Matthew M. Scase

Time-dependent plumes and jets with decreasing source strengths

The classical bulk model for isolated jets and plumes due to Morton, Taylor & Turner ( Proc. R. Soc. Lond . A, vol. 234, 1956, p. 1) is generalized to allow for time-dependence in the various fluxes driving the flow. This new system models the spatio-temporal evolution of jets in a homogeneous ambient fluid and Boussinesq and non-Boussinesq plumes in stratified and unstratified ambient fluids. Separable time-dependent similarity solutions for plumes and jets are found in an unstratified ambient fluid, and proved to be linearly stable to perturbations propagating at the velocity of the ascending plume fluid. These similarity solutions are characterized by having time-independent plume or jet radii, with appreciably smaller spreading angles (

Boussinesq plumes and jets with decreasing source strengths in stratified environments

\tan^{-1}(2\alpha/3)

The effect of sudden source buoyancy flux increases on turbulent plumes

) than either constant-source-buoyancy-flux pure plumes (with spreading angle

Temporal Variation of Non-Ideal Plumes with Sudden Reductions in Buoyancy Flux

\tan^{-1}(6\alpha/5)

Internal wave fields generated by a translating body in a stratified fluid: an experimental comparison

) or constant-source-momentum-flux pure jets (with spreading angle

Local implications for self-similar turbulent plume models

\tan^{-1}(2\alpha)

Internal wave fields and drag generated by a translating body in a stratified fluid

), where

The Inhibition of the Rayleigh-Taylor Instability by Rotation

\alpha

A simplified computational analysis of turbulent plumes and jets

is the conventional entrainment coefficient. These new similarity solutions are closely related to the similarity solutions identified by Batchelor ( Q. J. R. Met. Soc ., vol. 80, 1954, p. 339) in a statically unstable ambient, in particular those associated with a linear increase in ambient density with height. If the source buoyancy flux (for a rising plume) or source momentum flux (for a rising jet) is decreased generically from an initial to a final value, numerical solutions of the governing equations exhibit three qualitatively different regions of behaviour. The upper region, furthest from the source, remains largely unaffected by the change in buoyancy flux or momentum flux at the source. The lower region, closest to the source, is an effectively steady plume or jet based on the final (lower) buoyancy flux or momentum flux. The transitional region, in which the plume or jet adjusts between the states in the lower and upper regions, appears to converge very closely to the newly identified stable similarity solutions. Significantly, the predicted narrowing of the plume or jet is observed. The size of the narrowing region can be determined from the source conditions of the plume or jet. Minimum narrowing widths are considered with a view to predicting pinch-off into rising thermals or puffs.

Magnetically Induced Rotating Rayleigh-Taylor Instability

Solutions to the equations of Morton et al. (Proc. R. Soc. Lond. A, vol. 234, 1956, p. 1) describing turbulent plumes and jets rising in uniformly stratified environments are identified for the first time. The evolution of plumes and jets with sources whose driving flux decreases with time is considered in a stratified environment. Numerical calculations indicate that as the source buoyancy flux, for a Boussinesq plume (or source momentum flux, for a Boussinesq jet), is decreased, a transitional narrowing region with characteristic spreading angle tan -1 (2α/3) is formed, where α is the well-known entrainment coefficient. The plume or jet dynamics are modelled well by a separable solution to the governing equations which predicts stalling in the plume at a critical stall time t s = π/N and stalling in the jet at a critical stall time t s = π/(2N), where N is the buoyancy frequency of the ambient background stratification. This stall time is independent of the driving source conditions, a prediction which is verified by numerical solution of the underlying evolution equations.