Modulated rotating waves and triadic resonances in spherical fluid systems: The case of magnetized spherical Couette flow

Abstract

The existence of triadic resonances in the magnetized spherical Couette system (MSC) is related to the development of modulated rotating waves, which are quasiperiodic flows understood in terms of bifurcation theory in systems with symmetry. In contrast to previous studies in spherical geometry the resonant modes are not inertial waves but related with the radial jet instability which is strongly equatorially antisymmetric. We propose a general framework in which triadic resonances are generated through successive Hopf bifurcations from the base state. The study relies on an accurate frequency analysis of different modes of the flow, for solutions belonging to two different bifurcation scenarios. The azimuthal and latitudinal nonlinear coupling among the resonant modes is analysed and interpreted using spherical harmonics and the results are compared with previous studies in spherical geometry.

Noise induced effects in the axisymmetric spherical Couette flow

“…The origin of the flow instability in this case is the instability of the radial jet, directed along the equatorial plane toward the outer sphere [13]. More recently, it was shown that similar instabilities to those considered above were also observed in thin and wide layers when a magnetic field was applied to the spherical gap filled with an electrically conducting fluid [14–19]. In particular, it was revealed that centrifugally unstable SCF in a thin gap can amplify the magnetic field [17]; non-axisymmetric instability may be suppressed by the imposed magnetic field [16] and dynamo action was found to occur when the flow instability arises in a wide gap [15].…”

A hybrid GNA instability

“…This analysis could be appropriately extended to investigate the GNA instability, probing the interior crustal structure of neutron stars under the dynamic action of several realistic factors yet to be well considered. A number of such important active factors are the: (1) Electromagnetic forces and vortex interactions are to be properly included 8 , 11 ; (2) Effects of the Coriolis rotations ( rad s −1 ) need inclusion 11 , 53 , and strong magnetic spinning ( G) 11 , 53 ; (3) Analysis is carried out here only in the low-frequency regime, the higher-order modes being auto-ignored; thereby, paving the intriguing way for inclusive refinements in the futuristic studies; (4) Relativistic dynamical effects 54 are to be well considered; (5) Neutron superfluidic flow, both around and through the constitutive nuclei 10 , is yet to be well simulated; (6) Averaged (mean-fluidic) small-scale perturbation response characteristics are only revealed; thereby, opening an active chapter for a kinetic formalism 55 ; (7) Assumed spherically symmetric geometry (gravity dominant) needs to include both the polar and azimuthal counterparts through spherical harmonics 56 ; (8) Role of neutrino in the coupled modal stability is yet to be incorporated 57 ; (9) Entropy wave (second sound due to superfluidity) is to be regarded well 12 ; (10) Hard-core simulation platform to see the temporal evolution of the GNA instability is to be illustrated; (11) Vital possibility for a global (non-local) stability analysis with the diversified equilibrium inhomogeneities and gradient fields inclusively relevant for a fully integrated stability description is herewith opened, and so forth. At the last, we strongly believe that an appropriate comprehensive model refinement in the direction of the proposed investigation of neutron star crust characterization is needed.…”

“…43) excited in the inner crust region of neutron stars are basically dictated by the multiparametric dispersion windows featuring the interior of neutron stars (described judiciously by Eqs. [44][45][46][47][48][49][50][51][52][53][54][55][56]. ( 42)…”

“…The small-amplitude spherical normal mode analysis yields a linear dispersion relation (Eq. 43), modulated by an atypical set of coefficients (Eqs [44][45][46][47][48][49][50][51][52][53][54][55][56],. multiparametrically dependent on the diversified inner crust features.…”