Buoyancy gradient ($\nabla b$)

The spatial gradient of buoyancy determines the buoyancy anomaly produced by a small parcel displacement: $b^{\prime }=-\mathbf{\xi }\cdot \nabla \bar{b}$. Its vertical component is the squared buoyancy frequency in a stably stratified Boussinesq approximation. A horizontal component enters thermal wind and the propagation of a Boundary Rossby wave.