Buoyancy perturbation ($b^{\prime }$)

A buoyancy perturbation is the departure $b^{\prime }$ from a prescribed basic buoyancy field. In a fluid with constant buoyancy frequency $N$, vertical velocity $w^{\prime }$ changes it according to $({\partial }_t+\mathbf{U}\cdot \nabla )b^{\prime }=-N^2{w}^{\prime }$.