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Hathaway, DH, Somerville RCJ.  1986.  Nonlinear Interactions between Convection, Rotation and Flows with Vertical Shear. Journal of Fluid Mechanics. 164:91-&.   10.1017/s0022112086002483   AbstractWebsite

A three-dimensional and time-dependent numerical model is used to study the nonlinear interactions between thermal convective motions, rotation, and imposed flows with vertical shear. All cases have Rayleigh numbers of 104 and Prandtl numbers of 1.0. Rotating cases have Taylor numbers of 104.For the non-rotating cases, the effects of the shear on the convection produce longitudinal rolls aligned with the shear flow and a downgradient flux of momentum. The interaction between the convection and the shear flow decreases the shear in the interior of the fluid layer while adding kinetic energy to the convective motions. For unit Prandtl number the dimensionless flux of momentum is equal to the dimensionless flux of heat.For rotating cases with vertical rotation vectors, the shear flow favours rolls aligned with the shear and produces a downgradient flux of momentum. However, the Coriolis force turns the flow induced by the convection to produce a more complicated shear that changes direction with height. As in the non-rotating cases, the convective motions become more energetic by extracting energy from the mean flow. For Richardson numbers larger than about − 1.0, the dominant source of eddy kinetic energy is the shear flow rather than buoyancy.For rotating cases with tilted rotation vectors the results depend upon the direction of the shear. For weak shear, convective rolls aligned with the rotation vector are favoured. When the shear flow is directed to the east along the top, the rolls become broader and the convection weaker. For large shear in this direction, the convective motions are quenched by the competition between the shear flow and the tilted rotation vector. When the shear flow is directed to the west along the top, strong shear produces rolls aligned with the shear. The heat and momentum fluxes become large and can exceed those found in the absence of a tilted rotation vector. Countergradient fluxes of momentum can also be produced.

Somerville, RCJ.  1967.  A Nonlinear Spectral Model of Convection in a Fluid Unevenly Heated from Below. Journal of the Atmospheric Sciences. 24:665-676.: American Meteorological Society   10.1175/1520-0469(1967)024<0665:ansmoc>2.0.co;2   AbstractWebsite

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 temperature, and respond very slightly to changes in Prandtl number. As the top temperature is decreased below the temperature of the warm side of the bottom, however, the possibility is indicated that the single cell may be modified by a Bénard-like multi-cellular structure.

Iacobellis, SF, Frouin R, Razafimpanilo H, Somerville RCJ, Piper SC.  1994.  North African savanna fires and atmospheric carbon dioxide. Journal of Geophysical Research-Atmospheres. 99:8321-8334.   10.1029/93jd03339   AbstractWebsite

The effect of north African savanna fires on atmospheric CO2 is investigated using a tracer transport model. The model uses winds from operational numerical weather prediction analyses and provides CO2 Concentrations as a function of space and time. After a spin-up period of several years, biomass-burning sources are added, and model experiments are run for an additional year, utilizing various estimates of CO2 sources. The various model experiments show that biomass burning in the north African savannas significantly affects CO2 concentrations in South America. The effect is more pronounced during the period from January through March, when biomass burning in South America is almost nonexistent. During this period, atmospheric CO2 concentrations in parts of South America typically may increase by 0.5 to 0.75 ppm at 970 mbar, the average pressure of the lowest model layer. These figures are above the probable uncertainty level, as model runs with biomass-burning sources estimated from independent studies using distinct data sets and techniques indicate. From May through September, when severe biomass burning occurs in South America, the effect of north African savanna fires over South America has become generally small at 970 mbar, but north of the equator it may be of the same magnitude or larger than the effect of South American fires. The CO2 concentration increase in the extreme northern and southern portions of South America, however, is mostly due to southern African fires, whose effect may be 2-3 times larger than the effect of South American fires at 970 mbar. Even in the central part of the continent, where local biomass-burning emissions are maximum, southern African fires contribute to at least 15% of the CO2 concentration increase at 970 mbar. At higher levels in the atmosphere, less CO2 emitted by north African savanna fires reaches South America, and at 100 mbar no significant amount of CO2 is transported across the Atlantic Ocean. The vertical structure of the CO2 concentration increase due to biomass burning differs substantially, depending on whether sources are local or remote. A prominent maximum Of CO2 concentration increase in the lower layers characterizes the effect of local sources, whereas a more homogenous profile of CO2 concentration increase characterizes the effect of remote sources. The results demonstrate the strong remote effects of African biomass burning which, owing to the general circulation of the atmosphere, are felt as far away as South America.

Hathaway, DH, Somerville RCJ.  1985.  Numerical simulation in three space dimensions of time-dependent thermal convection in a rotating fluid. Lectures in Applied Mathematics. 22:309-319. Abstract

Three-dimensional time-dependent convection in a plane layer of fluid, uniformly heated from below and subject to vertical shear and to rotation about an axis tilted from the vertical, was simulated by the numerical solution of the Boussinesq equations, including all Coriolis terms. Rotation about a vertical axis produces smaller convection cells with diminished heat fluxes and considerable vorticity. When the rotation axis is tilted from the vertical to represent tropical latitudes, the convection cells become elongated in a N-S direction. Imposed flows with constant vertical shear produce convective rolls aligned with the mean flow. When the rotation vector is tilted from the vertical, the competing effects due to rotation and shear can stabilize the convective motions.

Somerville, RCJ, Galchen T.  1979.  A Numerical Simulation of Convection with Mean Vertical Motion. Journal of the Atmospheric Sciences. 36:805-815.   10.1175/1520-0469(1979)036<0805:nsocwm>2.0.co;2   AbstractWebsite

The flow in a convectively unstable layer of fluid may be strongly influenced by large-scale ascent or descent. We consider cellular convection between horizontal surfaces on which vertical velocity is maintained at a constant value. Using an efficient numerical model to simulate the evolution of the convection in three space dimensions and time, we investigate the effect of the imposed vertical velocity on the flow.For moderately supercritical values of the Rayleigh number and for Prandtl numbers near unity, convection is known to occur in the form of steady rolls if the specified mean vertical motion is zero, i.e., in the case of the conventional Bénard problem for a Boussinesq fluid. Our model also produces rolls under these circumstances. For sufficiently large values of the imposed vertical velocity, however, the numerically simulated rolls are replaced by polygonal cells in which the direction of flow depends on whether ascent or descent is prescribed at the boundaries, in accordance with recent theoretical and laboratory results of R. Krishnamurti. We have also investigated the dependence of the convection on the Rayleigh and Prandtl numbers within limited ranges of these parameters, and we discuss several aspects of agreement and disagreement among analytical theory, laboratory experiment and numerical simulation.

Somerville, RCJ, Lipps FB.  1973.  A Numerical Study in Three Space Dimensions of Bénard Convection in a Rotating Fluid. Journal of the Atmospheric Sciences. 30:590-596.: American Meteorological Society   10.1175/1520-0469(1973)030<0590:ansits>2.0.co;2   AbstractWebsite

The primitive, nonlinear, Boussinesq equations of motion, continuity and thermodynamic energy are integrated numerically in three space dimensions and time to study convection driven by unstable vertical density gradients and subject to Coriolis forces. Parameter values are chosen to permit quantitative comparison with data from laboratory experiments for rotating Bénard convection in water. The model realistically simulates the structure of the convection cells, their horizontal scale, and the mean vertical heat transport. The experimentally observed phenomenon of a non-monotone dependence of heat transport on rotation rate is reproduced and shown to be a consequence of the rotational constraint on the wavelength of the cells.

Galchen, T, Somerville RCJ.  1975.  Numerical-Solution of Navier-Stokes Equations with Topography. Journal of Computational Physics. 17:276-310.   10.1016/0021-9991(75)90054-6   AbstractWebsite

A finite difference scheme for solving the equations of fluid motion in a generalized coordinate system has been constructed. The scheme conserves mass and all the first integral moments of the motion. The scheme also advectively “almost conserves” second moments, in that the magnitude of implicit numerical smoothing is typically about an order smaller than explicit viscosity and diffusion. Calculations with the model support the theoretical conjecture that the difference scheme is stable whenever the analogous Cartesian scheme is stable. The scheme has been used to calculate dry atmospheric convection due to differential heating between top and bottom of mountainous terrain. The general small-scale characteristics of mountain up-slope winds have been simulated. In addition, the results have demonstrated the crucial role played by the eddy diffusivities and the environmental stability, in determining both the quantitative and the qualitative features of the circulation.