Symmetric, 2-D Squall Line Tropical Squall Lines: (Zipser, 1977) Frontal Squall Lines: (Carbone, 1982) Severe Mid-Latitude Squall Lines: (Newton, 1963) Basic Equations: 2D Squall Line - Or, more simply, consider the 2D horizontal vorticity equation: where *Also, no vortex tilting or stretching Optimal condition for cold pool lifting C/u > 1 C/u = 1 C/u < 1 RKW Theory Rotunno et al. (JAS, 1988) Early System Evolution Optimal C/u 1 Mature System: 2D Convective System Evolution: C/u 1 Weak shear, strong cold pool: rapid evolution Strong shear, weak cold pool: slow evolution 2D Convective System Evolution: So, whats optimal?? C/u 1 RKW Theory: all other things being equal (e.g., same external forcing), squall line strength/longevity is optimized when the circulation associated with the system- generated cold pool remains in balance with the circulation associated with the low- level vertical wind shear. Issue: Squall-lines are observed to be strong and long-lived for a wider range of environments than suggested by the models (e.g., weaker shears, deeper shears,.). So, what is the utility of RKW theory? Thorpe et al. (1982) (2D) Squall Lines steadiest when shear confined to low-levels! Fovell (1988) (2D) Weisman et al. (1988) (3D) Weisman and Rotunno (2004) Total Rainfall 1-6 h Total Condensation 1-6 h Wmax (ms-1) 3-6 h RKW Theory: all other things being equal (e.g., same external forcing), squall line strength/longevity is optimized when the circulation associated with the system- generated cold pool remains in balance with the circulation associated with the low- level vertical wind shear. Issue: Squall-lines are observed to be strong and long-lived for a wider range of environments than suggested by the models (e.g., weaker shears, deeper shears,.). So, what is the utility of RKW theory? Now Consider a 3D Squall Line.without Coriolis: - 20 ms-1 shear, no Coriolis forcing 5 May :48 GMT How can we systematically produce the observed line-end vortex pattern? Weisman and Davis (1998) Optimal C/u ~ 1C/u > 1 Mature System: Weisman and Davis (1998) Vortex Lines: Us=20 ms-1 over 2.5 km t=4h Weisman and Davis (1998) Mature Phase: Line-end vortex mechanisms: Weisman and Davis (1998) f=0 Vortex Tube Circulation: Vertical Vorticity: flux form Circulation: Weisman and Davis (1998) f=0 (Davis and Weisman, 1994; Weisman and Davis, 1998; Davis and Galarneau, 2009) tilting of system-generated horizontal vorticity Rear-inflow jet Role of Line-End Vortices Focuses and Intensifies Rear-Inflow Jet Now Consider a 3D Squall Line.with Coriolis: - 20 ms-1 shear, Coriolis forcing