Simple scheme generating an axisymmetrically anisotropic initial flow of incompressible turbulence using a normal random number vector

The present study introduces a simple scheme for generating an axisymmetrically anisotropic incompressible initial flow. In addition, the proposed scheme is used to examine the effects of kinetic energy conservation errors on the time evolution of the anisotropic initial flows. In the analysis of the present study, an inviscid flow is analyzed. In this inviscid flow, the kinetic energy characteristics are known analytically. The kinetic energy conservation error is obtained using the Crank-Nicolson (CN) method. The scheme of the present study generates an axisymmetrically anisotropic initial flow by obtaining the weights of normal random vector components using an anisotropic parameter. The analysis of the flow field is performed using a fourth-order differential scheme that explicitly conserves kinetic energy with a fourth-order Runge-Kutta scheme. Because of the kinetic energy conservation error, the kinetic energy obtained using the CN method increases with time. The magnitude of the initial anisotropy obtained by this scheme decreases with time. This result is only slightly affected by kinetic energy conservation errors. On the other hand, kinetic energy conservation error affects the magnitude of the pressure-strain correlation term.