  This paper examines the questions of whether smaller asteroids that burst in
the air over water can generate tsunamis that could pose a threat to distant
locations. Such air burst-generated tsunamis are qualitatively different than
the more frequently studied earthquake-generated tsunamis, and differ as well
from impact asteroids. Numerical simulations are presented using the shallow
water equations in several settings, demonstrating very little tsunami threat
from this scenario. A model problem with an explicit solution that demonstrates
and explains the same phenomena found in the computations is analyzed. We
discuss the question of whether compressibility and dispersion are important
effects that should be included, and show results from a more sophisticated
model problem using the linearized Euler equations that begins to addresses
this.
