ترغب بنشر مسار تعليمي؟ اضغط هنا

Hyperchaotic Intermittent Convection in a Magnetized Viscous Fluid

179   0   0.0 ( 0 )
 نشر من قبل Marek Strumik
 تاريخ النشر 2014
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We consider a low-dimensional model of convection in a horizontally magnetized layer of a viscous fluid heated from below. We analyze in detail the stability of hydromagnetic convection for a wide range of two control parameters. Namely, when changing the initially applied temperature difference or magnetic field strength, one can see transitions from regular to irregular long-term behavior of the system, switching between chaotic, periodic, and equilibrium asymptotic solutions. It is worth noting that owing to the induced magnetic field a transition to hyperchaotic dynamics is possible for some parameters of the model. We also reveal new features of the generalized Lorenz model, including both type I and III intermittency.


قيم البحث

اقرأ أيضاً

Tidal dissipation in planets and stars is one of the key physical mechanisms driving the evolution of star-planet and planet-moon systems. Several signatures of its action are observed in planetary systems thanks to their orbital architecture and the rotational state of their components. Tidal dissipation inside the fluid layers of celestial bodies are intrinsically linked to the dynamics and the physical properties of the latter. This complex dependence must be characterized. We compute the tidal kinetic energy dissipated by viscous friction and thermal diffusion in a rotating local fluid Cartesian section of a star/planet/moon submitted to a periodic tidal forcing. The properties of tidal gravito-inertial waves excited by the perturbation are derived analytically as explicit functions of the tidal frequency and local fluid parameters (i.e. the rotation, the buoyancy frequency characterizing the entropy stratification, viscous and thermal diffusivities) for periodic normal modes. The sensitivity of the resulting possibly highly resonant dissipation frequency-spectra to a control parameter of the system is either important or negligible depending on the position in the regime diagram relevant for planetary and stellar interiors. For corresponding asymptotic behaviors of tidal gravito-inertial waves dissipated by viscous friction and thermal diffusion, scaling laws for the frequencies, number, width, height and contrast with the non-resonant background of resonances are derived to quantify these variations. We characterize the strong impact of the internal physics and dynamics of fluid planetary layers and stars on the dissipation of tidal kinetic energy in their bulk. We point out the key control parameters that really play a role and demonstrate how it is now necessary to develop ab-initio modeling for tidal dissipation in celestial bodies.
116 - S.A. Berman , K.A. Mitchell 2020
We examine the motion of rigid, ellipsoidal swimmers subjected to a steady vortex flow in two dimensions. Numerical simulations of swimmers in a spatially periodic array of vortices reveal a range of possible behaviors, including trapping inside a si ngle vortex and motility-induced diffusion across many vortices. While the trapping probability vanishes at a sufficiently high swimming speed, we find that it exhibits surprisingly large oscillations as this critical swimming speed is approached. Strikingly, at even higher swimming speeds, we find swimmers that swim perpendicular to their elongation direction can again become trapped. To explain this complex behavior, we investigate the underlying swimmer phase-space geometry. We identify the fixed points and periodic orbits of the swimmer equations of motion that regulate swimmer trapping inside a single vortex cell. For low to intermediate swimming speeds, we find that a stable periodic orbit surrounded by invariant tori forms a transport barrier to swimmers and can trap them inside individual vortices. For swimming speeds approaching the maximum fluid speed, we find instead that perpendicular swimmers can be trapped by asymptotically stable fixed points. A bifurcation analysis of the stable periodic orbit and the fixed points explains the complex and non-monotonic breakdown and reemergence of swimmer trapping as the swimmer speed and shape are varied.
361 - J.D. Carter , A. Govan 2015
In this paper, we derive a viscous generalization of the Dysthe (1979) system from the weakly viscous generalization of the Euler equations introduced by Dias, Dyachenko, and Zakharov (2008). This viscous Dysthe system models the evolution of a weakl y viscous, nearly monochromatic wave train on deep water. It contains a term which provides a mechanism for frequency downshifting in the absence of wind and wave breaking. The equation does not preserve the spectral mean. Numerical simulations demonstrate that the spectral mean typically decreases and that the spectral peak decreases for certain initial conditions. The linear stability analysis of the plane-wave solutions of the viscous Dysthe system demonstrates that waves with wave numbers closer to zero decay more slowly than waves with wave numbers further from zero. Comparisons between experimental data and numerical simulations of the NLS, dissipative NLS, Dysthe, and viscous Dysthe systems establish that the viscous Dysthe system accurately models data from experiments in which frequency downshifting was observed and experiments in which frequency downshift was not observed.
How fast must an oriented collection of extensile swimmers swim to escape the instability of viscous active suspensions? We show that the answer lies in the dimensionless combination $R=rho v_0^2/2sigma_a$, where $rho$ is the suspension mass density, $v_0$ the swim speed and $sigma_a$ the active stress. Linear stability analysis shows that for small $R$ disturbances grow at a rate linear in their wavenumber $q$, and that the dominant instability mode involves twist. The resulting steady state in our numerical studies is isotropic hedgehog-defect turbulence. Past a first threshold $R$ of order unity we find a slower growth rate, of $O(q^2)$; the numerically observed steady state is {it phase-turbulent}: noisy but {it aligned} on average. We present numerical evidence in three and two dimensions that this inertia driven flocking transition is continuous, with a correlation length that grows on approaching the transition. For much larger $R$ we find an aligned state linearly stable to perturbations at all $q$. Our predictions should be testable in suspensions of mesoscale swimmers [D Klotsa, Soft Matter textbf{15}, 8946 (2019)].
A detailed comparison between data from experimental measurements and numerical simulations of Lagrangian velocity structure functions in turbulence is presented. By integrating information from experiments and numerics, a quantitative understanding of the velocity scaling properties over a wide range of time scales and Reynolds numbers is achieved. The local scaling properties of the Lagrangian velocity increments for the experimental and numerical data are in good quantitative agreement for all time lags. The degree of intermittency changes when measured close to the Kolmogorov time scales or at larger time lags. This study resolves apparent disagreements between experiment and numerics.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا