Resolvent analysis of the linearized Navier-Stokes equations provides useful insight into dynamics transitional and turbulent flows can provide a model for dominant coherent structures within flow, particularly with large gain separation. Direct computation force response modes using singular value decomposition full resolvent matrix is feasible only simple problems; despite recent progress, co...

and Applied Analysis 3 In the case k t t/Γ α 1 , where α > 0, and Γ · denotes the Gamma function, it is also said that R t t∈ 0,τ is an α-times integrated a,C -resolvent family; in such a way, we unify the notion of local α-times integrated C-semigroups a t ≡ 1 and cosine functions a t ≡ t 1, 13, 14 . Furthermore, in the case k t : ∫ t0K s ds, t ∈ 0, τ , where K ∈ Lloc 0, τ and K/ 0, we obtain ...

We investigate discrepancies between the two-dimensional cylinder flow and a quasilinear model (i.e.~resolvent analysis) from an energy transfer perspective at Re=100. The balances achieved by true are characterized compared to predictions resolvent analysis. impact of neglected nonlinear on mode shapes is clarified analyzing spatial distribution mechanisms. This provides insights into extent w...

The purpose of this note is to obtain semiclassical resolvent estimates for long range perturbations of the Laplacian on asymptotically Euclidean manifolds. For an estimate which is uniform in the Planck constant h we need to assume that the energy level is non-trapping. In the high energy limit (that is, when we consider ∆ − λ, as λ → ∞, which is equivalent to h∆ − 1, h → 0), this corresponds ...

We study the Reynolds-number scaling and the geometric self-similarity of a gainbased, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier–Stokes equations. Under this formulation,...