Nonlinear dynamics of forced baroclinic critical layers II

Wang, Chen; Balmforth, N. J.

doi:10.1017/jfm.2021.297

Cited by 3 publications

(11 citation statements)

References 35 publications

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“…In addition, we will show that the critical layer evolution contains two different regimes: first, an unsteady inviscid phase followed by a second viscous phase that can be steady or can evolve nonlinearly depending on the parameters. Such evolution is similar to that evidenced by Wang & Balmforth (2020, 2021) in their studies of forced baroclinic critical layers. They have also reported the subsequent development of a two-dimensional shear instability and studied its nonlinear evolution by means of a reduced model.…”

Section: Introductionsupporting

confidence: 87%

“…As shown by Wang & Balmforth (2021), the exact solution of (4.34) can be found by means of a Fourier transform in using (4.21). This gives In the appendix an approximation of (4.35) valid for large time is found in the form where This approximation shows that saturates and tends towards (4.37 a ) for for .…”

Section: Asymptotic Analysesmentioning

confidence: 99%

“…Following Boulanger et al. (2007) and Wang & Balmforth (2020, 2021), we assume that the Reynolds number is large and consider only the vicinity of the critical radius by introducing a rescaled radius such that . We also assume that the evolution occurs over the slow time .…”

Section: Asymptotic Analysesmentioning

confidence: 99%

“…As shown by Wang & Balmforth (2020, 2021), the solution is where When , the upper bound in the integral can be replaced by infinity so that (4.21) recovers the steady solution (Boulanger et al. 2007) where is the Scorer's function (Abramowitz & Stegun 1972).…”

Section: Asymptotic Analysesmentioning

confidence: 99%

“…Our investigations are based on direct numerical simulations (DNS) coupled to asymptotic analyses of the critical layer in the limit of a small non-traditional Coriolis parameter following the lines of Boulanger et al. (2007, 2008), Wang & Balmforth (2020, 2021).…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of a stratified vortex under the complete Coriolis force: two-dimensional three-components evolution

Toghraei

Billant

2022

J. Fluid Mech.

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We study the dynamics of an initially axisymmetric and vertical Lamb–Oseen vortex in a stratified-rotating fluid under the complete Coriolis force on the $f$ plane, i.e. in the presence of a background rotation both along the vertical and horizontal directions. By a combination of direct numerical simulations and asymptotic analyses for small horizontal background rotation, we show that a critical layer appears at the radius where the angular velocity of the vortex is equal to the buoyancy frequency when the Froude number is larger than unity. This critical layer generates a vertical velocity that is invariant along the vertical and which first increases linearly with time and then saturates at an amplitude scaling like $Re^{1/3}/\widetilde{Ro}$ , where $Re$ is the Reynolds number and $\widetilde {Ro}$ the non-traditional Rossby number based on the horizontal component of the background rotation. In turn, a quasi-axisymmetric anomaly of vertical vorticity is produced at the critical radius through the non-traditional Coriolis force. Below a critical $\widetilde {Ro}$ depending on $Re$ , the Rayleigh's inflectional criterion is satisfied and a shear instability is subsequently triggered rendering the vertical vorticity fully non-axisymmetric. The decay of the angular velocity is then enhanced until it is everywhere lower than the buoyancy frequency. A theoretical criterion derived from the Rayleigh condition predicts well the instability. It shows that this phenomenon can occur even for a large non-traditional Rossby number $\widetilde {Ro}$ for large $Re$ . Hence, the non-traditional Coriolis force might have much more impact on geophysical vortices than anticipated by considering the order of magnitude of $\widetilde {Ro}$ .

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Section: Introductionsupporting

confidence: 87%

Section: Asymptotic Analysesmentioning

confidence: 99%

Section: Asymptotic Analysesmentioning

confidence: 99%

Section: Asymptotic Analysesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Dynamics of a stratified vortex under the complete Coriolis force: two-dimensional three-components evolution

Toghraei

Billant

2022

J. Fluid Mech.

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Baroclinic critical layer in a viscous stratified boundary layer flow on an undulated tilted surface

2023

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The present paper investigates theoretically and experimentally the boundary layer generated by a stably stratified fluid flowing horizontally along a surface tilted in the transverse direction and deformed by sinusoidal undulations with crests perpendicular to the flow direction. In the absence of undulations, a weak transverse velocity proportional to the normal velocity is created such that the flow remains purely horizontal. In the presence of undulations of amplitude $h$ , a stronger transverse flow is generated that exhibits a singular behaviour at the critical altitude where the frequency of the perturbation matches the buoyancy frequency of the fluid. This baroclinic critical layer was previously analysed by Passaggia et al. (J. Fluid Mech., vol. 751, 2014, pp. 663–684) for a boundary layer flow with a small sliding velocity on the surface. Here, the no-slip boundary condition of the experimental flow is applied. For this purpose, we solve the viscous sub-layer to obtain a complete theoretical model for the solution in the critical layer without any adjusting parameter. The theoretical predictions for the transverse velocity are compared with experimental measurements, and a good quantitative agreement is demonstrated. Compared with the sliding case, the no-slip boundary condition on the surface reduces the amplitude of the critical layer solution by a factor $Re^{-1/3}$ , where the Reynolds number Re is defined using the velocity at infinity and the thickness of the boundary layer. As a consequence, the transverse velocity has a maximum in the critical layer of order $h$ , but it still induces a shear rate of order $h\,Re^{1/3}$ .

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Concurrence of a Kelvin-Helmholtz instability and Kármán vortex street in the Sun’s corona

Wei,

Huang,

Long

et al. 2023

A&A

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Context. Instabilities are crucial to understanding the mass transportation and energy transformation in the solar atmosphere. Observations of the concurrence among the Kelvin-Helmholtz instability (KHI) and Kármán vortex street (KVS) in conditions as extreme as the Sun’s corona have yet to be reported. Aims. We aim to find evidence of a concurrence between the KHI and KVS in the Sun’s corona. Methods. We analyzed high-resolution data from Extreme Ultraviolet Imager aboard Solar Orbiter and the Atmospheric Imaging Assembly aboard Solar Dynamics Observatory. Results. Thanks to the high temporal resolution of EUI data, in an interacting region between a jet and coronal plumes, we observed the development of ruffles and breakdown of blobs. The intrinsic parameters of this dynamic system suggest the possibility of both the KHI and KVS occurring in the corona. The observations also show that the coupling of the two instabilities has facilitated the formation of vortices, which may therefore have enhanced the transformation from kinetic energy to thermal energy, as well as mass mixing among systems across magnetic field lines in the Sun’s corona. Conclusions. The present study reports the very first EUI observations of a concurrence of the KHI and KVS and their coupling in the coronal conditions.

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Nonlinear dynamics of forced baroclinic critical layers II

Abstract: Abstract

Cited by 3 publications

References 35 publications

Dynamics of a stratified vortex under the complete Coriolis force: two-dimensional three-components evolution

Dynamics of a stratified vortex under the complete Coriolis force: two-dimensional three-components evolution

Baroclinic critical layer in a viscous stratified boundary layer flow on an undulated tilted surface

Concurrence of a Kelvin-Helmholtz instability and Kármán vortex street in the Sun’s corona

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