Physics of the amplification of vortex disturbances in shear flows

Chagelishvili, G. D.; Chanishvili, R.; Ломинадзе, Д. Г.

doi:10.1134/1.567072

Cited by 20 publications

(23 citation statements)

References 15 publications

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“…In fact, we mean that as a result of transformation the time scale of a wave process changes essentially. This new kind of wave transformation existing in shear flows was described for the first time by Chagelishvili et al [1996aChagelishvili et al [ , 1996b for the case of magnetohydrodynamic waves. The physics of the process is simple and easy to understand by means of an example of a system of connected linear oscillators.…”

Section: General Analysis Of the Problemmentioning

confidence: 99%

“…[55] The basis of energy exchange between wave disturbances and shear flow is the so-called lift-up mechanism [Landahl, 1975;Chagelishvili et al, 1996aChagelishvili et al, , 1996b, by which disturbances transfer fluid from the regions with a higher flow velocity to the ones with a lower velocity, and vice versa. The energy exchange between SFH and a mean flow is as intensive, as faster propagate the perturbed elements of the fluid along the shear, in other words, the as larger is the projection of the velocity of SFH perturbations' along the shear (in our case, along the Y axis).…”

Section: General Analysis Of the Problemmentioning

confidence: 99%

“…Unexpected new results have already been obtained within the framework of this approach. They include in particular the evolution of acoustic disturbances and an energy exchange between the corresponding SFH and a horizontal shear flow [Chagelishvili et al, 1994;Chagelishvili et al, 1996aChagelishvili et al, , 1996b, and the discovery of a new mechanism of linear transformation of waves in shear flows [Chagelishvili and Chkhetiani, 1995;Chagelishvili et al, 1997].…”

Section: Introductionmentioning

confidence: 99%

“…With this approach, the modified initial problem (Cauchy problem) is solved by tracing the evolution of spatial Fourier-harmonics (SFH) of wave disturbances in time and not using any spectral expansion with respect to time [Graik and Criminale, 1986;Farrell and Ioannou, 1993;Chagelishvili et al, 1994;Chagelishvili et al, 1996aChagelishvili et al, , 1996bKalashnik et al, 2004]. Being an optimal ''language,'' the nonmodal approach greatly simplifies a mathematical description of the dynamics of shear flow disturbances and makes it possible to reveal the key phenomena, caused by the nonorthogonality of linear dynamics, which have escaped notice in the case of modal analysis.…”

Section: Introductionmentioning

confidence: 99%

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Mechanism of the planetary Rossby wave energy amplification and transformation in the ionosphere with an inhomogeneous zonal smooth shear wind

2006

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[1] The generation and further dynamics of planetary magnetized Rossby waves and inertia waves are investigated in the rotating dissipative ionosphere in the presence of a smooth inhomogeneous zonal wind (shear flow). Magnetized Rossby waves appear as a result of the interaction of the medium with the spatially inhomogeneous geomagnetic field and are an ionospheric manifestation of usual tropospheric Rossby waves. An effective linear mechanism responsible for the intensification and mutual transformation of Rossby and inertia waves is found. For shear flows, the operators of the linear problem are not self-adjoint, and therefore the eigenfunctions of the problem maybe nonorthogonal and can hardly be studied by the canonical modal approach. Hence it becomes necessary to use the so-called nonmodal mathematical analysis which has been actively developed in recent years. The nonmodal approach shows that the transformation of wave disturbances in shear flows is due to the nonorthogonality of eigenfunctions of the problem in the conditions of linear dynamics. Thus there arises a new degree of freedom and a new way for the evolution of disturbances in the medium. Using numerical modeling, we illustrate the peculiar features of the interaction of waves with the background flow as well as the mutual transformation of wave disturbances in the D, E, and F regions of the ionosphere. It is established that the presence of a geomagnetic field, Hall and Pedersen currents in the ionospheric medium, improves the interaction and mutual energy exchange between waves and a shear flow.

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Section: General Analysis Of the Problemmentioning

confidence: 99%

Section: General Analysis Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mechanism of the planetary Rossby wave energy amplification and transformation in the ionosphere with an inhomogeneous zonal smooth shear wind

2006

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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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Temporal behaviour of global perturbations in compressible axisymmetric flows with free boundaries

Zhuravlev¹,

Шакура²

2009

Astron Nachr

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The dynamics of small global perturbations in the form of a linear combination of a finite number of non-axisymmetric eigenmodes is studied in the two-dimensional approximation. The background flow is assumed to be an axisymmetric perfect fluid with adiabatic index γ = 5/3 rotating with a power law angular velocity distribution Ω ∝ r −q , 1.5 < q < 2.0, confined by free boundaries in the radial direction. The substantial transient growth of acoustic energy of optimized perturbations is discovered. An optimal energy growth G is calculated numerically for a variety of parameters. Its value depends essentially on the perturbation azimuthal wavenumber m and increases for higher values of m. The closer the rotation profile to the Keplerian law, the larger growth factors can be obtained but over a longer time. The highest acoustic energy increase found numerically is of order ∼ 10 2 over ∼ 6 typical Keplerian periods. Slow neutral eigenmodes with corotation radius beyond the outer boundary mostly contribute to the transient growth. The revealed linear temporal behaviour of perturbations may play an important role in angular momentum transfer in toroidal flows near compact relativistic objects.

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Physics of the amplification of vortex disturbances in shear flows

Cited by 20 publications

References 15 publications

Mechanism of the planetary Rossby wave energy amplification and transformation in the ionosphere with an inhomogeneous zonal smooth shear wind

Mechanism of the planetary Rossby wave energy amplification and transformation in the ionosphere with an inhomogeneous zonal smooth shear wind

Dynamics of Plasma Blobs in a Shear Flow

Temporal behaviour of global perturbations in compressible axisymmetric flows with free boundaries

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