text: Consider a parcel of water or gas that has density . This parcel is in an environment of other water or gas particles where the density of the environment is a function of height: . If the parcel is displaced by a small vertical increment , and it maintains its original density so that its volume does not change,' it will be subject to an extra gravitational force against its surroundings of:
  where  is the gravitational acceleration, and is defined to be positive. We make a linear approximation to , and move  to the RHS:
  The above second-order differential equation has the following solution:
  where the Brunt–Väisälä frequency  is:
  For negative , the displacement  has oscillating solutions (and N gives our angular frequency). If it is positive, then there is run away growth – i.e. the fluid is statically unstable.