Boundary Condition

Now let us discuss about the boundary conditions.

Figure 25.1

Consider Fig. 25.1, we shall call B1 and B3 as bottom wall. Similar kind of boundary conditions are aplicable on B1 and B3. At the nodal points which are coinciding with the solid wall we can directly put and Since the line B1-B2-B3 is a streamline, any constant value of on it is acceptable. The usual choice is The wall vorticity is an extremely important evaluation. At no-slip boundaries, is produced. It is the diffusion and subsequent advection of the wall produced vorticity which governs the physics. Using boundary B1 as an example, we expend by a Taylor series as

(25.1)

But by no-slip condition and

Again,

Along the wall, [because constant ].

Thus,

Substituting this into (25.1) and solving for with gives

More general from regardless of the wall orientation or value of at the boundary, it can be written as

(25.2)

where is the distance from to () in the normal direction [ denotes at the wall].