arXiv subjects

Bernard Knaepen

Publications and source records attributed to Bernard Knaepen.

12 recordsLinked to original sources

arXiv2024

Optimal transient growth and transition to turbulence in the MHD pipe flow subject to a transverse magnetic field

We consider the influence of a transverse magnetic field on the transient growth of perturbations in a liquid-metal circular pipe flow with an electrically insulating or conducting wall. In this configuration, the mean flow profile and the amplification of perturbations are strongly affected by the applied magnetic field, leading to a rich dynamical landscape depending on its intensity. The analysis is performed for Reynolds numbers 5000 and 10 000, close to the transitional regime for moderate values of the Hartmann number, a non-dimensional parameter proportional to the applied magnetic field's intensity. Aside from a slight modification of hydrodynamic optimal perturbations at very small Hartmann numbers, we observe three other characteristic topologies of optimal perturbations depending on the intensity of the magnetic field. Their growth mechanisms differ, with the lift-up effect dominating at low Hartmann numbers and the Orr-mechanism becoming increasingly important as the magnetic field intensity is increased. In particular, we show in the intermediate regime of Hartmann numbers how transient growth occurs in two stages, with initial growth through the lift-up effect followed by a further increase of energy through the Orr-mechanism. We also conduct three-dimensional nonlinear simulations to track the time evolution of optimal perturbations, illustrating their nonlinear growth and eventual breakdown to a sustained turbulent state or the return of the system to a laminar state.

physics.flu-dyn↗

arXiv2023

On the instability of the magnetohydrodynamic pipe flow subject to a transverse magnetic field

The linear stability of a fully-developed liquid-metal MHD pipe flow subject to a transverse magnetic field is studied numerically. Because of the lack of axial symmetry in the mean velocity profile, we need to perform a BiGlobal stability analysis. For that purpose, we develop a two-dimensional complex eigenvalue solver relying on a Chebyshev-Fourier collocation method in physical space. By performing an extensive parametric study, we show that in contrast to Hagen-Poiseuille flow known to be linearly stable for all Reynolds numbers, the MHD pipe flow with transverse magnetic field is unstable to three-dimensional disturbances at sufficiently high values of the Hartmann number and wall conductance ratio. The instability observed in this regime is attributed to the presence of velocity overspeeds in the so-called Roberts layers and the corresponding inflection points in the mean velocity profile. The nature and characteristics of the most unstable modes are investigated, and we show that they vary significantly depending on the wall conductance ratio. A major result of this paper is that the global critical Reynolds number for the MHD pipe flow with transverse magnetic field is $Re=45230$, and it occurs for a perfectly conducting pipe wall and the Hartmann number $Ha=19.7$.

physics.flu-dyn↗

arXiv2005

The Effect of Coherent Structures on Stochastic Acceleration in MHD Turbulence

We investigate the influence of coherent structures on particle acceleration in the strongly turbulent solar corona. By randomizing the Fourier phases of a pseudo-spectral simulation of isotropic MHD turbulence (Re $\sim 300$), and tracing collisionless test protons in both the exact-MHD and phase-randomized fields, it is found that the phase correlations enhance the acceleration efficiency during the first adiabatic stage of the acceleration process. The underlying physical mechanism is identified as the dynamical MHD alignment of the magnetic field with the electric current, which favours parallel (resistive) electric fields responsible for initial injection. Conversely, the alignment of the magnetic field with the bulk velocity weakens the acceleration by convective electric fields $- \bfu \times \bfb$ at a non-adiabatic stage of the acceleration process. We point out that non-physical parallel electric fields in random-phase turbulence proxies lead to artificial acceleration, and that the dynamical MHD alignment can be taken into account on the level of the joint two-point function of the magnetic and electric fields, and is therefore amenable to Fokker-Planck descriptions of stochastic acceleration.

astro-ph↗

arXiv2005

Statistical Properties of Dissipative MHD Accelerators

We use exact orbit integration to investigate particle acceleration in a Gauss field proxy of magnetohydrodynamic (MHD) turbulence. Regions where the electric current exceeds a critical threshold are declared to be `dissipative' and endowed with super-Dreicer electric field ${\bf E}_Ω= η{\bf j}$. In this environment, test particles (electrons) are traced and their acceleration to relativistic energies is studied. As a main result we find that acceleration mostly takes place within the dissipation regions, and that the momentum increments have heavy (non-Gaussian) tails, while the waiting times between the dissipation regions are approximately exponentially distributed with intensity proportional to the particle velocity. No correlation between the momentum increment and the momentum itself is found. Our numerical results suggest an acceleration scenario with ballistic transport between independent `black box' accelerators.

astro-ph↗

arXiv2000

Couplings of gravity to antisymmetric gauge fields

We classify all the first-order vertices of gravity consistently coupled to a system of 2-form gauge fields by computing the local BRST cohomology H(s|d) in ghost number 0 and form degree n. The consistent deformations are at most linear in the undifferentiated two-form, confirming the previous results of [1] that geometrical theories constructed from a nonsymmetric gravity theory are physically inconsistent or trivial. No assumption is made here on the degree of homogeneity in the derivatives nor on the form of the gravity action.

hep-th↗

arXiv1999

Local BRST cohomology for p-form gauge theories

In this thesis, we compute within the field-antifield formalism the local BRST cohomology of various theories involving p-form gauge fields. A particular emphasis is put on the cohomology groups corresponding to the consistent local interactions, counterterms and candidate anomalies.

hep-th↗

arXiv1999

The Wess-Zumino Consistency Condition For p-Form Gauge Theories

The general solution of the antifield-independent Wess-Zumino consistency condition is worked out for models involving exterior form gauge fields of arbitrary degree. We consider both the free theory and theories with Chapline-Manton couplings. Our approach relies on solving the full set of descent equations by starting from the last element down ("bottom").

hep-th↗

arXiv1999

A Theorem on First-Order Interaction Vertices for Free p-Form Gauge Fields

The complete proof of a theorem announced in [1] on the consistent interactions for (non-chiral) exterior form gauge fields is given. The theorem can be easily generalized to the analysis of anomalies. Its proof amounts to computing the local BRST cohomology H^0(s|d) in the space of local n-forms depending on the fields, the ghosts, the antifields and their derivatives.

hep-th↗

arXiv1998

Couplings between generalized gauge fields

We analyze the BRST field-antifield construction for generalized gauge fields consisting of massless mixed representations of the Lorentz Group and we calculate all the strictly gauge invariant interactions between them. All these interactions are higher derivative terms constructed out from the derivatives of the curl of field strength.

hep-th↗

arXiv1998

All consistent interactions for exterior form gauge fields

We give the complete list of all first-order consistent interaction vertices for a set of exterior form gauge fields of form degree >1, described in the free limit by the standard Maxwell-like action. A special attention is paid to the interactions that deform the gauge transformations. These are shown to be necessarily of the Noether form "conserved antisymmetric tensor" times "p-form potential" and exist only in particular spacetime dimensions. Conditions for consistency to all orders in the coupling constant are given. For illustrative purposes, the analysis is carried out explicitly for a system of forms with two different degrees p and q (1<p<q<n).

hep-th↗

arXiv1997

BRST cohomology of the Chapline-Manton model

We completely compute the local BRST cohomology $H(s|d)$ of the combined Yang-Mills-2-form system coupled through the Yang-Mills Chern-Simons term ("Chapline-Manton model"). We consider the case of a simple gauge group and explicitely include in the analysis the sources for the BRST variations of the fields ("antifields"). We show that there is an antifield independent representative in each cohomological class of $H(s|d)$ at ghost number 0 or 1. Accordingly, any counterterm may be assumed to preserve the gauge symmetries. Similarly, there is no new candidate anomaly beside those already considered in the literature, even when one takes the antifields into account. We then characterize explicitly all the non-trivial solutions of the Wess-Zumino consistency conditions. In particular, we provide a cohomological interpretation of the Green-Schwarz anomaly cancellation mechanism.

hep-th↗

arXiv1996

Characteristic cohomology of $p$-form gauge theories

The characteristic cohomology $H^k_{char}(d)$ for an arbitrary set of free $p$-form gauge fields is explicitly worked out in all form degrees $k<n-1$, where $n$ is the spacetime dimension. It is shown that this cohomology is finite-dimensional and completely generated by the forms dual to the field strengths. The gauge invariant characteristic cohomology is also computed. The results are extended to interacting $p$-form gauge theories with gauge invariant interactions. Implications for the BRST cohomology are mentioned.

hep-th↗