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1. Introduction
The existence of 1-10-m-scale (i.e., sub-tornado scale) vortices embedded within a larger (100-m-1-km scale) tornado vortex was first postulated based on analyses of airborne photographs of cycloidal damage marks on the ground, which Fujita et al. (1970) initially referred to as “suction spots” (highly localized regions of intense upward motion) and later as “suction vortices” (Fujita 1981). Following Fujita’s pioneering work, many “multiple vortex” tornadoes have been observed by storm chasers and the public (e.g., Bluestein 2013), so they are much more common than originally thought. They have been difficult to analyze in nature because the multiple vortices (also known as “secondary”1 vortices) are narrow (too small to resolve with most radar systems operating at relatively long ranges), short lived, and difficult, if not impossible, to predict. In many instances, tornadoes may undergo transitions both to and from single- and multiple-vortex structures (e.g., Wurman 2002; Alexander and Wurman 2005; Wurman and Kosiba 2013; Wurman et al. 2014; Bluestein et al. 2015).
It is well known that for axisymmetric flow in a laboratory tornado chamber or numerical simulation thereof, secondary vortices, which are smaller in horizontal scale than their parent vortex (which in nature is ~100 m-1 km in scale), can occur when the swirl ratio (Lewellen 1962; Davies-Jones 1973) is relatively high (Church et al. 1979; Davies-Jones et al. 2001; Rotunno 2013). The swirl ratio is a measure of the relative amount of azimuthal velocity at the edge of the updraft to the vertical velocity of the updraft in a laboratory chamber or, equivalently, R(υ02πR)/(2wπR2), where υ0 is the azimuthal wind at the edge of the updraft of radius R, and w is the updraft. When the swirl ratio in the chamber is high, the vortex widens as a central downdraft is forced by a downward-directed perturbation pressure gradient force; a zone of strong lateral shear of the azimuthal wind develops radially inward of the ring of strongest azimuthal wind, which could, for some highly idealized flows, become unstable with respect to small perturbations (e.g., Rotunno 1978; Staley and Gall 1979), such that small-scale vortices develop within the larger vortex and rotate around with the broader-scale flow. Walko and Gall...