Statistical properties of MHD turbulence and the mechanism of turbulent dynamo are investigated by direct numerical simulations of three-dimensional MHD equations. It is assumed that the turbulent field has a high symmetry and that the fluid has hyperviscosity and hypermagnetic diffusivity. An external force is exerted on the fluid as kinetic energy and helicity sources. The main concern of the present study is whether magnetic fields of scales comparable to the dominant fluid motions can be generated or not. It is shown that the turbulent dynamo is effective if hypermagnetic diffusivity is smaller than a critical value. The total energy spectrum is close to the k−5/3 power law in the inertial range. The energy transfer between kinetic and magnetic fields is discussed.
The instability and transition of flow past two circular cylinders arranged in tandem are investigated numerically. A steady symmetric flow is realized at small Reynolds numbers, but the flow becomes unstable above a critical Reynolds number and makes a transition to an oscillatory flow. We obtained the symmetric flow numerically and analyze its stability by applying linear stability theory. The nonlinear oscillatory flow arising from the instability is obtained not only by numerical simulation but also by direct numerical calculation of the equilibrium solution, and the bifurcation diagram for the nonlinear equilibrium solution is depicted. We focused our attention on the effect of the gap spacing between the two cylinders on the stability and transition of the flow. The transition of the flow from a steady state to an oscillatory state is clarified to occur due to a supercritical or subcritical Hopf bifurcation depending upon the gap spacing. We found that there is a certain range of the gap spacing where physical quantities such as the drag and lift coefficients and the Strouhal number show an abrupt change when the gap spacing is continuously changed. We identified the origin of the abrupt change as the existence of multiple stable solutions for the flow.
The stability of a two-dimensional flow in a symmetric channel with a suddenly expanded part is investigated numerically and analyzed by using the method of the nonlinear stability theory. From results of the numerical simulation, it is shown that the flow is steady, symmetric and unique at very low Reynolds numbers, while the symmetric flow loses its stability at a critical Reynolds number resulting in an appearance of asymmetric flow. The transition from the steady symmetric flow to the steady asymmetric one is found to occur due to the symmetry breaking pitchfork bifurcation when the aspect ratio, the ratio of the length of the expanded part to its width, is large. It is also found that the bifurcated flow becomes symmetric again when the Reynolds number is increased and the resultant symmetric flow loses its stability becoming periodic in time as the Reynolds number is further increased. On the other hand, when the aspect ratio is small there occurs no pitchfork bifurcation and the direct transition from the steady symmetric flow to a periodic flow occurs due to a Hopf bifurcation. The critical aspect ratio is found to be about 2.3. The critical Reynolds numbers for these bifurcations are evaluated.
The stability and transition of flow past a pair of circular cylinders in a side-by-side arrangement are investigated by numerical simulations and linear stability analyses. Various flow patterns around the cylinders have been reported to appear due to an instability of the steady symmetric flow that is realized at small Reynolds numbers, among which deflected oscillatory flow is particularly noticeable. The physical origin of the flow is explored by bifurcation analyses of the numerical data. We found that the deflected oscillatory flow arises from the steady symmetric flow through sequential instabilities due to stationary and oscillatory unstable modes. Steady asymmetric flow with respect to the streamwise centreline between the two cylinders was also found to be induced by the instability due to a stationary mode in a very narrow range of the gap width between the two cylinders. We classify the instability modes of the steady symmetric flow into four groups in the parameter space of the gap width, and evaluate the critical Reynolds number for each mode of instability.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.