The pioneering work of Taylor on the turbulent dispersion of aerosols is one century old and provides an interesting way to introduce both diffusive processes and turbulence at an undergraduate level. Low mass particles transported by a turbulent flow exhibit a Brownian-like motion over time scales larger than the velocity correlation time. Aerosols and gases are, therefore, subjected to an effective turbulent diffusion at large length scales. However, the case of a source of pollutant much smaller than the integral scale is not completely understood. Here, we present experimental results obtained by undergraduate students in the context of the COVID-19 pandemic. The dispersion of a fog of oil droplets by a turbulent flow is studied in a wind tunnel designed for pedagogical purposes. It shows a ballistic-like regime at short distance, followed by Taylor's diffusive-like regime, suggesting that scale-free diffusion by the turbulent cascade process is bypassed. Measurements show that the dispersion of CO2 emitted when breathing in a natural, indoor air flow is not isotropic but rather along the flow axis. The transverse spread is ballistic-like, leading to the concentration decaying as the inverse-squared distance to the mouth. The experiment helps students understand the role of fluctuations in diffusive processes and in turbulence. A Langevin equation governing aerosol dispersion based on a single correlation time allows us to model the airborne transmission risk of pathogens, indoors and outdoors. The results obtained in this study have been used to provide public health policy recommendations to prevent transmission in shopping malls.

1.
G. K.
Batchelor
,
An Introduction to Fluid Dynamics
, 14th ed. (
Cambridge U. P., Cambridge
,
2010
), pp.
211
235
.
2.
G. I.
Taylor
, “
Diffusion by continuous movements
,”
Proc. London Math. Soc.
s2–20
,
196
212
(
1922
).
3.
E.
Villermaux
and
C.
Innocenti
, “
On the geometry of turbulent mixing
,”
J. Fluid Mech.
393
,
123
147
(
1999
).
4.
E.
Villermaux
,
C.
Innocenti
, and
J.
Duplat
, “
Short circuits in the Corrsin–Obukhov cascade
,”
Phys. Fluids
13
,
284
289
(
2001
).
5.
G. K.
Batchelor
, “
The application of the similarity theory of turbulence to atmospheric diffusion
,”
Q. J. R. Meteorol. Soc.
76
,
133
146
(
1950
).
6.
T.
Greenhalgh
et al, “
Ten scientific reasons in support of airborne transmission of SARS-CoV-2
,”
Lancet
397
,
1603
1605
(
2021
).
7.
H.
Risken
and
T.
Frank
,
The Fokker-Planck Equation: Methods of Solution and Applications
, 2nd ed. (
Springer
,
Berlin, Heidelberg
,
1989
), pp.
32
37
.
8.
J. P. L. C.
Salazar
and
L. R.
Collins
, “
Two-particle dispersion in isotropic turbulent flows
,”
Annu. Rev. Fluid Mech.
41
,
405
432
(
2009
).
9.
B.
Sawford
, “
Turbulent relative dispersion
,”
Annu. Rev. Fluid Mech.
33
,
289
317
(
2001
).
10.
M.
Lesieur
,
Turbulence in Fluids
, 4th ed. (
Springer
,
Dordrecht
,
2008
), pp.
187
208
.
11.
G. K.
Batchelor
, “
Diffusion in a field of homogeneous turbulence. I. Eulerian analysis
,”
Aust. J. Chem.
2
,
437
450
(
1949
).
12.
G. K.
Batchelor
, “
Diffusion in a field of homogeneous turbulence: II. The relative motion of particles
,”
Math. Proc. Cambridge Philos. Soc.
48
,
345
362
(
1952
).
13.
B. L.
Sawford
, “
Reynolds number effects in Lagrangian stochastic models of turbulent dispersion
,”
Phys. Fluids A
3
,
1577
1586
(
1991
).
14.
K.-C.
Cheng
et al, “
Modeling exposure close to air pollution sources in naturally ventilated residences: Association of turbulent diffusion coefficient with air change rate
,”
Environ. Sci. Technol.
45
,
4016
4022
(
2011
).
15.
J.
Bec
et al, “
Acceleration statistics of heavy particles in turbulence
,”
J. Fluid Mech.
550
,
349
358
(
2006
).
16.
L.
Biferale
et al, “
Lagrangian structure functions in turbulence: A quantitative comparison between experiment and direct numerical simulation
,”
Phys. Fluids
20
,
065103
(
2008
).
17.
F.
Toschi
and
E.
Bodenschatz
, “
Lagrangian properties of particles in turbulence
,”
Annu. Rev. Fluid Mech.
41
,
375
404
(
2009
).
18.
M.
Bourgoin
, “
Turbulent pair dispersion as a ballistic cascade phenomenology
,”
J. Fluid Mech.
772
,
678
704
(
2015
).
19.
J.
Bec
et al, “
Turbulent pair dispersion of inertial particles
,”
J. Fluid Mech.
645
,
497
528
(
2010
).
20.
M.
Bourgoin
et al, “
The role of pair dispersion in turbulent flow
,”
Science
311
,
835
838
(
2006
).
21.
L.
Morawska
et al, “
A paradigm shift to combat indoor respiratory infection
,”
Science
372
,
689
691
(
2021
).
22.
K.
Randall
et al, “
How did we get here: What are droplets and aerosols and how far do they go? A historical perspective on the transmission of respiratory infectious diseases
,”
Interface Focus
11
,
1
10
(
2021
).
23.
L.
Bourouiba
,
E.
Dehandschoewercker
, and
J. W. M.
Bush
, “
Violent expiratory events: On coughing and sneezing
,”
J. Fluid Mech.
745
,
537
563
(
2014
).
24.
R.
Mittal
,
R.
Ni
, and
J.-H.
Seo
, “
The flow physics of COVID-19
,”
J. Fluid Mech.
894
,
F2-1-14
(
2020
).
25.
L.
Bourouiba
, “
The fluid dynamics of disease transmission
,”
Annu. Rev. Fluid Mech.
53
,
473
508
(
2021
).
26.
S. N.
Rudnick
and
D. K.
Milton
, “
Risk of indoor airborne infection transmission estimated from carbon dioxide concentration
,”
Indoor Air
13
,
237
245
(
2003
).
27.
M. Z.
Bazant
and
J. W. M.
Bush
, “
A guideline to limit indoor airborne transmission of COVID-19
,”
Proc. Natl. Acad. Sci.
118
,
e2018995118
(
2021
).
28.
J. W.
Tang
et al, “
A schlieren optical study of the human cough with and without wearing masks for aerosol infection control
,”
J. R. Soc. Interface
6
,
S727
736
(
2009
).
29.
S.
Verma
,
M.
Dhanak
, and
J.
Frankenfield
, “
Visualizing the effectiveness of face masks in obstructing respiratory jets
,”
Phys. Fluids
32
,
061708-1-7
(
2020
).
30.
T.
Greenhalgh
,
M.
Ozbilgin
, and
D.
Contandriopoulos
, “
Orthodoxy, illusio, and playing the scientific game: A Bourdieusian analysis of infection control science in the COVID-19 pandemic
,”
Wellcome Open Res.
6
,
126-1-32
(
2021
).
31.
E.
Balkovsky
and
B. I.
Shraiman
, “
Olfactory search at high Reynolds number
,”
Proc. Natl. Acad. Sci.
99
,
12589
12593
(
2002
).
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.