The Skill of ECMWF Medium-Range Forecasts during the Year of Tropical Convection 2008

This study uses the European Centre for Medium-Range Weather Forecasts (ECMWF) model-generated high-resolution 10-day-long predictions for the Year of Tropical Convection (YOTC) 2008. Precipitation forecast skills of the model over the tropics are evaluated against the Tropical Rainfall Measuring Mission (TRMM) estimates. It has been shown that the model was able to capture the monthly to seasonal mean features of tropical convection reasonably. Northward propagation of convective bands over the Bay of Bengal was also forecasted realistically up to 5 days in advance, including the onset phase of the monsoon during the first half of June 2008. However, large errors exist in the daily datasets especially for longer lead times over smaller domains. For shorter lead times (less than 4-5 days), forecast errors are much smaller over the oceans than over land. Moreover, the rate of increase of errors with lead time is rapid over the oceans and is confined to the regions where observed precipitation shows large day-to-day variability. It has been shown that this rapid growth of errors over the oceans is related to the spatial pattern of near-surface air temperature. This is probably due to the one-way air-sea interaction in the atmosphere-only model used for forecasting. While the prescribed surface temperature over the oceans remain realistic at shorter lead times, the pattern and hence the gradient of the surface temperature is not altered with change in atmospheric parameters at longer lead times. It has also been shown that the ECMWF model had considerable difficulties in forecasting very low and very heavy intensity of precipitation over South Asia. The model has too few grids with ``zero'' precipitation and heavy (>40 mm day(-1)) precipitation. On the other hand, drizzle-like precipitation is too frequent in the model compared to that in the TRMM datasets. Further analysis shows that a major source of error in the ECMWF precipitation forecasts is the diurnal cycle over the South Asian monsoon region. The peak intensity of precipitation in the model forecasts over land (ocean) appear about 6 (9) h earlier than that in the observations. Moreover, the amplitude of the diurnal cycle is much higher in the model forecasts compared to that in the TRMM estimates. It has been seen that the phase error of the diurnal cycle increases with forecast lead time. The error in monthly mean 3-hourly precipitation forecasts is about 2-4 times of the error in the daily mean datasets. Thus, effort should be given to improve the phase and amplitude forecast of the diurnal cycle of precipitation from the model.

Mixed Convection Induced in a Gas Flowing Past a Hot Horizontal Flat Plate

A boundary layer analysis of mixed convective motion over a hot horizontal flat plate is performed under the conditions of steady flow and low speed. Use of the Howarth-Dorodnytsyn transformation makes it possible to dispense with the usual Boussinesq approximation, and variable gas properties are accounted for via the assumption that dynamic viscosity and thermal conductivity are proportional to the absolute temperature. The formulation presented enables the entire mixed convection regime to be described by a single set of equations. Finite difference solutions when the Prandtl number is 0.72 are obtained over the entire range of the mixed convection parameter ξ from 0 (free convection) to 1 (forced convection) and heating parameter ▵ values from 2 to 12. The effects of both ξ and ▵on the velocity profiles, the temperature profiles, and the variation of skin friction and heat transfer functions are clearly illustrated in tables and graphs.

Unsteady mixed convection flow in stagnation region adjacent to a vertical surface

The unsteady two-dimensional laminar mixed convection flow in the stagnation region of a vertical surface has been studied where the buoyancy forces are due to both the temperature and concentration gradients. The unsteadiness in the flow and temperature fields is caused by the time-dependent free stream velocity. Both arbitrary wall temperature and concentration, and arbitrary surface heat and mass flux variations have been considered. The Navier-Stokes equations, the energy equation and the concentration equation, which are coupled nonlinear partial differential equations with three independent variables, have been reduced to a set of nonlinear ordinary differential equations. The analysis has also been done using boundary layer approximations and the difference between the solutions has been discussed. The governing ordinary differential equations for buoyancy assisting and buoyancy opposing regions have been solved numerically using a shooting method. The skin friction, heat transfer and mass transfer coefficients increase with the buoyancy parameter. However, the skin friction coefficient increases with the parameter lambda, which represents the unsteadiness in the free stream velocity, but the heat and mass transfer coefficients decrease. In the case of buoyancy opposed flow, the solution does not exist beyond a certain critical value of the buoyancy parameter. Also, for a certain range of the buoyancy parameter dual solutions exist.

Non-Boussinesq conjugate natural convection in a vertical annulus

Non-Boussinesq conjugate natural convection in a vertical annulus with a centrally located vertical heat generating rod is studied numerically, taking into account variable transport properties. Results are presented for maximum solid temperatures, average Nusselt numbers and average pressure. In general, the Boussinesq model predicts higher temperatures in the solid and lower average Nusselt numbers on the inner and outer boundaries. (C) 2010 Elsevier Ltd. All rights reserved.

Analysis of conjugate laminar mixed convection cooling in a shrouded array of electronic components

The temperature variation in the insulation around an electronic component, mounted on a horizontal circuit board is studied numerically. The flow is assumed to be laminar and fully developed. The effect of mixed convection and two different types of insulation are considered. The mass, momentum and energy conservation equations in the fluid and conduction equation in the insulation are solved using the SIMPLER algorithm. Computations are carried out for liquid Freon and water, for different conductivity ratios, and different Rayleigh numbers. It is demonstrated that the temperature variation within the insulation becomes important when the thermal conductivity of the insulation is less than ten times the thermal conductivity of the cooling medium.

Nonsimilar boundary layers for non-Darcy mixed convection flow about a horizontal surface in a saturated porous medium

The nonsimilar non-Darcy mixed convection flow about a heated horizontal surface in a saturated porous medium has been studied when the surface temperature is a power function of distance (Tw = T∞ ± Axλ). The analysis is performed for the cases of parallel and stagnation flows with favourable induced pressure gradient. The partial differential equations governing the flow have been solved numerically using the Keller box method. The heat transfer is enhanced due to the buoyancy parameter and wall temperature, but the non-Darcy parameter reduces it. For non-Darcy flow, the similarity solution exists only for the case of parallel flow.

Effect of Turbulence on Emerging Magnetic Flux Tubes in the Convection Zone

Working under the hypothesis that magnetic flux in the sun is generated at the bottom of the convection zone, Choudhuri and Gilman (1987; Astrophys. J. 316, 788) found that a magnetic flux tube symmetric around the rotation axis, when released at the bottom of the convection zone, gets deflected by the Coriolis force and tends to move parallel to the rotation axis as it rises in the convection zone. As a result, all the flux emerges at rather high latitudes and the flux observed at the typical sunspot latitudes remains unexplained. Choudhuri (1989; Solar Physics, in press) finds that non-axisymmetric perturbations too cannot subdue the Coriolis force. In this paper, we no longer treat the convection zone to be passive as in the previous papers, but we consider the role of turbulence in the convection zone in inhibiting the Coriolis force. The interaction of the flux tubes with the turbulence is treated in a phenomenological way as follows: (1) Large scale turbulence on the scale of giant cells can physically drag the tubes outwards, thus pulling the flux towards lower latitudes by dominating over the Coriolis force. (2) Small scale turbulence of the size of the tubes can exchange angular momentum with the tube, thus suppressing the growth of the Coriolis force and making the tubes emerge at lower latitudes. Numerical simulations show that the giant cells can drag the tubes and make them emerge at lower latitufes only if the velocities within the giant cells are unrealistically large of if the radii of the flux tubes are as small as 10 km. However, small scale turbulence can successfully suppress the growth of the Coriolis force if the tubes have radii smaller than about 300 km which may not be unreasonable. Such flux tubes can then emerge at low latitudes where sunspots are seen.

Nonaxisymmetric unsteady motion over a rotating disk in the presence of free convection and magnetic field

The nonaxisymmetric unsteady motion produced by a buoyancy-induced cross-flow of an electrically conducting fluid over an infinite rotating disk in a vertical plane and in the presence of an applied magnetic field normal to the disk has been studied. Both constant wall and constant heat flux conditions have been considered. It has been found that if the angular velocity of the disk and the applied magnetic field squared vary inversely as a linear function of time (i.e. as (1??t*)?1, the governing Navier-Stokes equation and the energy equation admit a locally self-similar solution. The resulting set of ordinary differential equations has been solved using a shooting method with a generalized Newton's correction procedure for guessed boundary conditions. It is observed that in a certain region near the disk the buoyancy induced cross-flow dominates the primary von Karman flow. The shear stresses induced by the cross-flow are found to be more than these of the primary flow and they increase with magnetic parameter or the parameter ? characterizing the unsteadiness. The velocity profiles in the x- and y-directions for the primary flow at any two values of the unsteady parameter ? cross each other towards the edge of the boundary layer. The heat transfer increases with the Prandtl number but reduces with the magnetic parameter.

Non-Darcy mixed convection flow with thermal dispersion on a vertical cylinder in a saturated porous medium

The non-Darcy mixed convection flow on a vertical cylinder embedded in a saturated porous medium has been studied taking into account the effect of thermal dispersion. Both forced flow and buoyancy force dominated cases with constant wall temperature condition have been considered. The governing partial differential equations have been solved numerically using the Keller box method. The results are presented for the buoyancy parameter which cover the entire regime of mixed convection flow ranging from pure forced convection to pure free convection. The effect of thermal dispersion is found to be more pronounced on the heat transfer than on the skin friction and it enhances the heat transfer but reduces the skin friction.

Free convection about cylinders of elliptic cross section embedded in a porous medium

Numerical solutions are presented for the free convection boundary layers over cylinders of elliptic cross section embedded in a fluid-saturated porous medium. The transformed conservation equations of the nonsimilar boundary layers are solved numerically by an efficient finite-difference method. The theory was applied to a number of cylinders and the results compared very well with published analytical solutions. The results are of use in the design of underground electrical cables, power plant steam, and water distribution lines, among others.

Unsteady free convection flow under the influence of a magnetic field

The unsteady free convection boundary layer at the stagnation point of a two-dimensional body and an axisymmetric body with prescribed surface heat flux or temperature has been studied. The magnetic field is applied parallel to the surface and the effect of induced magnetic field has been considered. It is found that for certain powerlaw distribution of surface heat flux or temperature and magnetic field with time, the governing boundary layer equations admit a self-similar solution locally. The resulting nonlinear ordinary differential equations have been solved using a finite element method and a shooting method with Newton's corrections for missing initial conditions. The results show that the skin friction and heat transfer coefficients, and x-component of the induced magnetic field on the surface increase with the applied magnetic field. In general, the skin friction, heat transfer and x-component of the induced magnetic field for axisymmetric case are more than those of the two-dimensional case. Also they change more when the surface heat flux or temperature decreases with time than when it increases with time. The skin friction, heat transfer and x-component of the induced magnetic field are significantly affected by the magnetic Prandtl number and they increase as the magnetic Prandtl number decreases. The skin friction and x-component of the magnetic field increase with the dissipation parameter, but heat transfer decreases.