Convection of Isolated Masses of a Buoyant Fluid: A Numerical Calculation

Abstract

The equations of motion for an incompressible fluid have been integrated numerically, as an initial value problem, for the axially-symmetric motion produced by release of an isolated lighter mass of the same fluid. The effect of viscosity is included only implicitly in the finite-difference numerical process. The numerical solutions exhibit the similarity (shape-preserving) stage assumed in theoretical treatments and observed in tank experiments. The computations have been repeated for different values of the total weight deficiency (or excess) of the ?thermal.? The results agree approximately with the relationships predicted by dimensional analysis. The values of various parameters are compared with those obtained in tank experiments and encouraging agreement between them is found. Truncation errors involved in the numerical integration are briefly discussed.