# DJL equations

The Dubreil-Jacotin-Long (DJL) equation is derived from the steady, incompressible Euler equations. The result is a single, non-linear equation for the isopycnal displacement . Here are a few cases:

## Boussinesq with constant background current

where . is the far upstream density profile, is a constant reference density ,and is the acceleration due to gravity.

## Boussinesq with non-constant background current

Again, .

## Non-Boussinesq constant background current

where .