Direct numerical simulation of the laminar-turbulent transition in a thick spherical layer

Zhilenko, D. Yu.; Krivonosova, O. E.; Nikitin, N.

doi:10.1134/s0015462807060038

Cited by 13 publications

(6 citation statements)

References 11 publications

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“…By analogy with [12], where transitions between two-and three-dimensional turbulence were studied in the presence of the azimuthal jet counter to the direction of the rotation of cylinders, we chose the case of the counter rotation of spheres. Under stationary boundary conditions, oppositely directed vortices with an interface between them are formed in the meridional plane of such a flow (see figure 1, which is similar to figure 1 in [13]). A similar circulation can be observed in the case of the rotation of only the inner sphere in the presence of altitude-inhomogeneous external heating [14], typical of the atmosphere.…”

Section: Introductionsupporting

confidence: 49%

“…Discretization in space was performed on grids nonuniform in r and θ directions with concentration near the boundaries and equatorial plane and the total number of nodes 5.76 × 10 5 . The sensitivity of the results to the parameters of grid was analyzed in detail in [13], [19]. This algorithm was used for calculations with both stationary [11] and periodic [19] boundary conditions.…”

Section: Methods Of Calculationmentioning

confidence: 99%

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The Different Types of Turbulence in Rotating Spherical Layers

Zhilenko

Krivonosova

Gritsevich

2018

J. Phys.: Conf. Ser.

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Abstr act. Turbulent flows of a viscous incompressible fluid in a layer between rotating concentric spheres under the action of the modulation of the velocity of one of the spheres have been studied experimentally and numerically. The form of spectra of turbulent pulsations of the azimuthal velocity depends on the sphere whose rotational velocity is modulated, as well as on the amplitude and frequency of modulation. The possibility of the formation of turbulence with spectra qualitatively similar to spectra obtained in measurements in the upper atmosphere is established: with the slope close to -3 at low frequencies and close to -5/3 at high frequencies and with the negative longitudinal velocity structure function of the third order. It has been shown that such spectra are formed in the regions of a flow that are strongly synchronized under the action of the modulation of the rotational velocity.

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Section: Introductionsupporting

confidence: 49%

Section: Methods Of Calculationmentioning

confidence: 99%

The Different Types of Turbulence in Rotating Spherical Layers

Zhilenko

Krivonosova

Gritsevich

2018

J. Phys.: Conf. Ser.

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“…These equations are integrated with respect to time until the solution reaches the asymptotic behaviour ∼ exp (σ t). In the general case, σ is a complex number: σ = λ + i2π f. The growth or decay of the perturbation is determined by the sign of λ, while the imaginary part determines the frequency f and phase velocity c = 2π f /m of the mode m. To reduce the number of grid knots, meshes were squeezed in the radial direction near rigid boundaries [46]. The parameter ε r characterizes the degree of the mesh size non-uniformity in the radial direction and equals the ratio of the minimum cell size to the maximum one.…”

Section: Methodsmentioning

confidence: 99%

Noise induced effects in the axisymmetric spherical Couette flow

Krivonosova

Gritsevich

Zhilenko

et al. 2023

Phil. Trans. R. Soc. A.

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We study the axisymmetric, wide gap, spherical Couette flow in the presence of noise in numerical simulations and experiments. Such studies are important because most of the flows in nature are subjected to random fluctuations. Noise is introduced into the flow by adding fluctuations to the inner sphere rotation which are random in time with zero mean. Flows of a viscous incompressible fluid are induced either by rotation of the inner sphere only or by the co-rotation of the spheres. Mean flow generation was found to occur under the action of additive noise. A higher relative amplification of meridional kinetic energy compared to the azimuthal component was also observed under certain conditions. Calculated flow velocities were validated by laser Doppler anemometer measurements. A model is proposed to elucidate the rapid growth of meridional kinetic energy for flows induced by varying the co-rotation of the spheres. Our linear stability analysis for flows induced by the rotation of the inner sphere revealed a decrease in the critical Reynolds number, corresponding to the onset of the first instability. Also, in this case, a local minimum of the mean flow generation on approaching the critical Reynolds number was observed, which is consistent with the available theoretical predictions. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical Transactions paper (part 2)’.

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“…Despite the fact that some numerical and experimental studies have verified the existence of symmetric and asymmetric Taylor vortices in wide gaps (b [ 0:3), yet three-dimensional numerical simulations of Taylor vortices in wide gaps are few even if the laminar-turbulent transition for b ¼ 1 had been simulated by Zhilenko [35]. The aim of this study is to investigate the existence regime in the ðb; ReÞ plane for Taylor vortices in wide gaps and the transition detail from asymmetric vortex to basic flows with increasing Re via numerical solution of the three-dimensional incompressible Navier-Stokes equations.…”

Section: Introductionmentioning

confidence: 99%

Existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical Couette flow

Abbas

Shah

2018

J Braz. Soc. Mech. Sci. Eng.

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We study the existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical Couette flow by time marching the three-dimensional incompressible Navier-Stokes equations numerically. Three wide-gap clearance ratios, b ¼ R 2 À R 1 ð Þ =R 1 ¼ 0:33, 0.38 and 0.42 are investigated for a range of Reynolds numbers respectively. Using the 1-vortex flow for clearance ratio b ¼ 0:18 at Reynolds number Re ¼ 700 as the initial conditions and suddenly increasing b to the target value, we can compute Taylor vortices for the three wide gaps. For b ¼ 0:33, Taylor vortices exist in the range 450 Re 2050. With increasing Re the steady symmetric 1-vortex flow becomes steady asymmetric at Re ¼ 1850, and then become periodic at Re ¼ 2000. When Re [ 2050 the flow returns back to the steady basic flow state with no Taylor vortices. For b ¼ 0:38, Taylor vortices can exist in the range 500 Re 1400. With increasing Re, the steady symmetric 1-vortex flow become steady asymmetric at Re ¼ 1200, and then the flow evolves into the steady basic flow for Re [ 1400. For b ¼ 0:42, Taylor vortices can exist in the range 650 Re 1300. With increasing Re, steady asymmetric Taylor vortices occur at Re ¼ 1150, and then the flow evolves into the steady basic flow for Re [ 1300. The present numerical results are in good agreement with available numerical and experimental results. Furthermore, the existence regime of Taylor vortices in the ðb; ReÞ plane for b ! 0:33 and the three-dimensional transition process from periodic asymmetric vortex flow to steady basic flow with increasing Re are presented for the first time. Keywords Spherical Couette flow Á Wide gap Á Symmetric Taylor vortices Á Asymmetric Taylor vortices

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Direct numerical simulation of the laminar-turbulent transition in a thick spherical layer

Cited by 13 publications

References 11 publications

The Different Types of Turbulence in Rotating Spherical Layers

The Different Types of Turbulence in Rotating Spherical Layers

Noise induced effects in the axisymmetric spherical Couette flow

Existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical Couette flow

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