Linear Mechanism of Wave Emergence from Vortices in Smooth Shear Flows

Chagelishvili, G. D.; Tevzadze, Alexander G.; Bodo, G.; Moiseev, S. S.

doi:10.1103/physrevlett.79.3178

Cited by 91 publications

(122 citation statements)

References 25 publications

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“…At later times (at t t * ), the characteristic time-scale of the wave mode becomes much shorter than that of the vortex mode and the modes are clearly distinguishable. The nature of the wave generation phenomenon (also called conversion of vortices into waves) is described in detail for the simplest shear flow in Chagelishvili et al (1997).…”

Section: Dynamics Of Non-symmetric Perturbationsmentioning

confidence: 99%

“…The progress involves an elaboration of a concept-the so-called bypass concept-of self-sustaining turbulence in spectrally stable shear flows (Trefethen et al 1993;Gebhardt and Grossmann 1994;Baggett et al 1995;Grossmann 2000;Reshotko 2001;Chagelishvili et al 2002;Chapman 2002). Among the novelties one should stress, in the context of the present paper, is the discovery of a new linear mechanism of transformation of vortices into acoustic waves at moderate and high shear rates in smooth compressible flows (Chagelishvili et al 1997). It should be noted that the non-normality of the linear dynamics of perturbations in shear flows was recognized by the meteorological community in 1990 (cf.…”

Section: Introductionmentioning

confidence: 99%

“…This analysis, originally by Kelvin (1887), has had a wide distribution since 1990 (cf. Craik and Criminale 1986;Criminale and Drazin 1990;Gustavsson 1991;Butler and Farrell 1992;Chagelishvili et al 1997). By means of this so-called non-modal approach, substantial progress has been achieved in the understanding of shear flow phenomena in recent years.…”

Section: Introductionmentioning

confidence: 99%

“…We also show that vortex and wave modes are coupled; pure vortical perturbations gain basic flow energy and then are transformed into non-symmetric shear internal waves at Ro > 0.4. This kind of wave generation by vortices is also typical of shear flows (Chagelishvili et al 1997) and indicates that fast wave motions, commonly ignored (filtered) in traditional quasi-geostrophic models of geophysical hydrodynamics, play an important role in the question of flow stability (Pedlosky 1987;Dimnikov and Filatov 1990;Doljanski et al 1990;Shakina 1990). Coupling among modes of different time-scales occurs also in stratified, rigidly (without shear) rotating flows (Bartello 1995), but in that case the coupling is of nonlinear origin, while in our problem the mode coupling due to the flow shear is already present in the linear regime.…”

Section: Introductionmentioning

confidence: 99%

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Linear dynamics of non‐symmetric perturbations in geostrophic horizontal shear flows

Калашник¹,

Mamatsashvili²,

Chagelishvili³

et al. 2006

Quart J Royal Meteoro Soc

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SUMMARYThe linear dynamics of non-symmetric wave and vortex mode perturbations in spectrally stable geostrophic zonal flows with a constant horizontal shear along the meridional direction, when a fluid is incompressible and stratified, is investigated. Specific features of these dynamics are closely related to the non-normality of the linear operators governing perturbation evolution in shear flows and are well interpreted in the framework of the nonmodal approach-by tracing the linear dynamics of spatial Fourier harmonics of perturbations in time. If the Rossby number Ro < 1, there occurs an algebraic (asymptotically linear) amplification of non-symmetric shear internal waves. It is shown that at Ro > 1, in addition, there takes place an exponential/explosive transient growth of the waves that precedes the time interval of algebraic amplification. We also describe the evolution of pure vortex mode perturbations imposed initially on the mean flow. It is shown that at Ro ∼ 1, pure vortex (aperiodic) perturbations are able to gain basic flow energy and then generate non-symmetric shear internal waves. The studied linear phenomena are specific to geostrophic zonal flows and cast doubt on the filtering of fast wave perturbations in the traditional quasi-geostrophic models of geophysical hydrodynamics.

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Section: Dynamics Of Non-symmetric Perturbationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Linear dynamics of non‐symmetric perturbations in geostrophic horizontal shear flows

Калашник¹,

Mamatsashvili²,

Chagelishvili³

et al. 2006

Quart J Royal Meteoro Soc

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“…This decomposition is also referred to as spatial Fourier harmonics (SFH) (see Chagelishvili et al [13,14] and references therein). We investigate the evolution of the SFH of fluctuations without any prior spectral decomposition in time in order to capture transients related to blob dynamics.…”

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confidence: 99%

Dynamics of Plasma Blobs in a Shear Flow

et al. 2008

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The global dynamic of plasma blobs in a shear flow is investigated in a simple magnetized torus using the spatial Fourier harmonics (k-space) framework. Direct experimental evidence of a linear drift in k space of the density fluctuation energy synchronized with blob events is presented. During this drift, an increase of the fluctuation energy and a production of the kinetic energy associated with blobs are observed. The energy source of the blob is analyzed using an advection-dissipation-type equation that includes blob-flow exchange energy, linear drift in k space, nonlinear processes, and viscous dissipations. We show that blobs tap their energy from the dominant E Â B vertical background flow during the linear drift stage. The exchange of energy is unidirectional as there is no evidence that blobs return energy to the flow. In magnetic fusion devices, it is well known that substantial amounts of plasma appearing as coherent structures elongated [1] along the magnetic field lines can propagate to the outer wall, ultimately causing erosion problems. A fair amount is already known about the propagation of these coherent structures; relatively little is understood about their generation and their interaction with the background sheared flow. The velocity shear in a flow is a source of diverse energy-intensive processes (e.g., coherent structures, vortices), which occur in astrophysical objects, in hydrodynamics, in laboratory plasmas, and biological systems. Vortex and coherent structure dynamics are being actively investigated in order to address the recurring dilemma caused by the relationship between the onset and the maintenance of turbulence in shear flows [2].Recent investigations in plasma physics have revealed the presence of coherent structures of density (also referred to as blobs) in the scrape-off layer of tokamaks [1,3], in simple magnetized torus (SMT) [4,5], and in linear devices [6,7]. In addition to the presence of blobs in SMT, the existence of a shear in the background E Â B flow velocity was recently shown in Ref. [5]. In this Letter, we focus on the energy exchange dynamics of blobs with the background flow in the presence of shear. In particular, we present a global analysis in k space of plasma fluctuations in the presence of intermittent and coherent structures also known as plasma blobs in TORPEX [8] with no prior Fourier decomposition in time. This approach, also referred to as non-normal, is generally utilized to better capture the time evolution of these structures in k space. First, within this framework, we show experimental evidence of a linear drift of radial wave numbers in time. This drift is associated with an increase of the kinetic energy of the fluctuations associated with the blob, and is similar to numerical investigations of self-sustained coherent vortices in a shear flow reported by Kim and co-workers [9]. In addition to the drift, we deduce the blob time of flight to the edge of the plasma cross section. Second, the key question pertaining to the source of energy provi...

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Asymptotic behavior of the two‐phase flow around the planar Couette flow in three‐dimensional space

Zhang,

Tang

2024

Math Methods in App Sciences

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This paper is concerned with the nonlinear stability of planar Couette flow for the three‐dimensional NS‐NS equations, which are used to model the motion of two‐phase flow. Our result shows that the planar Couette flow is asymptotically stable for the initial perturbations sufficiently small in some Sobolev space if the background velocity and the Reynolds number are sufficiently small. Moreover, it is proved that the solution converges to the stationary state at an algebraic time decay rate, and we also give the decay rate of the relative velocity.

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Linear Mechanism of Wave Emergence from Vortices in Smooth Shear Flows

Cited by 91 publications

References 25 publications

Linear dynamics of non‐symmetric perturbations in geostrophic horizontal shear flows

Linear dynamics of non‐symmetric perturbations in geostrophic horizontal shear flows

Dynamics of Plasma Blobs in a Shear Flow

Asymptotic behavior of the two‐phase flow around the planar Couette flow in three‐dimensional space

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