A fluid can be thought of as a collection of small particles moving
beside each other. Instead of following each of these particles individually,
we shall rather divide the space where they move
into imaginary small cubes
having a volume of, say, 
. At a given time, we can
(in principle) make measurements of the average velocity, pressure and density
of the fluid in each of the cubes. This procedure give a description
of the state of the system of the fluid. In the ideal limit where we could take
the cubes arbitrarily small, the fluid is described as a continuous
medium. The equation of evolutions (based on Newton's equations) and the fact
that matter is not created or annihilated during the fluid motion, can
be expressed in terms of partial differential equations that we will
not attempt to describe here (see introduction).
A fluid is in general viscous. This means that if a source of energy is not used to sustain the motion, the fluid will ultimately end up being at rest. In the example of a layer of fluid heated from below, the fluid at the bottom becomes warmer, less dense and tends to move to the upper part of the layer. If a sufficiently large difference of temperature is applied, convection rolls develop. When the difference of temperature is just enough to allow convection rolls, the velocities are time-independent. This type of fluid motion is called a steady flow. Despite the fact that we need a very large number of variables to describe the state of the system, we can represent a steady flow as a point in this large (ideally infinite) dimensional space. When the difference of temperature is increased, periodic time-dependent patterns appear. When the difference of temperature is further increased, intricated time-dependent motion develop. This sequence of changes is called the onset of turbulence.