Transition to turbulence in quasi-two-dimensional MHD flow driven by lateral walls

Camobreco, Christopher J.; Pothérat, Alban; Sheard, Gregory J.

doi:10.1103/physrevfluids.6.013901

Cited by 4 publications

(21 citation statements)

References 64 publications

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“…Thus, the thinner pulsatile boundary layers are always more stable than their thicker counterpart exhibited by steady base flows. Note that in the high H regime, when the boundary layers are isolated for any frequency pulsation, the stability results are defined solely by the dynamics of an isolated boundary layer, as observed in steady MHD or Q2D studies [17,22,23,45], and for high frequency oscillatory hydrodynamic flows [34]. Second, variations in the pulsation frequency and amplitude roughly act to translate the stability curves, without significantly changing the overall trends (a slight change, the local minimums in Fig.…”

Section: Iii2 Long-term Behaviormentioning

confidence: 92%

“…3(d). In steady Q2D flows [17,22,23], α crit also scales with H 1/2 for high H, like Re crit . However, perplexingly for the pulsatile cases, the α crit trends are as H q , with a lower exponent than the steady case, q ≤ 1/2.…”

Section: Iii2 Long-term Behaviormentioning

confidence: 98%

“…Instability occurs via Tollmien-Schlichting (TS) waves originating in the Shercliff layers. The instabilities become isolated at the duct walls with increasing magnetic field strength [17,22], eventually behaving as per an instability in an isolated exponential boundary layer [17,22,24]. To the authors' knowledge, oscillatory or pulsatile Q2D flows are yet to be analysed under a transverse magnetic field.…”

Section: Introductionmentioning

confidence: 98%

“…[17]. As the magnetic field is strongly stabilizing, the critical Reynolds number for a steady base flow, beyond which modal instabilities grow, scales as Re crit,s = 4.835 × 10 4 H 1/2 for H 1000 [17,22,23].…”

Section: Introductionmentioning

confidence: 99%

“…The normalized time t P = t/2π is also defined. To assess the degree of destabilization, the Reynolds number ratio r s = [Re/(1 + 1/Γ)]/Re crit,s is defined, comparing the Reynolds number in this problem to the critical Reynolds number for a purely steady base flow [17,22,23]. The wave number is similarly rescaled, as α s = α/α crit,s .…”

Section: Introductionmentioning

confidence: 99%

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Stability of pulsatile quasi-two-dimensional duct flows under a transverse magnetic field

Camobreco¹,

Pothérat²,

Sheard³

2021

Preprint

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This manuscript has been accepted for publication in Physical Review Fluids, see https://journals.aps.org/prfluids/accepted/53075Se8O0b1b109b1cc0061b280aaa122f0f92dc. The stability of a pulsatile quasi-two-dimensional duct flow was numerically investigated. Flow was driven, in concert, by a constant pressure gradient and by the synchronous oscillation of the lateral walls. This prototypical setup serves to aid understanding of unsteady magnetohydrodynamic flows in liquid metal coolant ducts subjected to transverse magnetic fields, motivated by the conditions expected in magnetic confinement fusion reactors. A wide range of wall oscillation frequencies and amplitudes, relative to the constant pressure gradient, were simulated. Focus was placed on the driving pulsation optimized for the greatest reduction in the critical Reynolds number, for a range of friction parameters H (proportional to magnetic field strength). An almost 70% reduction in the critical Reynolds number, relative to that for the steady base flow, was obtained toward the hydrodynamic limit (H = 10 −7 ), while just over a 90% reduction was obtained by H = 10. For all oscillation amplitudes, increasing H consistently led to an increasing percentage reduction in the critical Reynolds number. This is a promising result, given fusion relevant conditions of H ≥ 10 4 . These reductions were obtained by selecting a frequency that both ensures prominent inflection points are maintained in the base flow, and a growth in perturbation energy in phase with the deceleration of the base flow. Nonlinear simulations of perturbations driven at the optimized frequency and amplitude still satisfied the no net growth condition at the greatly reduced critical Reynolds numbers. However, two complications were introduced by nonlinearity. First, although the linear mode undergoes a symmetry breaking process, turbulence was not triggered. Second, a streamwise invariant sheet of negative velocity formed, able to arrest the linear decay of the perturbation. Although the nonlinearly modulated base flow maintained a higher time-averaged energy, it also stabilized the flow, with exponential growth not observed at supercritical Reynolds numbers.

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Section: Iii2 Long-term Behaviormentioning

confidence: 92%

Section: Iii2 Long-term Behaviormentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stability of pulsatile quasi-two-dimensional duct flows under a transverse magnetic field

Camobreco¹,

Pothérat²,

Sheard³

2021

Preprint

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Subcritical transition to turbulence in quasi-two-dimensional shear flows

2023

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The transition to turbulence in conduits is among the longest-standing problems in fluid mechanics. Challenges in producing or saving energy hinge on understanding promotion or suppression of turbulence. While a global picture based on an intrinsically 3-D subcritical mechanism is emerging for 3-D turbulence, subcritical turbulence is yet to even be observed when flows approach two dimensions, e.g. under intense rotation or magnetic fields. Here, stability analysis and direct numerical simulations demonstrate a subcritical quasi-two-dimensional (quasi-2-D) transition from laminar flow to turbulence, via a radically different 2-D mechanism to the 3-D case, driven by nonlinear Tollmien–Schlichting waves. This alternative scenario calls for a new line of thought on the transition to turbulence and should inspire new strategies to control transition in rotating devices and nuclear fusion reactor blankets.

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Stability of pulsatile quasi-two-dimensional duct flows under a transverse magnetic field

2021

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Transition to turbulence in quasi-two-dimensional MHD flow driven by lateral walls

Cited by 4 publications

References 64 publications

Stability of pulsatile quasi-two-dimensional duct flows under a transverse magnetic field

Stability of pulsatile quasi-two-dimensional duct flows under a transverse magnetic field

Subcritical transition to turbulence in quasi-two-dimensional shear flows

Stability of pulsatile quasi-two-dimensional duct flows under a transverse magnetic field

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