From AMS Glossary
(Also called Brunt–Douglas isallobaric wind.) The wind velocity when the Coriolis force exactly balances a locally accelerating geostrophic wind.
Mathematically, the isallobaric wind Vis is defined in terms of the local accelerations but approximated by the allobaric gradient as follows:
where k is the vertical unit vector, f the Coriolis parameter, Vg the geostrophic wind, α the specific volume, ∇H the horizontal del operator, and p the pressure. The isallobaric wind is thus directed normal to the isallobars toward falling pressure, with magnitude proportional to the allobaric gradient. Because the isallobaric wind is associated with transient effects and because of the many assumptions used in deriving its equation, observational evidence of this wind is unsatisfactory.
Haurwitz, B. 1941. Dynamic Meteorology. 155–159.