Three-dimensional Analytical Models of Background Winds Interacting with Thunderstorm Outflows

Thunderstorm outflows interact with background atmospheric boundary layer winds in complex ways: opposing background winds can decelerate the outflow, while aligned winds can amplify it. Moreover, as the background winds pass through a thunderstorm outflow, they lose momentum due to the turbulence interaction with the outflow. Despite this, an analytical framework to model the deceleration of background winds as they penetrate a thunderstorm outflow has been lacking. This study introduces the first set of analytical expressions to quantify this interaction using a turbulence drag law adapted from classical atmospheric boundary layer theory. Two models are proposed: (1) a bulk interaction model, which characterizes the background and downburst winds using their representative (constant) velocities, and (2) an explicit interaction model, which incorporates the spatial variation of the downburst wind field. Turbulence drag coefficients for both models are derived from wind tunnel experiments. While the bulk model offers a simplified approach, it closely approximates the results of the more detailed explicit model, demonstrating its robustness. Our findings also reveal that simple vector addition of undisturbed wind fields can significantly overestimate, and occasionally underestimate, actual wind speeds within the interaction zone. Finally, we compare both models with a field observation of a downburst event, demonstrating the utility of the analytical framework for practical applications.