Kengo Deguchi

Canonical exact coherent structures embedded in high Reynolds number flows

The applications and implications of two recently addressed asymptotic descriptions of exact coherent structures in shear flows are discussed. The first type of asymptotic framework to be discussed was introduced in a series of papers by Hall & Smith in the 1990s and was referred to as vortex–wave interaction theory (VWI). New results are given here for the canonical VWI problem in an infinite region; the results confirm and extend the results for the infinite problem inferred the recent VWI computation of plane Couette flow. The results given define for the first time exact coherent structures in unbounded flows. The second type of canonical structure described here is that recently found for asymptomatic suction boundary layer and corresponds to freestream coherent structures (FCS), in boundary layer flows. Here, it is shown that the FCS can also occur in flows such as Burgers vortex sheet. It is concluded that both canonical problems can be locally embedded in general shear flows and thus have widespread applicability.

Linear instability in Rayleigh-stable Taylor-Couette flow

Rayleighs stability criterion describes the inviscid stability of rotating fluid flows. Despite the limitations of the criterion due to the assumptions used, it has been widely viewed as a general stability barrier in various rapidly rotating flows. However, contrary to previous belief, a linear instability is identified in Rayleigh-stable Taylor-Couette flow. The instability is found in cyclonic rapid rotation regime, for almost the entire range of the radius ratio of the cylinders.

The relationship between free-stream coherent structures and near-wall streaks at high Reynolds numbers

The present work is based on our recent discovery of a new class of exact coherent structures generated near the edge of quite general boundary layer flows. The structures are referred to as free-stream coherent structures and were found using a large Reynolds number asymptotic approach to describe equilibrium solutions of the Navier–Stokes equations. In this paper, first we present results for a new family of free-stream coherent structures existing at relatively large wavenumbers. The new results are consistent with our earlier theoretical result that such structures can generate larger amplitude wall streaks if and only if the local spanwise wavenumber is sufficiently small. In a Blasius boundary layer, the local wavenumber increases in the streamwise direction so the wall streaks can typically exist only over a finite interval. However, here it is shown that they can interact with wall curvature to produce exponentially growing Görtler vortices through the receptivity process by a novel nonparallel mechanism. The theoretical predictions found are confirmed by a hybrid numerical approach. In contrast with previous receptivity investigations, it is shown that the amplitude of the induced vortex is larger than the structures in the free-stream which generate it. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

Exact Coherent State with Travelling Hairpin Vortex in Plane Couette Flow

A new type of travelling wave solution is obtained in plane Couette flow. The solution appears via a Hopf bifurcattion from the so-called stationary hairpin vortex state found recently by [1] and [2]. The most striking feature of the solution is an anti-symmetric mean flow profile. The fluctuating flow patterns propagate in the streamwise direction with the phase velocity being zero at its onset and increasing gradually as the Reynolds number is increased.

Linear and nonlinear instabilities of sliding Couette flow

We consider an incompressible viscous fluid with the kinematic viscosity v between two infinitely long concentric cylinders with radii a and b (b > a). The fluid experiences a shear motion produced by pulling the inner cylinder with the axial speed U while keeping the outer cylinder at rest (see Fig.1). The axial basis flow at the radius r,

Free-stream coherent structures in parallel boundary-layer flows

U_{B}(r) = R\frac{\ln(r(1 - \eta)/2)}{\ln(\eta)},

Mirror-symmetric exact coherent states in plane Poiseuille flow

can be obtained as an exact solution of the Navier-Stokes equation, where \(R = U(b - a)/2v\) is the Reynolds number and \(\eta = a/b\) is the radius ratio.