This paper presents an application of a buoyancy-modified $\kappa$-$\varepsilon$ model of turbulence to the problem of two-dimensional unsteady heated surface jet into a reservoir in an uniform stagnant water.
The governing partial differential equations (continuity, vertical and horizontal momentum, thermal energy, turbulent kinetic energy $\kappa$ and its dissipation rate $\varepsilon$) are solved by means of the finite difference procedure (SIMPLER) of Patanker and Spalding for elliptic unsteady differential equations.
Considering buoyancy effects in the present study, the buoyancy-modified $\kappa$-$\varepsilon$ model of Bradshaw's $R_f$ correction has been used. The structure of the mean velocity and temperature in surface jet has been studied for a range of the inlet Richardson number $Ri_o$ from 0.0013 to 0.123. The predictions are compared in detail with previous experimental measurements. Mean velocity and temperature profiles are in good agreement with measerments, which shows that the present model successfully accounts for the buoyancy effects in surface jets.
The results also show that the warm layer penetrates more rapidly into the cold layer at lower Richardson number because of strong turbulent diffusion and decrease of its stability.
