A Closure for the Virtual Origin of Turbulent Plumes

An isolated source of surface buoyancy, be it a campfire or burning city, gives rise to a turbulent plume. Well above the surface, the plume properties asymptote to the well-known solutions of Morton, Taylor, and Turner (MTT), but a closure is still lacking for the virtual origin. A closure for the virtual origin is sought here in the case of a turbulent plume sustained by a circular source of surface buoyancy in an unstratified and unsheared fluid. In the high Reynolds number limit, it is argued that all such plumes asymptote to a single solution. Direct numerical simulation (DNS) of this solution exhibits a virtual origin located a distance below the surface equal to 1.1 times the radius of the buoyancy source. This solution is compared to the previously used assumption that the MTT plume is fully spun-up at the surface, and that assumption is found to give buoyancies that are off by an order of magnitude. With regards to the citywide firestorm triggered by the nuclear attack on Hiroshima, it is found that the spun-up-at-surface MTT solution would have trapped radioactive soot within about a hundred meters of the surface, whereas the DNS solution presented here corroborates observations of the plume reaching well into the troposphere.

IWC Analysis of Turbulent Plume Fires

Plumes fires are characterized by a turbulent nature with a large number of different scales. LES is used to solve the largest structures and to model the smallest ones. Grid size and time steps become decisive to place a limit between solved and modelled turbulence. A spectral analysis, both in frequency and wavenumber domain of the specific turbulent kinetic energy is an instrument to check for the information investigated. Unfortunately, the spectra in the wavenumber domain can be difficult to achieve adequately, because the specific turbulent kinetic energy values should be available in many points. This issue can be overcome by identifying a correlation law between frequencies and wavenumbers. An approach to identify this correlation law can be to adopt the IWC method. Here, for a test case of a turbulent reacting plume of burning propane, specific turbulent kinetic energy is analysed both in frequency and wavenumber and a correlation law between them is identified by using the IWC method. A study has been performed to evaluate the grid dependency of the specific turbulent kinetic energy spectra, by assessing the extension of the Kolmogorov power law region. The correlation results are discussed and compared with the Taylor’s hypothesis.

Conditional sampling of a high Péclet number turbulent plume and the implications for entrainment

We present simultaneous two-dimensional velocity and scalar measurements on a central vertical plane in an axisymmetric pure turbulent plume. We use an edge-detection algorithm to determine the edge of the plume, and compare the data obtained in both a fixed Eulerian frame and a frame relative to local coordinates defined in terms of the instantaneous plume edge. In an Eulerian frame we observe that the time-averaged distributions of vertical and horizontal velocity are self-similar, the vertical velocity being well represented by a Gaussian distribution. We condition these measurements on whether fluid is inside or outside of the plume, and whether fluid inside is mixed plume fluid or engulfed ambient fluid. We find that, on average, 5 % of the total vertical volume transport occurs outside the plume and this figure rises to nearly 14 % at heights between large-scale coherent structures. We show that the fluxes of engulfed fluid within the plume envelope are slightly larger than the vertical transport outside the plume – indicating that ambient fluid is engulfed into the plume envelope before being nibbled across the turbulent/non-turbulent interface (TNTI) and then ultimately irreversibly mixed. Our new measurements in the plume coordinate (following the meandering fluctuating plume) show the flow within the plume and in the nearby ambient fluid is strongly influenced by whether an eddy is present locally within the plume, or absent. When an eddy is present and the plume is wide, the vertical velocities near the plume edge are small and hence all vertical transport is inside the plume. In regions where the plume is narrow and there is no eddy, large vertical velocities and hence transport are observed outside the plume suggesting that pressure forces associated with the eddies accelerate ambient fluid which is then engulfed into the plume. Finally, we show that observing significant vertical velocities beyond the scalar edge of the plume does not suggest that the characteristic width of the velocity distribution is greater than that of the scalar field; on the contrary, we show our observations to be consistent with a buoyancy distribution that is up to 20 % wider than that of the velocity. Measurements in the plume coordinates show that the mixing of momentum across the plume results in a distribution for which the differential entropy is close to maximal and the mixing of momentum is uninhibited (i.e. not bounded) by the TNTI of the plume. Furthermore, our measurements suggest that the scalar mixing across the plume may also result in a distribution for which the differential entropy is close to maximal but, in contrast to the momentum, the scalar mixing is strictly bounded by the plume edge.

Emptying filling boxes – free turbulent versus laminar porous media plumes

We examine the transient evolution of a negatively buoyant, laminar plume in an emptying filling box containing a uniform porous medium. In the long time limit, $\unicode[STIX]{x1D70F}\rightarrow \infty$, the box is partitioned into two uniform layers of different densities. However, the approach towards steady state is characterized by a lower contaminated layer that is continuously stratified. The presence of this continuous stratification poses non-trivial analytical challenges; we nonetheless demonstrate that it is possible to derive meaningful bounds on the range of possible solutions, particularly in the limit of large $\unicode[STIX]{x1D707}$, where $\unicode[STIX]{x1D707}$ represents the ratio of the draining to filling time scales. The validity of our approach is confirmed by drawing comparisons against the free turbulent plume case where, unlike with porous media plumes, an analytical solution that accounts for the time-variable continuous stratification of the lower layer is available (Baines & Turner, J. Fluid Mech., vol. 37, 1969, pp. 51–80; Germeles, J. Fluid Mech., vol. 71, 1975, pp. 601–623). A separate component of our study considers time-variable forcing where the laminar plume source strength changes abruptly with time. When the source is turned on and off with a half-period, $\unicode[STIX]{x0394}\unicode[STIX]{x1D70F}$, the depth and reduced gravity of the contaminated layer oscillate between two extrema after the first few cycles. Different behaviour is seen when the source is merely turned up or down. For instance, a change of the source reduced gravity leads to a permanent change of interface depth, which is a qualitative point of difference from the free turbulent plume case.

The contribution of turbulent plume dynamics to long-range spotting

Spotting can start fires up to tens of kilometres ahead of the primary fire front, causing rapid spread and placing immense pressure on suppression resources. Here, we investigate the dynamics of the buoyant plume generated by the fire and its ability to transport firebrands. We couple large-eddy simulations of bushfire plumes with a firebrand transport model to assess the effects of turbulent plume dynamics on firebrand trajectories. We show that plume dynamics have a marked effect on the maximum spotting distance and determine the amount of lateral and longitudinal spread in firebrand landing position. In-plume turbulence causes much of this spread and can increase the maximum spotting distance by a factor of more than 2 over that in a plume without turbulence in our experiments. The substantial impact of plume dynamics on the spotting process implies that fire spread models should include parametrisations of turbulent plume dynamics to improve their accuracy and physical realism.