 The three-dimensional form of the frontogenesis equation is

where each dimension begins with a diabatic term; in the formula_2 direction

formula_3

in the formula_4 direction

formula_5

and in the formula_6 direction

formula_7.The equation also includes horizontal and vertical deformation terms; in the formula_2 direction

formula_9

and in the formula_4 direction

formula_11

and in the vertical formula_6 direction

formula_13.The final terms are the tilting term and the vertical divergence term; the tilting term is represented in the three-dimensional frontogenesis equation in the formula_2 and formula_4 directions

formula_16

formula_17

and the vertical divergence term is present as

formula_18


1.