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By contrast, fluid parcel path lengths in the present high-speed turbulent flames are found to be substantially greater than laminar path lengths, resulting in fluid parcels that travel 4 and 7 times further than in a laminar flame for the two different turbulence intensities considered here.
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The resulting thermochemical trajectories are used to examine the evolution of thermodynamic quantities and chemical composition, as well as measure fluid parcel residence times and path lengths during different phases of the combustion process.
For each fluid parcel a limited reservoir of silica was specified to be consumed by diatoms.
The atmospheric waves have a finite impedance, i.e., the ratio of pressure perturbation in a fluid parcel to its vertical velocity.
Since the self-catalytic reaction is initiated by the mixing of the fresh liquid with the reacted one, we use the mean age of the fluid parcel as the conditioning variable.
As a related consequence of advection, fluid parcel residence times are found to be smaller than in a laminar flame and the ratio of turbulent to laminar residence times decreases from roughly 0.8 to 0.6 as the turbulence intensity increases.
Turbulence in the heating region behind the shock increases the time a fluid parcel spends in that region and, importantly, turbulent pressure helps in overcoming the ram pressure of accretion (see next section and Couch and O'Connor (2014)).
Here, P − ρgW and Z have the physical meaning, respectively, of the wave-induced pressure variation in a moving fluid parcel (i.e., Lagrangian pressure perturbation) and the boundary impedance (Godin 2012).
The importance of interior pathways is confirmed although we note that fluid parcels generally take complex paths and frequently make multiple attempts to enter the northern hemisphere or multiple treks around gyres.
Then, fluid parcels are tracked in the calculated flow field.
The stochastic reactor describes the evolution of soot in fluid parcels following Lagrangian trajectories in a turbulent flow field.
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