Fig. 5.

Jet characteristics in the simulation of the breathing and speaking signals shown in Fig. 4 A–D. (A) Example of calculation of jet length $L$ and angle $\alpha$ for S75, based on the emitted tracer particles color coded here by residence time, as described in Fig. 4 E–H. $L\left(t\right)$ is such that 90% of the particles are located upstream of $x=L$ at time $t$. The cone angle $\alpha$ is calculated to enclose 90% of the particles and is a cone passing through the mouth exit (radius is 1 cm at $x=0$). This angle is verified to remain stable with time after the initial cycles. (B) Principle of the calculation of the cycle-averaged velocity fields presented in C and D. The velocity is time averaged independently over each cycle. (C and D) Progressive formation, along increasing cycles of exhalation and inhalation, of a turbulent jet-like velocity profile $v\left(x\right)$ in the far field. Examples of cases C50 (C) and S50 (D): cycle-averaged axial velocity along the $x$ axis from the mouth exit to 2.0 m downstream, for different cycles, extending to 14 cycles or 56 s. The black dashed line is the $v\left(x\right)\propto 1/x$ scaling, plotted here as a guide for the eye, which is suggested by a model of a steady turbulent jet. (E) Evolution of the nondimensional jet length $L/a$ as a function of $2v_{0}t/\left(a\alpha \right)$ (Eq. 2), with $a\approx 1.22$ cm the equivalent radius of the mouth exit and $v_0$ the average axial speed during exhalation for the different simulations. Two power laws are plotted as a guide for the eye to assess the evolution of $L$ with time. Raw data for $L\left(t\right)$ are plotted in SI Appendix, Fig. S2.