Hydrodynamic Stability: Foreword by John Miles

By J. Miles. 2004

1,410 citations recorded by the source corpus.

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Citations in the corpus

Structural sensitivity of the first instability of the cylinder wake (2007, methodology): “These waves are governed by the Orr–Sommerfeld equation (Drazin & Reid 1981) which yields the local linear dispersion relation ω = Ωl(k, x) between the complex frequency ω and the complex wavenumber k at the streamwise station x under consideration.”
Three-dimensional instabilities in compressible flow over open cavities (2008, methodology): “The centrifugal instability problem was first considered for swirling inviscid flow by Rayleigh, who derived a circulation criterion for stability (e.g. Drazin & Reid 1981).”
Characterization of noise amplifiers with global singular modes: the case of the leading-edge flat-plate boundary layer (2013, background): “[30], based on the positiveness of −u′v′∂yU , the dominant production term in a boundary layer.”
The Minimum Wind Speed for Sustainable Turbulence in the Nocturnal Boundary Layer (2012, background): “It fact, those statements are founded in classical theory on hydrodynamic stability (Drazin and Reid 2004).”
Statistical mechanics of two-dimensional and geophysical flows (2011, background): “(108) have no neutral modes (this situation of a linear operator with no modes may seem strange, it is however not unusual for a non-normal23 linear operator; for instance one can prove that (108) has no mode as soon as U is monotonic in a channel geometry [64], this is also true for the Kolmogorov ”
Information stored in Faraday waves: the origin of a path memory (2011, methodology): “In that case, the general solution (see (4.87) in Drazin & Reid 1981) reads as ξ (r, t) = ∞∑ m=1 am(t)Sm(r) with Sm(r) + k 2 mSm(r) = 0, (6.2) where am(t) satisfies an ODE (see below) and Sm(r) is a complete set of orthogonal axisymmetric eigenfunctions of the two-dimensional Laplace operator with…”
On coherent structure in wall turbulence (2013, methodology): “Falco (1977) presented additional observations from smoke visualization and hot wire measurements, although these were interpreted somewhat differently by the author.”
On the stability threshold for the 3D Couette flow in Sobolev regularity (2015, background): “[29, 46, 42, 49, 50, 43, 15, 36] for a small representative subset or the texts [19, 48, 53] and the references therein.”
Gevrey stability of Prandtl expansions for 2-dimensional Navier–Stokes flows (2016, background): “On the other hand, when U (T, Y ) = U(Y ) and U(t, y) = U(y) are time independent, our stability issue connects to the long history of the stability of steady shear flows [3].”
Kelvin waves and the singular modes of the Lamb–Oseen vortex (2006, background): “This property is generic to the generalized Airy functions with a balanced/dominant behaviour (Drazin & Reid 1981).”
Well-posedness of the Prandtl equation without any structural assumption (2018, background): “Another example is the so-called Tollmien-Schlichting wave, that is typical of viscous ﬂows at high but ﬁnite Reynolds number [5, 15].”
Instability and sensitivity of the flow around a rotating circular cylinder (2010, methodology): “This approach is compared with the analysis of the perturbation kinetic energy production, a classic † Email address for correspondence: luca@mech.kth.se approach in linear stability analysis (Drazin & Reid 1981; Huerre & Rossi 1998).”
Leading-edge effects in bypass transition (2007, background): “The dominant frequency in the wavepackets in this experiment corresponds to the most unstable one, which is around β = ωδ∗/U∞ ∼ 0.1 (Jordinson 1970; Drazin & Reid 1981).”
Convex integration and phenomenologies in turbulence (2019, background): “The vanishing viscosity limit ν → 0 leads to the consideration of boundary layers which typically separate from the wall; one of the fundamental driving mechanisms for the transition from a laminar to a turbulent regime [108, 57].”
Onset of convection in a gravitationally unstable diffusive boundary layer in porous media (2005, background): “For steady base states, linear stability theory leads to an algebraic eigenvalue problem (Drazin & Reid 1981; Nield & Bejan 1999).”
Enhanced Dissipation and Inviscid Damping in the Inviscid Limit of the Navier–Stokes Equations Near the Two Dimensional Couette Flow (2014, background): “the classical texts [24, 55] and the references therein).”
The influence of initial conditions on turbulent mixing due to Richtmyer–Meshkov instability† (2010, background): “It is assumed that the acceleration g(t) is very large and occurs over a very short period of time (see e.g. Richtmyer 1960; Drazin & Reid 2004), giving da dt = µk ua+0 At +, (2.1) where At+ = (ρ+2 − ρ+1 )/(ρ+1 + ρ+2 ) is the Atwood number, the plus (+) indicates a post-shock quantity, and µ is a…”
The Dynamics of Legged Locomotion: Models, Analyses, and Challenges (2006, background): “gl [105], but here we follow the biomechanical convention that avoids the square root [8].”