The Experts below are selected from a list of 213 Experts worldwide ranked by ideXlab platform
Ming Dong - One of the best experts on this subject based on the ideXlab platform.
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on Continuous Spectra of the orr sommerfeld squire equations and entrainment of free stream vortical disturbances
Journal of Fluid Mechanics, 2013Co-Authors: Ming DongAbstract:Small-amplitude perturbations are governed by the linearized Navier–Stokes equations, which are, for a parallel or nearly parallel shear flow, customarily reduced to the Orr–Sommerfeld (O-S) and Squire equations. In this paper, we consider Continuous Spectra (CS) of the O-S and Squire operators for the Blasius and asymptotic suction boundary layers, and address the issue of whether and when Continuous modes can represent free-stream vortical disturbances and their entrainment into the shear layer. For the Blasius boundary layer, we highlight two particular properties of the CS: (i) the eigenfunction of a Continuous mode simultaneously consists of two components with wall-normal wavenumbers , a phenomenon which we refer to as ‘entanglement of Fourier components’; and (ii) for low-frequency disturbances the presence of the boundary layer forces the streamwise velocity in the free stream to take a much larger amplitude than those of the transverse velocities. Both features appear to be non-physical, and cast some doubt about the appropriateness of using CS to characterize free-stream vortical disturbances and their entrainment into the boundary layer, a practice that has been adopted in some recent studies of bypass transition. A high-Reynolds-number asymptotic description of Continuous modes and entrainment is present, and it shows that the entanglement is a result of neglecting non-parallelism, which has a leading-order effect on the entrainment. When this effect is included, entanglement disappears, and moreover the streamwise velocity is significantly amplified in the edge layer when , where is the Reynolds number based on the local boundary-layer thickness. For the asymptotic suction boundary layer, which is an exactly parallel flow, both temporal and spatial CS may be defined mathematically. However, at a finite neither of them represents the physical process of free-stream vortical disturbances penetrating into the boundary layer. The latter must instead be characterized by a peculiar type of Continuous modes whose eigenfunctions increase exponentially with the distance from the wall. In the limit , all three types of CS are identical at leading order, and hence can be used to represent free-stream vortical disturbances and their entrainment. Low-frequency disturbances are found to generate a large-amplitude streamwise velocity in the boundary layer, which is reminiscent of longitudinal streaks.
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On Continuous Spectra of the Orr–Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances
Journal of Fluid Mechanics, 2013Co-Authors: Ming DongAbstract:Small-amplitude perturbations are governed by the linearized Navier–Stokes equations, which are, for a parallel or nearly parallel shear flow, customarily reduced to the Orr–Sommerfeld (O-S) and Squire equations. In this paper, we consider Continuous Spectra (CS) of the O-S and Squire operators for the Blasius and asymptotic suction boundary layers, and address the issue of whether and when Continuous modes can represent free-stream vortical disturbances and their entrainment into the shear layer. For the Blasius boundary layer, we highlight two particular properties of the CS: (i) the eigenfunction of a Continuous mode simultaneously consists of two components with wall-normal wavenumbers , a phenomenon which we refer to as ‘entanglement of Fourier components’; and (ii) for low-frequency disturbances the presence of the boundary layer forces the streamwise velocity in the free stream to take a much larger amplitude than those of the transverse velocities. Both features appear to be non-physical, and cast some doubt about the appropriateness of using CS to characterize free-stream vortical disturbances and their entrainment into the boundary layer, a practice that has been adopted in some recent studies of bypass transition. A high-Reynolds-number asymptotic description of Continuous modes and entrainment is present, and it shows that the entanglement is a result of neglecting non-parallelism, which has a leading-order effect on the entrainment. When this effect is included, entanglement disappears, and moreover the streamwise velocity is significantly amplified in the edge layer when , where is the Reynolds number based on the local boundary-layer thickness. For the asymptotic suction boundary layer, which is an exactly parallel flow, both temporal and spatial CS may be defined mathematically. However, at a finite neither of them represents the physical process of free-stream vortical disturbances penetrating into the boundary layer. The latter must instead be characterized by a peculiar type of Continuous modes whose eigenfunctions increase exponentially with the distance from the wall. In the limit , all three types of CS are identical at leading order, and hence can be used to represent free-stream vortical disturbances and their entrainment. Low-frequency disturbances are found to generate a large-amplitude streamwise velocity in the boundary layer, which is reminiscent of longitudinal streaks.
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On Continuous Spectra of the Orr-Sommerfeld/Squire Equations and Entrainment of Free-stream Vortical Disturbances in the Blasius Boundary Layer
43rd Fluid Dynamics Conference, 2013Co-Authors: Ming DongAbstract:Small-amplitude perturbations are governed by the linearized Navier-Stokes equations, which are, for a parallel or nearly parallel shear flow, customarily reduced to the OrrSommerfeld (O-S) and Squire equations. In this paper, we consider Continuous Spectra (CS) of the O-S and Squire operators for the Blasius boundary layer, and address the issue of whether and when Continuous modes can represent free-stream vortical disturbances and their entrainment into the shear layer. We highlight two particular properties of the CS: (a) the eigenfunction of a Continuous mode simultaneously consists of two components with wall-normal wavenumbers ±k2, a phenomenon which we refer to as ‘entanglement of Fourier components’; and (b) for low-frequency disturbances the presence of the boundary layer forces the streamwise velocity in the free stream to take a much larger amplitude than those of the transverse velocities. Both features appear to be non-physical, and cast some doubt about the appropriateness of using CS to characterize free-stream vortical disturbances and their entrainment into the boundary layer, a practice that has been adopted in some recent studies of bypass transition. A high-Reynolds-number asymptotic description of Continuous modes and entrainment is present, and it shows that the entanglement is a result of neglecting non-parallelism, which has a leading-order effect on the entrainment. When this effect is included, entanglement disappears, and moreover the streamwise velocity is significantly amplified in the edge layer when R ω 1, where R is the Reynolds number based on the local boundary-layer thickness.
Shinji Tokuda - One of the best experts on this subject based on the ideXlab platform.
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Regularization of singular eigenfunctions of an operator with Continuous Spectra: With applications for ballooning modes in toroidally rotating tokamaks
Physics of Plasmas, 2005Co-Authors: Masaru Furukawa, Zensho Yoshida, Shinji TokudaAbstract:Eigenfunction expansions of fields encounter practical difficulty when the generating operator has Continuous Spectra (as is common in magnetohydrodynamics theories). An appropriate “weight function” may remove the singularity of the eigenfunctions belonging to the Continuous spectrum and the complete set of regularized (square-integrable) eigenfunctions can be obtained. As an example, this method has been applied for ballooning modes in toroidally rotating tokamaks. While the weight function truncates the long-term behavior of modes, the regularized eigenfunctions can describe transient behavior within a finite time.
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A new eigenvalue problem associated with the two-dimensional Newcomb equation without Continuous Spectra
Physics of Plasmas, 1999Co-Authors: Shinji Tokuda, Tomoko WatanabeAbstract:A new eigenvalue problem associated with the two-dimensional Newcomb equation in an axisymmetric toroidal plasma, such as a tokamak, has been posed and solved numerically by using a finite element method. In the formulation of the eigenvalue problem, the weight functions (the kinetic energy integral) and the boundary conditions at rational surfaces are chosen such that the Spectra of the eigenvalue problem are comprised of only the real and denumerable eigenvalues (point Spectra) without Continuous Spectra. Applications to the ideal m=1 mode have verified that this formulation is able to identify stable states as well as unstable states, and that the numerically obtained eigenfunctions show the singular behavior predicted by the theory at rational surfaces.
Zensho Yoshida - One of the best experts on this subject based on the ideXlab platform.
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Regularization of singular eigenfunctions of an operator with Continuous Spectra: With applications for ballooning modes in toroidally rotating tokamaks
Physics of Plasmas, 2005Co-Authors: Masaru Furukawa, Zensho Yoshida, Shinji TokudaAbstract:Eigenfunction expansions of fields encounter practical difficulty when the generating operator has Continuous Spectra (as is common in magnetohydrodynamics theories). An appropriate “weight function” may remove the singularity of the eigenfunctions belonging to the Continuous spectrum and the complete set of regularized (square-integrable) eigenfunctions can be obtained. As an example, this method has been applied for ballooning modes in toroidally rotating tokamaks. While the weight function truncates the long-term behavior of modes, the regularized eigenfunctions can describe transient behavior within a finite time.
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Degenerate Continuous Spectra producing localized secular instability: an example in a non-neutral plasma
Journal of Plasma Physics, 2003Co-Authors: Makoto Hirota, Tomoya Tatsuno, Zensho YoshidaAbstract:Fluctuations in ambient shear flow exhibit interesting transient phe- nomena. Shear flow produces not only Kelvin-Helmholtz modes (global exponen- tial instabilities represented by point Spectra) but also local algebraic instabilities associated with multiple Continuous Spectra. Since the generating operator is non- Hermitian, the orthogonality of eigenmodes is broken, and unresolvable mode cou- plings (resonances) bring about secular behavior (algebraic instability). We analyze electrostatic fluctuations in a magnetized non-neutral (single species) plasma where the electrostatic potential parallels the stream function. This secular behavior is reproduced by solving the initial value problem with a renormalization method.
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Quasiperiodic perturbations for the Alfvén-wave Continuous Spectra.
Physical review letters, 1992Co-Authors: Zensho YoshidaAbstract:A two-dimensional periodic modulation of an ambient magnetic field generates a quasiperiodic perturbation for the Alfven wave. A simple quasiperiodic wave equation has been derived, which resembles the Schrodinger equation for a valence electron in a one-dimensional quasicrystal. Let a be the tangent of the angle between the direction of the unperturbed magnetic field and the periodicity of the perturbation. It a is an irrational number, the perturbed wave potential is quasiperiodic. By a large perturbation, the Alfven continuum is changed into point Spectra for almost all σ
Michael Demuth - One of the best experts on this subject based on the ideXlab platform.
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STABLE Continuous Spectra FOR DIFFERENTIAL OPERATORS OF ARBITRARY ORDER
Analysis and Applications, 2005Co-Authors: M. Baro, Michael Demuth, E. GiereAbstract:Perturbations of the Continuous Spectra of two self-adjoint operators H0 and H can be controlled by sandwiched differences of the form \[ \phi_{2}(H)[\phi_{1}(H)-\phi_{1}(H_{0})]\phi_{2}(H_{0}), \] where ϕj(·) are bounded functions of the operators involved. If ϕj(H0) and ϕj(H) are integral operators, we give general integral conditions for the kernels, such that the Continuous, the absolutely Continuous and the singular Continuous Spectra of H0 and H coincide. The abstract operator theoretical conditions are applied for H0 in L2(ℝd) of the form (-Δ)α/2, α∈ (0,2) and (-Δ)m, m∈ℕ. H is given as a perturbation of H0, where we allow perturbations by variable coefficients, potentials or obstacles.
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Schrödinger Operators with Empty Singularly Continuous Spectra
Mathematical Physics Analysis and Geometry, 1999Co-Authors: Michael Demuth, Kalyan B. SinhaAbstract:Let H be a semibounded perturbation of the Laplacian H _0 in L ^2(ℝ^ d ). For an admissible function ϕ sufficient conditions are given for the completeness of the scattering system ϕ( H ), ϕ( H _0). If ϕ is the exponential function and if e^− λ H is an integral operator we denote the kernel of the difference D _λ = e^− λ H − e^− λ H _0 by D _λ( x , y ), λ > 0. The singularly Continuous spectrum of H is empty if ∫ℝ^d dx ∫_ℝ ^d dy |D_λ(x,y)| (1 + |y|^2)^α< ∞ for some α > 1. This result is applied to potential perturbations and to perturbations by imposing Dirichlet boundary conditions.
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Schrödinger Operators with Empty Singularly Continuous Spectra
Mathematical Physics Analysis and Geometry, 1999Co-Authors: Michael Demuth, Kalyan B. SinhaAbstract:Let H be a semibounded perturbation of the Laplacian H0 in L2(ℝd). For an admissible function ϕ sufficient conditions are given for the completeness of the scattering system ϕ(H), ϕ(H0). If ϕ is the exponential function and if e− λ H is an integral operator we denote the kernel of the difference Dλ = e− λ H − e− λ H0 by Dλ(x, y), λ > 0. The singularly Continuous spectrum of H is empty if
E. Giere - One of the best experts on this subject based on the ideXlab platform.
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STABLE Continuous Spectra FOR DIFFERENTIAL OPERATORS OF ARBITRARY ORDER
Analysis and Applications, 2005Co-Authors: M. Baro, Michael Demuth, E. GiereAbstract:Perturbations of the Continuous Spectra of two self-adjoint operators H0 and H can be controlled by sandwiched differences of the form \[ \phi_{2}(H)[\phi_{1}(H)-\phi_{1}(H_{0})]\phi_{2}(H_{0}), \] where ϕj(·) are bounded functions of the operators involved. If ϕj(H0) and ϕj(H) are integral operators, we give general integral conditions for the kernels, such that the Continuous, the absolutely Continuous and the singular Continuous Spectra of H0 and H coincide. The abstract operator theoretical conditions are applied for H0 in L2(ℝd) of the form (-Δ)α/2, α∈ (0,2) and (-Δ)m, m∈ℕ. H is given as a perturbation of H0, where we allow perturbations by variable coefficients, potentials or obstacles.
