Experiments on the penetration of an interface by buoyant thermals

Abstract

Isolated masses of a dense aqueous solution (i.e. thermals) were released at the surface of a freshwater layer overlying one of salt water. While the whole of a thermal remained in the upper layer, the equations $z = n_1r, \; z^2 = k_1t$, with $k_1 = C_1 n_1^{\frac {3}{2}}(Mg| \rho)^{\frac {1}{2}}$, were obeyed, where z is the distance travelled, 2r the width of the thermal, t the elapsed time, M the mass excess (the difference between the masses contained within and displaced by the thermal while in the upper layer), and ρ the density of the displaced fluid. n₁ was constant for any one thermal, but varied between thermals over the range 1·9 to 7·5. C₁ had roughly the same value (0·73) for all thermals.

The behaviour after the leading extremity of the thermal (the ‘front’) entered the lower layer depended on the value of the parameter S = Vρ/M, where Δρ is the density difference between the upper and lower layers and V is the volume of the thermal when the widest part is at the level of the discontinuity. It was found that Y = 0 if S = β (‘weak’ thermals), and Y = 0·95−½S if 0·1 < S [les ] β (‘strong’ thermals), where Y is the fraction of the mass of the substance released which penetrated indefinitely into the lower layer. The constant β was approximately equal to 1.90.

In weak thermals, the equation z − s = a₁(t − t_s)² was obeyed while the front was in the lower layer, until the cluminating point z = s was reached at t = t_s. The acceleration a₁ was always negative, and constant for any one thermal, but varied between thermals. Also for weak thermals, $x = C_2 V^{\frac {1}{3}}|S$, where x is the distance from the interface to the culminating point and C₂ is a constant. C₂ was approximately equal to 3·5. For strong thermals, the distance travelled while the front was in the lower layer obeyed the equation z² = k₂t. The origins of z and t usually differed from those found in the upper layer, and generally k₂ ≠ k₁.