Flow modeling possibilities

eq. Helmholtz
incompressible fluid, no electromagnetic force
no advection and neutrally stable
no viscosity
Coriolis force considered
geostrophic fluid -> Taylor columns
no advection, no viscosity, no relative acceleration
incompressible fluid, no electromagnetic force
Coriolis force considered
no variation of the velocity along the z-direction
Poincaré fluid
no advection, no viscosity
no electromagnetic force
Coriolis force considered
no relative acceleration
motion = global rotation
Boussinesq approximation
eulerian density neglected when multiplied by the velocity, except in a term containing gravity
Coriolis force considered
eventually:
no advection, no viscosity, incompressible fluid, no electromagnetic force
eq. Greenspan
incompressible
non-advective fluid
no electromagnetic force
viscosity and Coriolis force considered
viscous, non rotating, non-advecting and conductor
viscous, rotating, non-advecting and conductor
viscous, rotating, advecting and conductor
+ turbulence

	Coriolis	Incompres- sibility	Relative accelaration	Advection	Viscosity	Electroma- gnetic force	Conduc- tivity	Divers
Eq. Helmholtz	x	x	x	-	-	-	-	Poincaré motion
Geostrophic Fluid	x	x	-	-	-	-	-	Taylor Column
Eq. Poincaré	x	-	-	-	-	-	-
Boussinesq approximation	x	-	x	-	-	-	-	Eulerian density neglected except
Eq. Greenspan	x	x	x	-	x	-	-	in terms involving gravity
Other possibilities
(1)	-	-	x	-	x	-	x	Non-rotating
(2)	x	-	x	-	x	-	x
(3)	x	-	x	x	x	-	x	Eventually turbulence

In the general equation:
LHS :: (1) relative acceleration . (mean density + eulerian density) = (1a) + (1b); (2) Coriolis acceleration . (mean density + eulerian density) = (2a) + (2b); (3) advection term . (mean density + eulerian density) = (3a) + (3b)
RHS :: (4) pressure (= additional pressure + eulerian density . gravity); (5) viscosity - viscous force; (6) force related to electromagnetic field; (7) force related to turbulence