Well, I'm not really sure about whether you wish to refer just to relativistic classical field theories or you are interested on non-relativistic ones as well.
Either way, you have:
- Classical thermodynamics, where you study the internal energy, entropy, temperature, pressure and volume fields of a classical sytem. This theory serves to:
Understand and apply at wish the
mechanisms of heat conduction
determining the hour of death of a
Make rough cosmological assesments
(heat death of the universe and the
Understand, measure and determine the
restrictions on life at a
thermodynamical level (need for
feeding, maximal safe temperature,
maximal attainable speed, construction
Understand how to construct, manage
and study combustion-powered engines
(Carnot efficiency, automotive
- Fluid dynamics, where you study the velocity, temperature, density and pressure fields of a (liquid or gaseous) fluid. This theory serves to:
Design fluid-efficient machines, whether they are flying machines - planes and spaceships -, running machines - Formula 1 cars - or navigating machines - ships and submarines -.
Understand and implement interesting flows through pipes, nozzles and turbines (we need them, for example, to conduct or transport liquids, gasses and colloids and to know how to expel them properly).
Get insight on some transport phenomena that occur in Biology (since water is an important component of most living creatures and of their environments).
Predict the weather on a given (not too big) zone, in a given time (not too far in the future).
Get knowledge on the important ocean currents and on how to predict tsunamis.
Have the correct tool for (fluid) acoustical engineering, since sound is no more than disturbances of the average pressure of the fluid.
- Magnetohydrodynamics, which studies the dynamics of electrically conducting fluids (like plasmas, liquid metals or salt water). Its equations are the mixture of Navier-Stokes' and Maxwell's. This theory serves to:
Model the core of the Earth as a liquid-metal dynamo (generation of its global magnetic field, Seismology).
Accurately describe the internal dynamics of stars and another space objects made mostly from plasma (predict the number, size and movement of the Sunspots).
Know how to cool high temperature systems by means of liquid metals.
Research a totally new generation of engines.
- Electrohydrodynamics, which studies the dynamics of ionised particles on the sine of a fluid, subject to electric fields. This theory serves to:
In general, to convert electrical energy into kinetic energy (and vice versa).
Know how to cool systems by means of ionized liquids.
Construct liquid electrical generators.
Build propulsion devices without moving parts (EHD thrusters).
Add some more pseudoscience to our already-too-magical world: Designing air ionizers and claiming that they have all kind of health benefits.