Single Convection Cell Research Articles

An Intense, Quasi-Steady Thunderstorm over Mountainous Terrain. Part I: Evolution of the Storm-Initiating Mesoscale Circulation

The evolution of mesoscale systems that eventually lead to the formation of large quasi-steady storm systems is investigated. The morphological and turbulent structure of the quasi-steady storm is described. Data obtained during the South Park Area Cumulus Experiment from surface meteorological stations, rawinsondes and tethered balloons, conventional and Doppler radars, powered aircraft, and satellites, indicate that on July 19, 1977, a north-south oriented line of intense convective cells formed and remained within South Park. Elevated surface heating created a region of low-level convergence, importing Pacific moisture from west of the Rockies. The mesoscale thunderstorm line formed over this convergence zone, and a single large convective cell was observed to grow on the southern end of the mesoscale line, exhibiting supercell characteristics and substantial modifications of the environmental flow.

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.

The geoid and single-cell mantle convection

The geoid shows an antisymmetric departure from the spheroid of best fit. A single zero-elevation contour divides its surface into nearly equal strips in one of which the elevation is everywhere positive and in the other everywhere negative. These two areas are interleaved roughly like the strips covering a tennis ball. This pattern may indicate global single-cell convection in the mantle. It is argued that on this convection hypothesis, the upcurrents underlie the low-geoid strip, although the opposite view could be supported. No simple relation is to be expected between the proposed whole-mantle convection and plate motions, because other constraints act on plates and because the asthenosphere will partially decouple the whole-mantle motions from the lithosphere. However, the proposed whole-mantle convective system is consistent with rapid northwestward motion of the Pacific plate, with fast spreading of the East Pacific Rise and with slow spreading of the North Atlantic Ridge. Seismological velocity anomalies in the mantle, while highly relevant to whole-mantle convection, do not at present decide for or against the hypothesis here advanced.

A Numerical Model of Convection Driven by a Surface Stress and Non-Uniform Horizontal Heating

This paper examines the two-dimensional convective motion of a nonrotating incompressible Boussinesq fluid heated non-uniformly from below. The fluid container is rectangular; the side and top boundaries are insulating and rigid. A linear temperature field is maintained along the bottom boundary. Using the DuFort-Frankel scheme for diffusion and the Arakawa scheme for advection, the governing vorticity and temperature equations are integrated numerically for two cases, the first having a stress-free bottom boundary and the second having a constant stress along the bottom boundary. In the first case, a single convective cell develops; an intense buoyant jet of fluid rises from the warmer section of the bottom while there is a more uniform sinking motion over the cooler section of the bottom. The cell asymmetry, the circulation, and the convective heat transfer increase markedly with increasing Rayleigh number (based here on fluid properties, cell height, and the horizontal temperature difference along the bottom). The flow is insensitive to changes in the Prandtl number σ, provided σ>1. A review of previous literature on this convective problem is given. In the second case, a uniform stress is applied along the heated bottom in opposition to the thermal driving. The magnitude of the stress is varied while the horizontal Rayleigh and Prandtl numbers are held constant. For weak stresses, the flow is that of the first case. A two-cell circulation pattern containing both thermal and stress-driven sections emerges for a moderate stress, while for large stresses the predominantly thermally driven cell disappears.

Finite-Amplitude thermal convection within a self-gravitating fluid sphere

Finite-difference calculations have been carried out to determine the structure of finite-amplitude thermal convection within a self-gravitating fluid sphere with uniform heat release. For a fixed-surface boundary condition single-cell convection breaks up into double-cell convection at a Rayleigh number of 3 × 104, at a Rayleigh number of 5 × 105 four-cell convection is observed. With a free-surface boundary condition only single cell convection is obtained up to a Rayleigh number of 5 × 106.

Free Convection in a Rotating Medium

Numerical techniques have been used to study natural convection in a fluid subjected to axial rotation. Axisymmetrical flows were studied in two different geometries for a variety of rotational speeds. For case I (R1 = 1.0, R2 = 2.5, H = 3.0), the computed flow patterns were qualitatively compared with those which would be expected from the basic rules of physics, and good agreement was obtained. Rotational speeds between Ω = 0, and Ω = 20 were studied for a Grashoff number of 3000. Increased rotational speed was found to decrease the over-all heat transfer rate. For case II (R1 = 1.0, R2 = 4.0, H = 1.0), rotational speeds of Ω = 0.0 to Ω = 40.0 were studied at a Grashoff number of 400. At low rotational speeds, a single convection cell was found, however, at higher rotational speeds, the single cell became unstable, and changed to a two-celled pattern. This transition resulted in a slight increase in the over-all heat transfer rate.

A Nonlinear Spectral Model of Convection in a Fluid Unevenly Heated from Below

Abstract A two-dimensional form of the Boussinesq equations is integrated numerically for the case of a rectangular channel with a temperature gradient maintained along the bottom. The side walls are insulating, the top wall has a constant temperature, and the velocity obeys free boundary conditions on all four walls. The fields of stream function and temperature departure are represented by truncated double Fourier series, and integration of the initial-value problem for the spectral amplitudes results in steady states which agree qualitatively with those of previous experimental and theoretical investigations. Calculations are presented at two levels of truncation (wave numbers 2 and 3) for a wide range of Prandtl numbers and a moderate range of horizontal Rayleigh numbers and top temperatures. For sufficiently large gravitational stability, a single asymmetric convection cell develops. Its intensity and asymmetry increase markedly with increasing horizontal Rayleigh number, decrease with increasing top...

The thermohaline Rayleigh-Jeffreys problem

The onset of convection induced by thermal and solute concentration gradients, in a horizontal layer of a viscous fluid, is studied by means of linear stability analysis. A Fourier series method is used to obtain the eigenvalue equation, which involves a thermal Rayleigh numberRand an analogous solute Rayleigh numberS, for a general set of boundary conditions. Numerical solutions are obtained for selected cases. Both oscillatory and monotonic instability are considered, but only the latter is treated in detail. The former can occur when a strongly stabilizing solvent gradient is opposed by a destablizing thermal gradient. When the same boundary equations are required to be satisfied by the temperature and concentration perturbations, the monotonic stability boundary curve in the (R, S)-plane is a straight line. Otherwise this curve is concave towards the origin. For certain combinations of boundary conditions the critical value ofRdoes not depend onS(for some range ofS) or vice versa. This situation pertains when the critical horizontal wave-number is zero.A general discussion of the possibility and significance of convection at ‘zero’ wave-number (single convection cell) is presented in an appendix.

Natural convection in a horizontal circular cylinder

In this paper we examine the steady, two-dimensional convective motion which occurs in a horizontal circular cylinder whose wall is non-uniformly heated. One observes several qualitatively different physical phenomena depending on the wall temperature distribution and the value of the Rayleigh number. The low-Rayleigh-number behaviour for the single convective cell heated from below is related to the classical Rayleigh stability problem. The critical Rayleigh number for the single circular cell is approximately five times the value for Rayleigh's multi-celluar configuration. The flow which exhibits a nearly parabolic velocity profile near the critical Rayleigh number, gradually changes to a rigidly-rotating-core behaviour as the Rayleigh number increases. The speed of core rotation is a function of the Prandtl number, whereas the boundary-layer thickness is primarily a function of the Rayleigh number. When the heating is from side to side, the solution shows that as the Rayleigh number increases the core motion is progressively arrested leaving a narrow circulating band of fluid adjacent to the wall. An oblique heating produces a hybrid phenomenon, a low-Rayleigh-number behaviour which is characteristic of the sideways heating case and a high-Rayleigh-number interior motion characteristic of the bottom heating case. To determine the core motion in the high-Rayleigh-number limit, Batchelor's work concerning the uniqueness of incompressible, exactly steady, closed streamline flows with small viscosity is extended to include flows with small thermal conductivity.

Regenerative drift of a thunderstorm squall of the southwest monsoon season

A squall line of the southwest monsoon season has been analysed based on the radarscope observations and the prevalent synoptic situations, It was found to have a regenerative drift. It dissipated gradually after travelling some distance over land. The dimension of a single convective cloud cell inferred from a study of the associated changes in the meteorological elements observed at Dum Dum and Alipore appeared to be much in exceis of what has been found in the Thunderstorm Project.