3.4 THE INTERACTION OF GRAVITY WAVES WITH TORNADOES AND MESOCYCLONES: THEORIES AND OBSERVATIONS Timothy A. Coleman* and Kevin R. Knupp The University of Alabama, Huntsville, Alabama 1. INTRODUCTION Careful examination of Doppler radar data from The purpose of this paper is to examine and model several tornadic thunderstorms in Alabama and two physical processes which may help explain the Tennessee reveals an intriguing yet strikingly consistent gravity wave/mesocyclone interaction: 1) vortex pattern. One or more relatively narrow bands of radar stretching due to horizontal convergence associated reflectivity approach a convective storm with a pre- with gravity waves, and 2) changing environmental wind existing mesocyclone, from its right flank (generally from shear due to wind perturbations within the waves. We a southerly direction). Then, upon interaction with the will then examine these hypotheses in the context of two storm, there is an intensification of the mesocyclone and cases in which apparent gravity wave interactions with sometimes tornadogenesis. The reflectivity bands in mesocyclones aided/initiated tornadogenesis. We will these cases, however, can not generally be attributed to also briefly look at the wave/bore-like features which density currents/outflow boundaries from other storms, were related to a rapid intensification of the tornado but instead appear to be gravity waves. (which was rated F5) in Birmingham, Alabama on 8 April The interactions between gravity waves and 1998 (Pence and Peters 2000, Kilduff 1999). convection have been well-investigated. Many have discussed the initiation or enhancement of convection 2. BRIEF REVIEW OF WAVE DYNAMICS by gravity waves (e.g., Uccellini 1975; Stobie et al. 1983; Corfidi 1998). Conversely, several others have Gravity waves may be excited when a parcel of air shown that convective storms can also initiate gravity is perturbed vertically within an area of static stability. waves (e.g., Alexander et al. 1995; Bosart and Cussen They may be initiated by convection, and also by other 1973; Koch and O’handley 1997; Brunk 1949). The processes, including geostrophic adjustment, relationship known as wave-CISK, whereby convective topography, and shear instability (Koch and O’Handley lines and gravity waves synergistically support one 1997). Gravity waves require some degree of static another, has been well-examined also (e.g., Cram et al. stability, but without a “duct” in place, wave energy 1992; Raymond 1984). However, the potential dynamic would leak rapidly upward, preventing the maintenance interactions between gravity waves and of a coherent wave (Lindzen and Tung 1976). However, mesocyclones/tornadoes have received limited Lindzen and Tung (1976) showed that a wave may be attention, and most of it has been observational in “ducted” by a stable layer near the surface, as long as nature. the stable layer 1) is deep enough to accommodate ¼ of The occurrence of a Florida tornado on 14 the vertical wavelength, 2) contains no critical level, and November 1949 was related to the intersection of two 3) is topped by a conditionally unstable layer with a “pressure jump lines” by Tepper (1950). In this case, Richardson number Ri < 0.25. The intrinsic phase -1 one of the jump lines was apparently connected to a speed for a ducted wave is given by c-U = 2NDπ , squall line, while the other may have been a gravity where c is the ground-relative wave phase speed, U is wave. Miller and Sanders (1980) observed that tornado the mean wave normal wind component in the duct, and production increased within some convective regions D is the depth of the stable duct. Therefore, the phase when wave packets overtook those regions during the speed may be determined through analysis of sounding Super Outbreak of April 1974. They posed a question in data. their paper as to whether or not the waves contained Eom (1975) developed a relatively simple model vorticity which aided the development of tornadoes. which simulates the gravity wave disturbance fairly well More recently, Kilduff (1999) observed the increase in using a plane wave form, which may be written as Q’ = storm rotational velocities and one case of Q’max cos (kx-ωt). Here, Q’ may represent any of the tornadogenesis upon interaction with gravity waves on perturbation variables in the gravity wave (ie., pressure 22 January 1999 in northwest Alabama (a case to be p, wave relative perturbation wind u*, and vertical studied in detail herein). Barker (2006) similarly finds a motion w), and Q’max would then represent the amplitude link between what he terms “reflectivity tags” moving of each variable (as in Eom 1975). Also, k is the quickly through a linear MCS and tornadogenesis, in the horizontal wavenumber, and ω is the angular frequency. case of the F3 Evansville, Indiana tornado of 6 Such a wave is illustrated in Figure 1. The November 2005. These tags are likely gravity waves. hydrostatically induced maximum p’ (H) at the surface is co-located with the wave ridge (location of maximum *Corresponding Author Address: Timothy A. Coleman, upward displacement) and with u*max (as indicated by Atmospheric Science Department, The University of the wind vectors). Similarly, the minimum p’ (L) is co- Alabama in Huntsville, 320 Sparkman Drive, Huntsville, located with the wave trough and with -u*max. Low-level AL 35805; Email: [email protected]. convergence ahead of the wave ridge produces upward be shown mathematically, assuming the sinusoidal horizontal wind perturbation of the Eom (1975) model, that the increase in vorticity due to the passage of only the convergent region of a gravity wave is given by ζ2 = ζ1 exp (2u*max/cR), where cR is the phase speed relative to the mesocyclone motion. This makes physical sense, in that higher amplitude waves (larger u*max) produce larger vorticity changes, and slower moving waves (smaller cR) have more time to act on the mesocyclone. For a typical mesoscale gravity wave, this indicates that the convergence ahead of the wave ridge may easily double, at least temporarily, the vorticity in a mesocyclone. Figure 1. Idealized plane gravity wave (traveling to the 3.2 Wind Shear right). Wind and vertical motion perturbations indicated by vectors, sinusoidal curve represents the Upon examination of the wind perturbations within displacement of an isentropic surface. (Adapted from a gravity wave (see Figure 1), it is clear that fairly Eom (1975); Bosart and Sanders (1986), and Cram et significant perturbation wind shear may also accompany al. (1992).) the wave, which significantly alters the environmental wind profile and storm-relative helicity. For the typical motion, and low-level divergence behind the ridge situation examined herein (a wave intersecting a produces downward motion, allowing the ridge to rotating storm from its right flank), the wave trough propagate to the right. region exhibits the perturbations which would typically It should be noted here that the highest likelihood enhance the vertical shear and the storm-relative for radar-detectable clouds and precipitation should helicity. logically be near or just ahead of the wave ridge. This is Consider the mesoscale gravity wave event of 10 supported by the observations of Miller and Sanders May 2006 in northeast Alabama discussed above. The (1980) and Sanders and Bosart (1985). So, a band of wave was moving ENE (from 250 deg) at 26 m s-1, had enhanced radar reflectivity would very nearly indicate a wave period of ~2 h, and its trough passed the HTX the position of a gravity wave ridge. radar around 1945 UTC. VAD wind profiles in the lowest 10 kft (~3 km MSL) (Figure 2) show the winds 3. DYNAMICS OF THE INTERACTIONS within about ½ a vertical wavelength of the wave, similar to that illustrated in Figure 1. Note the extreme backing 3.1 Convergence of the 2 kft winds (from 255 to 101 deg) between 1845 and 1945 UTC, associated with the negative u* wind The vorticity equation (e.g. Holton 1992) states perturbations ahead of the trough. Also note the slight that the time rate of increase in vertical vorticity veering and considerable increase in magnitude of the following the motion of a parcel is related to three winds at 10 kft (from 17 to 23 m s-1), associated with the processes: 1) stretching of pre-existing vorticity by positive u* perturbations near the ½ vertical wavelength horizontal convergence, 2) tilting of horizontal vorticity height, as predicted by the model wave. A time-height into the vertical, and 3) solenoidal effects. Typically, for section of the wave-normal wind field derived from this mesoscale systems, we may neglect solenoidal effects. VAD profile is shown in Figure 3. There is a significant For a plane gravity wave (as in Figure 1), increase in wave-normal bulk shear in the layer shown, convergence is maximized 90 deg ahead of the wave from 9.5 m s-1 at 1845 UTC, to 34.8 m s-1 at the wave ridge. This convergence is significant in some cases. trough (1945 UTC). This wave-induced shear has a Time-to-space conversion of the Hytop, Alabama (HTX) significant effect on the helicity of the environment. WSR-88D VAD wind profile data (see Figure 2) of a Even in a ground-relative sense (as shown in the mesoscale gravity wave in northeast Alabama on 10 hodographs in Figure 4), the helicity increases -4 -1 May 2006 revealed convergence as large as 5 x 10 s , dramatically within the wave trough (from near 0 at 1845 which is consistent with the results found by Bosart and to ~150 m2 s-2 at 1945 UTC), and considering that most Seimon (1988). In the plane wave, the only horizontal examined cases have storms moving to the right of the wind perturbations are perpendicular to the wave front (ie., in the direction of wave motion).