The effect of curvature and torsion on the flow in a helical pipe of circular cross-section is studied numerically by the spectral method. The calculations are carried out for 0 < s <0.6, 0 < f30 < 1.4 and 500 < o; <2000, where {) is the non-dimensional curvature, f30 the ratio of torsion to square root of curvature, and D n the Dean number. The results obtained indicate large effects of torsion on the flow: The conventional two-vortex secondary flow is distorted to become almost one single recirculating cell when f30 ;::: 0.8. The flux through the pipe at the given Dean number and curvature first decreases from that of the toroidally curved pipe as f30 increases from zero, reaches a minimum at f30 ~0.8, and then increases to values larger than that of the toroidally curved pipe. The minimum value decreases as {) increases.

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.

Dual solutions, i.e. two-vortex and four-vortex solutions, and their stability of flow through a slightly curved circular tube are numerically investigated by the spectral method in the range 96 '" Is.;«;10000. where D" is the Dean number. It is found that the two-vortex solution is stable in response to any small disturbances, while the four-vortex solution is unstable to asymmetric disturbances. Time evolution of the unsteady four-vortex flow is also studied by a numerical simulation of the Navier-Stokes equation when D" = 1000. The four-vortex flow eventually turns into a two-vortex flow.

Using linear stability analysis, the instability characteristics are examined of both planar wakes and mixing layers subjected to rigid-body rotation with axis of rotation perpendicular to the plane of the ambient flow. In particular, the tendency of rotation to stabilize or destabilize three-dimensional motions is addressed. In the inviscid limit the results are consistent with the criterion established by Pedley [J. Fluid Mech. 35, 97 (1969)] and Bradshaw [J. Fluid Mech. 36, 177 (1969)]. Cyclonic rotation and strong anticyclonic rotation tend to stabilize three-dimensional motions, whereas weaker anticyclonic rotation (Ro≳1) acts to destabilize these motions. This latter instability is in the form of streamwise rolls, similar to previous results obtained for boundary layer and channel flows. It is found that this instability is stronger than the coexisting Kelvin–Helmholtz instability for roughly the range 1.5&lt;Ro&lt;8, and its effect is maximum for Ro≂2. For the case of constant ambient shear, exact solutions are obtained which give further insight into the nature of the instability.

Flows through a curved duct of square cross-section are numerically studied by using the spectral method, and covering a wide range of curvature of the duct (0 < 0.5) and the Dean number Dn (0 < Dn 8000), where is non-dimensionalized by the half width of the square cross-section. The main concern is the relationship between the unsteady solutions, such as periodic, multi-periodic and chaotic solutions, and the bifurcation diagram of the steady solutions. It is found that the bifurcation diagram topologically changes if the curvature is increased and exceeds the critical value c ≈ 0.279645, while it remains almost unchanged for < c or > c . A periodic solution is found to appear if the Dean number exceeds the bifurcation point, whether it is pitchfork or Hopf bifurcation, where no steady solution is stable. It is found that the bifurcation diagram and its topological change crucially affect the realizability of the steady and periodic solutions. Time evolution calculations as well as their spectral analysis show that the periodic solution turns to a chaotic solution if the Dn is further increased no matter what the curvature is. It is interesting that the chaotic solution is weak for smaller Dn, where the solution drifts among the steady solution branches, for larger Dn, on the other hand, the chaotic solution becomes strong, where the solution tends to get away from the steady solution branches.