Dust devil winds: Assessing dry convective vortex intensity limits at planetary surfaces

doi:10.1016/j.icarus.2020.114062

Icarus

Volume 354, 15 January 2021, 114062

https://doi.org/10.1016/j.icarus.2020.114062 Get rights and content

Highlights

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Provides a simple expression to estimate worst-case vortex winds
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Tests expression against a wide range of field observations on Earth and mars
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Makes predictions of vortex winds for Titan and Venus

Abstract

An estimate of the maximum winds associated with dry convective vortices is determined simply as V_max = ΔT(2C_p/T_a)^0.5, where ΔT is equal to half of the maximum surface-atmosphere temperature contrast, C_p is the specific heat capacity, and T_a the background temperature of the atmosphere. The ΔT estimate, and the resultant winds, have strong support from a wide range of observations on Earth and Mars. The model results in maximum predicted vortex winds of 29, 53, 2.7 and 2.0 m/s for Earth, Mars, Titan and Venus respectively, the ΔT values for the latter two bodies being determined from surface energy balance models. The maximum vortex winds in well-documented observations on Earth and Mars appear to be ~25 m/s and ~ 30 m/s respectively, consistent with the model limits.

Introduction

A frequent question which confronts the designers of landers and other planetary exploration vehicles (Lorenz, 2018) is what the maximum wind speed encountered might be. This value may drive the buckling strength of structures such as masts, or the stability of the vehicle or deployed instruments against tip-over. For vehicles with aerial mobility, such as the Mars Helicopter Scout (Balaram et al., 2018), or the Dragonfly octocopter (Lorenz et al., 2018), wind environments may also drive the required flight control performance.

In desert environments on Earth, a frequent mechanism causing sudden strong wind is the vortex motion around convective plumes driven by strong solar heating: often these vortices lift surface particulates and thereby become visible and are called dust devils. These vortices are responsible (Lorenz et al., 2016) for typically several injuries per year (usually by, interaction with large area:mass ratio structures such as sheds or ‘bouncy castles’) as well as occasional deaths. A number of aviation accidents and fatalities (on balloons and parachutes as well as on planes and helicopters) are similarly attributed to dust devils (Lorenz and Myers, 2005.)

On Titan, as on Earth, moist convective processes (e.g. outflow from rainstorms or collapsing cumulus convection, e.g. Charnay et al., 2015) may be responsible for the most violent winds. However, deep moist convection appears to be heavily localized to the polar summer region (e.g. Turtle et al., 2018), and only occurs at low latitudes during the equinoxes. At low Titan latitudes during polar summer, then, the dominant source of wind gusts may therefore be dry convective vortices or ‘dust devils’ (Jackson et al., 2020). This is also likely to be the case in environments without abundant moisture, namely Mars and Venus. In this paper, we evaluate the likely maximum intensity of such winds.

Section snippets

Model formulation

AS Sadi Carnot observed in 1824, heat produces motion. A convective vortex is a heat engine that, rather than the ingenious machines carefully designed and fabricated in iron and steel, emerges spontaneously from the fluid dynamics of the solar-heated planetary boundary layer. But the same fundamental limits apply, as noted by Rennó et al. (1998) and many investigators before and since (see Appendix). Thermodynamically ideal conversion of sensible heat (C_p ΔT per unit mass, with C_p the specific

Model validation

There is strong support for eq. 2 from field data. A typical terrestrial ground-air temperature difference in strongly heated desert conditions is ~20 K (e.g. thermal imaging in a dust devil survey reported by Lorenz, 2010 shows ground temperatures of 56 °C, where the air temperature was 33 °C). This observation suggests a ΔT of 11 K. Ryan and Carroll (1970) at the moment of dust devil encounters recorded a mean difference between the ground temperature and that 30 cm above of 17 K with a

Predictions for Titan

With some empirical validation of the theory, we are now ready to apply it to Titan. Jackson et al. (2020) present a figure estimating dust devil velocities at Titan as a function of temperature perturbation using the Rennó et al. (1998) theory, making assumptions about the thickness of the planetary boundary layer. A large range of possible temperature fluctuations were plotted, leaving substantial uncertainty in the vortex intensity.

Here we use an energy balance model to determine ΔT – in

Application to Venus

Future missions to the surface of Venus may also need to consider gust winds. Although it is commonly assumed that locations on the surface of Venus see no temperature variations, this is not quite correct. As on Titan, although the lower atmosphere is too massive to respond as a whole to the diurnal change in shortwave forcing (which amounts to some ~100 W/m²), because this heat is deposited directly at the surface, there is a small temperature change. Lebonnois et al. (2018) show a sensible

Conclusions

We have suggested and validated a simple relationship for convective vortex winds as a function of ground-air temperature difference, with particular application to planetary exploration vehicle design, where a ‘realistic maximum’ wind must be estimated. The model results in maximum predicted vortex winds of 29, 53, 2.7 and 2.0 m/s for Earth, Mars, Titan and Venus respectively. For Earth and Mars these appear consistent with or somewhat exceed the maximum values encountered in extensive series

Declaration of Competing Interest

None.

Acknowledgements

This work is supported by the Dragonfly project, under NASA Contract NNN06AA01C and by InSight Participating Scientist Program Grant 80NSSC18K1626 The constructive comments of two anonymous referees are acknowledged.

References (58)

V. Cottini et al.
Spatial and temporal variations in Titan's surface temperatures from Cassini CIRS observations
Planetary Space Sci.
(2012)
L.K. Fenton et al.
Dust devil height and spacing with relation to the martian planetary boundary layer thickness
Icarus
(2015)
G. Franzese et al.
Electric properties of dust devils
Earth Planet. Sci. Lett.
(2018)
A.M. Harri et al.
Vertical pressure profile of Titan—observations of the PPI/HASI instrument
Planetary and Space Science
(2006)
S. Lebonnois et al.
Planetary boundary layer and slope winds on Venus
Icarus
(2018)
J.M. Lora et al.
A model intercomparison of Titan’s climate and low-latitude environment
Icarus
(2019)
R.D. Lorenz
Heuristic estimation of dust devil vortex parameters and trajectories from single-station meteorological observations: Application to InSight at Mars
Icarus
(2016)
R.D. Lorenz et al.
Solar panel clearing events, dust devil tracks, and in-situ vortex detections on Mars
Icarus
(2015)
R.D. Lorenz et al.
In-situ measurement of dust devil activity at La Jornada Experimental Range, New Mexico, USA
Aeolian Research
(2015)
I. Ordóñez-Etxeberria et al.
Strong Increase in Dust Devil Activity at Gale Crater on the Third Year of the MSL Mission and Suppression during the 2018 Global Dust Storm
(2020)

T.J. Ringrose et al.

Convective vortices on Mars: a reanalysis of Viking Lander 2 meteorological data, sols 1–60

Icarus

(2003)

L.R. Schurmeier et al.

Crater relaxation on Titan aided by low thermal conductivity sand infill

Icarus

(2018)

T. Tokano

Meteorological assessment of the surface temperatures on Titan: constraints on the surface type

Icarus

(2005)

K.E. Williams et al.

The surface energy balance at the Huygens landing site and the moist surface conditions on Titan

Planetary Space Sci.

(2012)

B. Balaram et al.

Mars helicopter technology demonstrator

M. Balme et al.

Friction wind speeds in dust devils: a field study

Geophys. Res. Lett.

(2003)

D. Banfield et al.

The Atmosphere of Mars as Observed by InSight

Nat. Geosci.

(2020)

L.J. Battan

Energy of a dust devil

J. Meteorol.

(1958)

B.A. Cantor et al.

Mars Orbiter Camera observations of Martian dust devils and their tracks (September 1997 to January 2006) and evaluation of theoretical vortex models

J. Geophys. Res.: Planets

(2006)

B. Charnay et al.

Methane storms as a driver of Titan’s dune orientation

Nat. Geosci.

(2015)

F.L. Curzon et al.

Efficiency of a Carnot engine at maximum power output

Am. J. Phys.

(1975)

R. Davy et al.

Initial analysis of air temperature and related data from the Phoenix MET station and their use in estimating turbulent heat fluxes

J. Geophys. Res.

(2010)

A. De Vos

Efficiency of some heat engines at maximum-power conditions

Am. J. Phys.

(1985)

H.J. Eisen et al.

Sojourner Mars Rover thermal performance, 28^th international conference on environmental systems, Danvers, MA July 13-16, 1998

M.D. Ellehoj et al.

Convective vortices and dust devils at the Phoenix Mars mission landing site

J. Geophys. Res.

(2010)

W.D. Flower

Sand devils

Lond. Meteorol. Off. Prof. Notes

(1936)

S.D. Fuerstenau

Solar heating of suspended particles and the dynamics of Martian dust devils

Geophys. Res. Lett.

(2006)

G.D. Hess et al.

Characteristics of dust devils in Australia

J. Appl. Meteorol.

(1990)

R.L. Ives

Behavior of dust devils

Bull. Am. Meteorol. Soc.

(1947)

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Dust devil winds: Assessing dry convective vortex intensity limits at planetary surfaces

Highlights

Abstract

Introduction

Section snippets

Model formulation

Model validation

Predictions for Titan

Application to Venus

Conclusions

Declaration of Competing Interest

Acknowledgements

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Earth Planet. Sci. Lett.

Planetary and Space Science

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Aeolian Research

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Planetary Space Sci.

Mars helicopter technology demonstrator

Friction wind speeds in dust devils: a field study

Geophys. Res. Lett.

The Atmosphere of Mars as Observed by InSight

Nat. Geosci.

Energy of a dust devil

J. Meteorol.

Mars Orbiter Camera observations of Martian dust devils and their tracks (September 1997 to January 2006) and evaluation of theoretical vortex models

J. Geophys. Res.: Planets

Methane storms as a driver of Titan’s dune orientation

Nat. Geosci.

Efficiency of a Carnot engine at maximum power output

Am. J. Phys.

Initial analysis of air temperature and related data from the Phoenix MET station and their use in estimating turbulent heat fluxes

J. Geophys. Res.

Efficiency of some heat engines at maximum-power conditions

Am. J. Phys.

Sojourner Mars Rover thermal performance, 28th international conference on environmental systems, Danvers, MA July 13-16, 1998

Convective vortices and dust devils at the Phoenix Mars mission landing site

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