Flow Structure Transition Research Articles

Transition and multiplicity of flows in natural convection in a narrow horizontal cylindrical annulus: Pr = 0.4

Natural convection in a narrow horizontal concentric annulus is numerically investigated for a fluid of Pr = 0.4. The combined effect of thermal and hydrodynamic instability at Pr = 0.4 yields complex multicellular flow patterns and interesting transition phenomena. After the onset of instability of the conduction regime, four branches of solutions and five kinds of multiple solutions characterized by the temporal behaviour and spatial structure of flows are found. As Gr increases, the transition of flow structure shows a gradual increase in the number of cells. When Gr is further increased, the flow in the vertical section of the annulus reverts to a nearly monocellular structure. A transition phenomenon from oscillatory to steady flow is found with an increase in Gr.

Competition of Coriolis instability with centrifugal instability and its effects on heat transfer in a rotating curved heated channel

The competition of the Coriolis instability with the centrifugal instability is examined numerically in terms of flow structure transitions by a finite volume method. The specific problem considered is a steady, hydrodynamically and thermally fully developed flow in a square channel with streamwise curvature, spanwise rotation and wall heating. The competition is found to be of considerable effects on flow structures and heat transfer. Several hitherto unknown flow structures are revealed. The results cover both transitions in flow structures and effects of the flow transitions on flow resistance and heat transfer.

Effect of spanwise rotation on centrifugal instability in rotating curved non-isothermal flows

The effect of spanwise rotation on the centrifugal instability is examined numerically in terms of flow structure transitions by a finite volume method. The specific problem considered is a steady, hydrodynamically and thermally fully developed flow in a square duct with a strong streamwise curvature, a spanwise rotation in both positive and negative directions and wall cooling. The rotation is found to be of considerable effect on flow structures. As well the effect is more complex for non-isothermal flows due to a buoyancy force which increases with the square of the rotation speed. Several hitherto unknown flow structures are revealed. The results cover both transitions in flow structures and effects of the flow transitions on temperature distributions.

Crenulated seafloor: Evidence for spreading-rate dependent structure of mantle upwelling and melting beneath a mid-oceanic spreading center

The availability of dense GEOSAT-GM satellite altimetry data south of 30°S [1] provides the first opportunity to compare at ∼ 25 km resolution seafloor generated at ridges spreading with a wide range of spreading rates. The axis of the slow-spreading Southwest Indian Ridge as well as the seafloor that it has generated has a distinctly crenulated appearance. This crenulated seafloor shows regularly spaced gravity lineations in the spreading direction, crenulations that record stationary centers of mantle upwelling over the life of the Southwest Indian Ridge. A similar pattern of crenulation is seen along sections of the slow-spreading northern Mid-Atlantic Ridge, but along the faster (intermediate) spreading southern Mid-Atlantic Ridge, while regularly spaced highs are apparent along sections of the spreading axis, stationary crenulation does not persist off the axis. This pattern implies that the faster spreading southern Mid-Atlantic Ridge has variable centers of time-dependent upwelling that migrate along the ridge. Crenulations are not visible near the axis of the fast-spreading Pacific-Antarctic Ridge. Crenulation amplitudes decrease strongly with increasing spreading rate. The absence of crenulation at high spreading rate could be due to a 3D/2D transition in flow structure or the effect of mechanisms to redistribute crust along axis. While crenulations are not ubiquitous, even at slowly spreading ridges, where they exist they provide a time record to observe the characteristics of mid-ocean ridge upwelling, melting and melt migration not only beneath active spreading centers but through a much longer spreading history.

Convection with internal heat sources and thermal turbulence in the Earth's mantle

SUMMARY The influence of internal heat sources on mantle convection is investigated using numerical calculations of 2-D thermal convection in an infinite Prandtl number, incompressible fluid. The geometry is a cylindrical annulus with inner and outer radii in proportion to the whole mantle. Time-dependent calculations are made starting from random initial conditions, with Rayleigh numbers RaT (based on boundary-temperature difference) and Ra, (based on internal-heat production) in the range 1dsRaTs lo7 and OsRa,524RaT. At fixed RaT, increasing Ra, results in transitions in flow structure from steady cells, to a pattern of stationary cells with time-variable amplitude, and finally to thermally turbulent convection with a non-stationary cell count. For RaT 10' and Ra, >RaT approximately, the travelling plumes disrupt the large-scale circulation, producing turbulent convection. At Ra, = lo7 the flow is fully developed thermal turbulence, and for Ra, > 0, consists of a rapidly fluctuating, irregular flow driven by transient rising and sinking sheets of buoyant fluid. Large fluctuations in total kinetic energy occur in this regime, with periodicities ranging from 40 to 1400Myr. The transition to thermal turbulence occurs in these calculations at Rayleigh numbers well below the value estimated for subsolidus convection in the mantle, suggesting thermally turbulent convection may occur in the mantle, a consequence of internal heat sources. Thermal turbulence offers an explanation for long-term fluctuations in the rate of subduction, sea-floor spreading and global volcanic activity.

Flow structure transition mechanisms in thermal convection of air in rectangular containers

Transition of convection roll patterns is evaluated empirically for horizontal moderate size containers of air heated below and cooled above. Characteristics of the transitions are of interest in the study of nonlinear dynamical systems, since the regime of convection roll flow structures precedes the appearance of turbulent convection in experiments with increasing buoyancy.

Multiple buoyancy-driven flows in a vertical cylinder heated from below

The structure of axisymmetric buoyancy-driven convection in a vertical cylinder heated from below is probed by finite-element solution of the Boussinesq equations coupled with computer-implemented perturbation techniques for detecting and tracking multiple flows and for determining flow stability. Results are reported for fluids with a Prandtl number of one and for cylinders with aspect ratio Λ (defined as the ratio of height to radius of the cylinder) between 0.5 and 2.25. Extensive calculations of the neutral stability curves for the static solution and of the nonlinear motions along the bifurcating flow families show a continuous change of the primary cellular motion from a single toroidal cell to two and three cells nested radially in the cylinder, instead of the sharp transitions found for a cylinder with shear-free sidewalls. The smooth transitions in flow structure with Rayleigh number and Λ are explained by nonlinear connectivity between the first two bifurcating flow families formed either by a secondary bifurcation point for Λ ⩽ Λ * ≃ 0.80 or by a limit point for Λ ⩽ Λ *. The transition between the two modes may be described by the theory of multiple limit point bifurcation.

Moving lithospheric plates and mantle convection

The coupling between a rigidly moving lithospheric plate and a convecting mantle is investigated using a simple two-dimensional numerical model that incorporates a horizontally moving upper boundary, simulating the effect of a moving plate, over a fluid layer heated from below. The moving boundary strongly controls the horizontal length scale of convection cells when its velocity is greater than the free convective velocity (i.e. the velocity with which the fluid would convect under a stationary boundary). In a box of aspect ratio 4 (width/depth), a transition in flow structure occurs from several equidimensional convection cells under a slowly moving boundary to a single long convection cell under a rapidly moving boundary. The flow structure transition occurs approximately when Pe/Ra2/3= 0.04, where the Peclet number, Pe, measures the (prescribed) velocity of the upper boundary, and the Rayleigh number, Ra, measures the heating of the fluid layer. Near the transition, the flow tends to be unsteady; this behaviour can be well understood in terms of the instability of the thermal boundary layers, which can be characterized by a local Rayleigh number. Using conventional estimates of mantle parameters, the mantle is either near or above the transition to single-cell convection, whether upper-mantle or whole-mantle convection is assumed. The net tangential force exerted by the fluid on the upper boundary varies approximately linearly with the boundary velocity above the transition, and it is positive (driving) for boundary velocities ranging from the value at the transition to about three times the transition value. Boundary velocities corresponding to zero net force are close to those expected for convection under a free-slip boundary. When scaled to whole-mantle convection, the shear stress on the upper boundary is of the order of 10 bar, and above the transition to a single cell the net force on a large plate is sufficient to overcome even kilobars of frictional resistance at plate boundaries. These results indicate that mantle convection and lithospheric plate motions are likely to be strongly coupled, with the rigid moving plates strongly controlling the mantle flow structure, with single cells under the faster plates, but with the mantle convection cells possibly exerting large driving forces on the plates.

Free-Convective Heat Transfer to a Supercritical Fluid

The influence of heater material on free-convective heat transfer from wires to carbon dioxide in the supercritical region was investigated. Three types of flow configuration were observed for nichrome and alumel wires: (a) conventional laminar-flow free convection, (b) an oscillating flow in which (a) and a bubble-like flow alternated, (c) a bubble-like flow in which masses of fluid similar to bubbles appeared successively near the heating surface. Neither (b) nor (c) was observed with a platinum wire. The heat-transfer rate increased suddenly when the flow configuration changed from (a) to (b). The transition in flow structure occurred when the temperature difference between the heater and fluid exceeded about 200 deg C.