi)" should be "(xi, eta)".
page 49, equation (2.2.3).
Thanks to Steve Yon and Mark Lee
The "phi" on the left-hand side should be f.
page 60, equations (2.3.25) and (2.3.26).
Thanks to Joel Tenne
Please replace the ``phi'' (lower case) with ``Phi'' (upper case) in one place on the right-hand side in each of these equations.
page 71, line4.
Thanks to Steve Yon
The word incompressible should be irrotational .
page 83, Equation (2.9.3).
Thanks to Steve Yon
"phi-caret" in the second and third entry of the column vector should be "phi-prime".
page 84, line 1.
Thanks to Steve Yon
The term "phi-prime" should be "phi" in two places.
page 89,
1. equation(2.10.7).
  The coefficient "(-1)" should be replaced by "(-n a)"
2. equation (2.10.8).
  The factor "2^1/2" should be inserted in front on the "sin" in the first line.
page 113, fourth line
Please change "(3.320)" to "(3.3.20)"
page109,
1. Table 3.2.2(a).
  Thanks to Marios Fyrillas
  The "2" in the numerator of the fraction of the sigma-phi and phi-sigma components
  of the matrix on the right-hand side should be "1".
2. Table 3.2.2(b).
  phi-phi component of the matrix on the right-hand side:
  The "2" inside the parentheses should be crossed out,
  and the numerator of the fraction before the parentheses should be switched from "1" to "2" to read " 2/r sin theta".
page 114, Table 3.4.1.
The "theta" on the left-hand side of the second equation should be "phi".
page 131, Inline equation at the middle of the page.
Please replace "partial n_x / dz" with "partial n_x /partial z".
page 133, Equation 3.6.20.
The second derivative on the left-hand side should be with respect to l²
page 140, Three lines above equation (3.8.7).
The "0" should be set in bold: "0".
page 142, equation (3.8.15).
Thanks to Keiko Nomura
Please cross out the term "k x" on the right-hand side of the first equation.
page 144
1. Equation 3.8.21.
  The left-hand side of the equation should be:
  (nu/sigma²) [partial²/(partial x²) +partial²/(partial sigma ²) - (1/sigma) partial/(partial sigma)] (sigma omega)
2. line8.
  Please delete: "the Laplacian on"
page 148, Equation (3.8.36).
Last integral on the right-hand side.
Please insert a centered dot "^." (inner product) between the two "omegas".
page 162, Table 4.2.1
1. End of the Table, expression for n above equation "D = ..."
  Please replace the second "f_theta" with "f_phi".
2. Southeastern corner of the Table, linearized form for "kappa_m".
  Thanks to P. N. Shankar
  Please add one "2" to the left-hand side and another "2" to the right-hand side to read:
  "2 kappa_m = 2/r- cot theta ... .
page 191, first line after equation (5.1.35).
Please insert a "2" to read: "h=Q/(2Ua)".
page ?, equation (5.1.21).
Thanks to Ryan Cabrera
Please replace "u(x, y)" with "u(y, z)".
page 236, line 6.
"...Eq. (6.2.18)..." should be "...Eq. (6.2.1)..."
page 249, line 11.
Thanks to Steve Yon
"chocking" should be "choking".
page 253, Equation (6.4.1) and paragraph after.
The "zero" on the right-hand side of this equation
and of the equation in the penultimate line
of the following paragraph should be set in bold.
page 269, Line 11.
Please replace "Stokes on" with "Stokeson".
page 316, Last line before equation (7.1.9).
Please cross out "+P_inf(t)".
page 317, Line after equation (7.1.12).
Please append the sentence:
``We have defined P_B(t) = p_B(t) - rho g .x_B , where x_B is a point
on the bubble surface that can be approximately shifted
to the bubble center.''
page 334, Second sentence of the third paragraph.
Please insert a minus sign ``-'' in front of the ``12''.
page 335, middle of the page.
"... expressed in terms of an incomplete elliptic integral of the first kind..."
should be replaced by "... evaluated in closed form ..."
page 336, First equation in (7.4.22).
The exponent ^1/2 should be ^-1/2.
page 365, First line after equation (7.9.3). Thanks to Yu-hsuan Huang
Please change ``f(z)'' to ``f(zeta)''.
page 379, equations (7.11.6), (7.11.7), and in between.
The lower limit of the last integral should be -1 instead of 0.
The expression "arcsin(2 zeta - 1)" on the right-hand should be "(arcsin(2zeta - 1)+pi/2)".
The expression "2a/pi" on the next line should be "a/pi".
"z" on the right-hand side of equation (7.11.7) should be "(2z-1)".
page 380
1. Equation (7.11.8).
  Thanks to Yu-Hsuan Huang
  Please change ``F(zeta)'' to ``f(zeta)'' on the left-hand side.
2. Paragraph following equation (7.11.8).
  Thanks to Yu-Hsuan Huang
  This three-line statement is incorrect. The correct statement is:
  ``Uniform flow along the xi axis in the zeta plane corresponds
  to flow due to a point source dipole located at the point x=0 y=b in the z plane.''
page 394, Equation (8.1.22).
Thanks to Mark Blyth
Please cross out the exponent ``2'' from ``chi'' inside the square root on the right-hand side.
page 426, Equation (9.2.4).
The left-hand side should read: "F(x, y)".
page 437, Line 18.
Please insert two primes so that the left-hand side of the equation reads:
"f'(eta⁺) - f'(eta^-)".
page 458, Third line of problem 9.7.1.
Thanks to Pak-Tao Leung
Please replace "c U₀" with "c/U₀" in two places.
page 451, Figure 9.6.1.
In the third line of the caption, please replace "width" with "semi-width".
In the figure label, please change "U" to "U" in one place.
page 460, Line 5.
Please change "eta_n" to "U_n.
page 465.
1. Problem 9.8.7, Line 3.
  Please insert a "-" (minus sign) after the "=" sign in front of the gradient.
2. Equation (9.8.29).
  Please insert an "i" (imaginary unit) right after "=-", before the first set of large parentheses.
page 472, Line after equation (9.9.40).
Please modify to read "(Yih 1963), where
page 474, Line 4 up.
Please delete the extraneous backslash "/".
page 486, right-hand side of equation (10.1.15).
The term" + sigma_0 " inside the first set of parentheses, and the term" - sigma " should be switched.
page 498, right-hand side of equation (10.4.7).
Please add a minus "-" sign after the equal "=" sign.
page 503, Equation (10.5.18).
A minus sign "-" should be inserted in front of the integral sign.
page 536, second paragraph.
At the end of the second paragraph, please add the following sentence:
"In the remainder of this section we will assume that "alpha" is a constant"
page 538, line 10.
Please change to read:
"... if they moving with the principal velocity while..."
page 540, second paragraph.
1. The paragraph beginning with "In the particular..." is erroneous.
  According to equation (11.4.33), the parameter alpha is a function of position over
  the vortex sheet. But previously, it was assumed that alpha is a constant.
  If alpha were not a constant, then equation (11.4.8) would be incorrect.
  Please disregard this whole paragraph.
2. middle of the page.
  The reference to "Rosenhead (1932)" should be changed to: "Rosenhead (1931)".
page 557, line 10
The reference to "Rosenhead (1932)" should be changed to: "Rosenhead (1931)".
page 585, equation (12.4.34)
The "2" in the denominators of the first
and penultimate fractions on the right-hand side should be "4".
page 588, equation (12.5.3)
Thanks to Jinchi Lu
The left-hand side should be "f_i,j,kⁿ⁺¹".
page 594, equations (12.6.30) and (12.6.31)
Thanks to Jitse Niesen
The term " (1+r)E_iⁿ" on the right-hand side of (12.6.30) should be replaced by "f_iⁿ"+rE_iⁿ"
The right-hand side of (12.6.31) should read: " 1/2 [f_iⁿ + f_i^* + ...]
Please also see equations (12.4.44) on page 587.
page 624, equation (13.4.6)
Thanks to Chih-Chung Yuan
The fraction on the right-hand side should be reversed to read " rho / Delta t "
page 636, equation (A.3.7)
Thanks to Erwin A. Villegas
The fourth partial derivative on the right-hand side should be taken with respect to "a₂" instead of "a₃.