Governing Equations and Structure of Turbulent Flows

The unsteady Navier-Stokes equations are generally considered to govern turbulent flows in the continuum regime. If this is the case, one might wonder why turbulent flows cannot be solved numerically as easily as laminar flows. The main problem is that the extremely small time and space scales of the turbulent motion result in a large number of grid points and small time steps. Direct numerical computation of turbulent flows for engineering purpose is therefore not yet practical because of computer limitations. Authorities disagree as to when computer technologies will have advanced to the point where turbulent flow calculations can be made from first principles (see Chapter 8). Some claim that for practical problems it will never be possible to resolve all the fine-scale flow structures with numerical solutions of the unsteady Navier-Stokes equations. For the remainder of this century the most advanced approach will likely involve solving the time-dependent Navier-Stokes equations for the evolution of the large eddies, which are responsible for most of the momentum transport, but modeling the smallest, subgrid-scale eddies. This approach is generally referred to as “large-eddy simulation.”, which will be discussed in greater details in Chapter 8.