A “gustnado” is a portmanteau of the words “gust” and “tornado.” Gustnadoes are short-lived, shallow mini-cylcone formations that develop on a gust front along with thunderstorms or showers.
 
The word “gustnado” has been cited from at least 1991; its origin is unknown, but the term is popular in Texas and other parts of Tornado Alley.
     
   
National Weather Service (Morristown, TN)
Gustnado definition
A slang term for a short-lived, ground-based, shallow, vortex that develops on a gust front associated with either thunderstorms or showers. They may only extend to 30 to 300 feet above the ground with no apparent connection to the convective cloud above. They may be accompanied by rain, but usually are ‘wispy’, or only visible as a debris cloud or dust whirl at or near the ground. Wind speeds can reach 60 to 80 mph, resulting in significant damage, similar to that of a F0 or F1 tornado. However, gustnadoes are not considered to be a tornado, and some cases, it may be difficult to distinguish a gustnado from a tornado. Gustnadoes are not associated with storm-scale rotation (i.e. mesocyclones) that is involved with true tornadoes; they are more likely to be associated visually with a shelf cloud that is found on the forward side of a thunderstorm. 
     
Barnhart Dictionary Companion
gustnado, guhst NAY doh, n., pl. gustnadoes or gustnados or gustnado.  {w}  Also written gust-nado.  1. a strong gust of wind, especially one from above, that produces effects similar to those of a tornado.  Compare microburst (DC 3.1).  Standard (used in technical North American contexts dealing especially with weather reports; common
(...)
Let’s not get too close, I’m thinking; let’s not get carried away!  At one point, the tumbleweeds on either side of the road go flying straight up in the air. It’s only what Davies-Jones calls a “gustnado” (a minor vortex), but for a moment it produces the convincing illusion that a funnel is forming directly over our heads.  William Hauptman, “On the dryline; chasing tornadoes in the Texas panhandle with meteorologists from the National Severe Storms Laboratory,” The Atlantic (Nexis), May 1984, p 76
(...)
1984 (for gustnado); 1996 (for gust-nado).  Composite (compound): formed from gust (OED: 1588) + (tor)nado (OED: 1626), meaning “a whirlwind.”
   
Wikipedia; Gustnado
A gustnado is a colloquial expression for a type of short-lived, shallow, cyclonic circulation that can form in a severe thunderstorm. While it derives its name from the tornado, it has little in common with tornadoes structurally in terms of vertical development, or in regard to intensity, longevity, and formative process (classic tornadoes are associated with mesocyclones).
 
The average gustnado lasts no more than a few seconds to a few minutes each, although there can be several generations and simultaneous swarms. Most have the winds of a F0 or F1 tornado, and are commonly mistaken for tornadoes. However, unlike tornadoes, the rotating column of air in a gustnado usually does not extend all the way to the base of the thundercloud. Gustnadoes actually have more in common with whirlwinds (which include dust devils, whirldwinds that form due to superheated surface layers and stretched vorticity, most commonly on sunny, warm days with light winds). They are not considered true tornadoes (unless they connect the surface to the ambient cloud base) by most meteorologists and are not included in tornado statistics. Sometimes referred to as spin-up tornadoes, that term more correctly describes the rare tornadic gustnado that connects the surface to the ambient cloued base, or to relatively brief tornadoes associated with a mesovortex.
 
The most common setting for a gustnado is on the outflow from a severe thunderstorm (58+ mph winds). They are triggered by gust fronts (hence the name) in thunderstorms. The cool air in the gust front acts like a mesoscale cold front, it slices under the warm air ahead of it, creating upward motions and turbulent interactions. The friction from this interaction creates spinning columns of air, or eddys, which can create a gustnado (to get the general idea of this, picture an area of leaves swirling on a windy day, just on a much larger scale).   
 
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From: .(JavaScript must be enabled to view this email address) (Brian Curran)
Date: 11 May 91 04:49:55 GMT
Local: Sat, May 11 1991 12:49 am
Subject: Re: willies willies/dust devils
 
“Greg Stumpf knows gustnadoes”
   
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From: .(JavaScript must be enabled to view this email address) (Marc Foster)
Date: Mon, 20 Jul 1992 15:38:48 GMT
Local: Mon, Jul 20 1992 11:38 am
Subject: DFW Gustnado
 
I saw my first gustnado in a long while yesterday at the north end of Dallas/Fort Worth International Airport.
 
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From: .(JavaScript must be enabled to view this email address) (Greg Stumpf)
Date: Thu, 23 Jul 1992 15:29:48 GMT
Local: Thurs, Jul 23 1992 11:29 am
Subject: Re: Gustnadoes
 
>a definition/my best understanding of what a gustnado is…
 
>Gustnadoes form on the leading edge of thunderstorms, where the outflow
>boundary/gustfront is located.  Now if you have a dust devil or some
>similar broad low power circulation ahead of the gust front, the interaction
>of the front with the circulation stretches the vortex and narrows the
>diameter.  Since energy must be conserved, the angular velocity is forced
>to increase (spinning figure skater bringing her arms close to the body).
>This is the basic form of the gustnado.  They don’t normally have winds
>in excess of F0, and don’t derive their energy in the same manner as a
>tornado, and since the circulation is not pendant to the base of the storm,
>it is not a tornado (by definition).  The only way they are visible from
>the dirt raised by the winds.
 
Good description.  Many argue that a gustnado *is* a tornado beacuse it is a violently rotating column of air on the ground, but seem to forget that the definition of a true tornado says that this column of air is *pendant from the cumulonimbus cloud*.  This does not mean, however, that you can have very damaging gustnadoes if conditions are met.  Also, some gustnadoes can be entrained into the thunderstorm updraft, becoming tornadoes (or hybrids).
   
8 October 1992, For Worth (TX) Star-Telegram (Google News Archives):
“We call it a ‘gustnado.’ It was a very small-scale tornado in northwest Dallas County on the leading edge of the squall line.”
 
8 November 1994, Syracuse (NY) Herald-Journal, pg. C3:
Weather experts say the rare twister was formed by a “gust front” generated from high winds flowing out of a nearby thunderstorm. This type of phenomena is also referred to as a “gustnado.”