Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties

Numerical simulations of forced isotropic turbulence are most often formulated in Fourier space, where forcing is applied to low-wavenumber modes. For applications in physical space, low-wavenumber forcing is difficult to implement. The linear forcing recently proposed by Lundgren “Linearly forced isotropic turbulence,” in Annual Research Briefs (Center for Turbulence Research, Stanford, 2003), pp. 461–473, where a force proportional to velocity is applied, is an attractive alternative but not much is known about its properties. Using numerical experimentation, various properties of the linear forcing are explored: (i) it is shown that when implemented in physical space, linear forcing gives the same results as in spectral implementations; (ii) it is shown that the linearly forced system converges to a stationary state that depends on domain size and Reynolds number, but not on the spectral shape of the initial condition; (iii) it is also shown that the extent of Kolmogorov −5∕3 range is similar to that achieved using the standard band-limited forcing schemes but the integral length scale l=urms3∕ε is smaller, thus reducing the effective scaling range for a given resolution. It is concluded that linear forcing is a useful alternative method that does not require transformation to Fourier space and is easily integrated into physical-space numerical codes.