DJL equations: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
Line 5: | Line 5: | ||
<math>\nabla^2 \eta + \frac{N^2(z-\eta)}{U_0^2}\eta = 0</math> | <math>\nabla^2 \eta + \frac{N^2(z-\eta)}{U_0^2}\eta = 0</math> | ||
where <math> N^2(z) = -\frac{g}{\rho_0}\frac{d\bar{\rho'(z)}}{dz}</math>. <math>\bar{\rho} | where <math> N^2(z) = -\frac{g}{\rho_0}\frac{d\bar{\rho'(z)}}{dz}</math>. <math>\bar{\rho}(z)</math> is the far upstream density profile and <math>g</math> is the acceleration due to gravity. | ||
== Boussinesq with non-constant background current <math>U_(z)</math> == | == Boussinesq with non-constant background current <math>U_(z)</math> == | ||
<math>\nabla^2 \eta + \frac{N^2(z-\eta)}{U(z-\eta)^2}\eta + \frac{U'(z-\eta)}{U(z-\eta)\left(1- \left(\eta_x2 +(1-\eta_z)^2\right)\right) = 0</math> | <math>\nabla^2 \eta + \frac{N^2(z-\eta)}{U(z-\eta)^2}\eta + \frac{U'(z-\eta)}{U(z-\eta)}\left(1- \left(\eta_x2 +(1-\eta_z)^2\right)\right) = 0</math> |
Revision as of 11:35, 7 July 2011
The Dubreil-Jacotin-Long (DJL) equation is derived from the steady Euler equations. The result is a single equation for the isopycnal displacement . Here are a few cases:
Boussinesq with constant background velocity
where . is the far upstream density profile and is the acceleration due to gravity.
Boussinesq with non-constant background current