In this erratum, the author wishes to make several corrections to Shukla (2001, “Hydrodynamics of Diffusive Processes,” ASME Appl. Mech. Rev., 54(5), pp. 391–404) in order to ensure that the content appropriately cites sources from which passages of text were obtained or paraphrased. The author regrets the earlier oversight.

Specifically, in the first paragraph of the introduction, the text “Suppose that a small parcel…will be repeated.” should read “Following Ref. [5], ‘suppose that a small parcel of fluid takes a small vertical displacement in a liquid layer in which the temperature and the salinity both increase with elevation. Assume that the parcel is initially more dense than the surrounding fluid, because it is cooler. The temperature of the fluid parcel will, however, become rapidly equalized with that of the surrounding fluid and the parcel will then be less dense because of its lower salinity. It will again rise, therefore, and the process will be repeated’.” On a related note, the paragraph before Eq. (66) should read “As explained in Ref. [5], ‘since we are interested in the stability of a quiescent layer of fluid oriented horizontally and subjected to linear gradients of both temperature and solute concentration, the stationary state to be tested for stability is, in the absence of generation of heat or mass, characterized by the following equations:’”

Also in the first paragraph of the introduction, the text “From a practical…conductors.” should read “As pointed out in Ref. [7], ‘from a practical point of view, many interesting processes involve thermally driven flows; among these are such diverse phenomena as convection in stars, the ocean, and the atmosphere, and the production of pure semiconductors’.” Similarly, the text “a fact which…flow.” in Sec. 4.1 should read “a fact which following [7] ‘can be qualitatively understood in simple terms: if λ is too large, the viscous drag from the horizontal boundaries will inhibit the flow’.”

In the second paragraph, the text “investigated the…mechanisms.” should read “‘investigated the dynamical origin of Benard's cells. His analysis yielded the basic result that a top-heavy fluid layer was stable under the joint influence of viscosity and heat diffusion until the vertical temperature drop was large enough to overcome these two dissipative and stabilizing mechanisms’ (Normand, C., Pomeau, Y., and Velarde, M. G., 1977, “Convective Instability: A Physicist's Approach,” Rev. Mod. Phys., 49(3): 581–624.”

Bullet (i) in the second paragraph of the introduction should read “‘The fluid must contain at least two components with different molecular diffusivities, each of which affects the density of the fluid. Chemists prefer to use the terms “isothermal ternary system,” referring to a solvent and two solutes or polymers, or “nonisothermal binary system,” thus distinguishing between thermal and other diffusion processes’ [6].”

In bullet (ii), the text “The Soret effect…convection” should read “As observed in Ref. [52], ‘the Soret effect is thus a mechanism by which an applied temperature gradient can establish a concentration gradient.’ Indeed, ‘the instability of such a mixture in the Bénard configuration has much in common with the problem of thermosolutal (thermohaline) convection’.”

In the final paragraph of Sec. 4.2, the text “It is not…disturbances.” should read “As observed in Ref. [34], ‘a negative density gradient is not a sufficient condition for stability for either monotonic disturbances or oscillatory disturbances’.”

The paragraph following Eq. (132) should read “As observed in Sec. 2.3 of the book Guckenheimer, J. and Holmes, P., 1983, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York, ‘this three mode truncation accurately reflects the dominant convective properties of the fluid for Rayleigh numbers p near 1. In particular, when p=1, the pure conductive solution of the partial differential fluid equations, having zero velocity and linear temperature gradient, becomes unstable to a solution containing steady convective rolls or cells. With stress free boundary conditions, the Lorenz equations are a minimal truncation of the fluid equations which embody the essential features of this bifurcation’.”

Further, the caption for Fig. 3 should read “Growth of Fourier coefficients. Reproduced from Fig. 1 in Lanford, O. E., 1982, ‘The Strange Attractor Theory of Turbulence,’ Ann. Rev. Fluid Mech., 14, pp. 347–364.” Notably, the content of the original figure was incorrectly rotated by 180 deg in this paper. Above this figure, the text “All three…and so on.” should read “As observed in Lanford, O.E., 1982, ‘The Strange Attractor Theory of Turbulence,’ Ann. Rev. Fluid Mech., 14, pp. 347–364, ‘all three stationary solutions are unstable. Orbits that start near the origin escape monotonically; those that start near the centers escape through growing oscillations. If a solution is computed starting from some more or less randomly chosen initial point, what is found without exception is that the orbit will, after an initial transient regime of variable length, settle down to a motion in which, most of the time, it can be thought of as performing oscillations about one of the centers. The oscillation grows in amplitude; when it reaches a critical size, the orbit abruptly makes a transition to oscillation about the other center. This oscillation again grows and the orbit eventually makes a transition back to oscillating about the first center, and so on.’”

Finally, the conclusion of the last paragraph of Sec. 5 should read “As pointed out by Roache, P.J., 1997, ‘Quantification of Uncertainty in Computational Fluid Dynamics,’ Ann. Rev. Fluid Mech., 29, pp. 123–160, ‘Lafon and Yee (1992) have given a large number of examples of nonlinear (chaotic) dynamics solutions in which spurious (grossly erroneous) solutions for steady-state problems with strongly nonlinear source terms are obtained for stable implicit algorithms applied beyond the linear stability limit. Their point is the danger of being misled by such calculations, and the need for further research to guarantee a priori accuracy.’”