Linear forcingin numerical simulations of isotropic turbulence: physical space implementations and convergence properties

C. Rosales & C. Meneveau

Department of Mechanical Engineering, Center for Environmental and Applied Fluid Mechanics The Johns Hopkins University, Baltimore MD 21218

ABSTRACT:

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, 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 $\ell=u^{3}_{\rr}/\varepsilon$ 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.

(2005), Phys. Fluids, 17, 095106.

full pdf article -- (©AIP, see http://ojps.aip.org/phf)

Reused with permission from Carlos Rosales, Physics of Fluids, 17, 095106 (2005). Copyright 2005, American Institute of Physics.