Transition of the scaling law in inverse energy cascade range caused by a nonlocal excitation of coherent structures observed in two-dimensional turbulent fields

摘要

We numerically investigate the inverse energy cascade range of two-dimensional Navier-Stokes turbulence.nOur focus is on the universality of the Kolmogorov’s phenomenology. In our direct numerical simulations,ntwo types of forcing processes, the random forcing and the deterministic forcing, are employed besides thensystematically varied numerical parameters.We first calculate the two-dimensional Navier-Stokes equations andnconfirm that results in the quasi steady state are consistent with the classical phenomenology for both types ofnforcing processes. It is also found that the difference in forcing process appears after the inverse energy cascadenrange reaches the system size; the dipole coherent vortices emerge and grow only when the random forcing isnadopted. Then we add a large-scale drag term to the Navier-Stokes equations to obtain the statistically stationarynstate. When the random forcing is used, the scaling exponent of the energy spectrum in the stationary state startsnto differ from the predicted −5/3 in the inverse energy cascade range as the infrared Reynolds number Rednincreases, where Red is defined as kf /kd with the forcing wave number kf and the large-scale drag wave numbernkd . That can be interpreted as a transition phenomenon in which the local maximum vorticity grows like an ordernparameter caused by excitation of strong coherent vortices. Strong coherent vortices emerge and grow after thenquasi steady state and destroy the scaling law when Red is over a critical value. These coherent vortices are notndue to the finite-size effect, unlike the dipole coherent vortices. On the other hand, when the deterministic forcingnis adopted, strong coherent vortices are hardly seen and the −5/3 scaling law holds independently of Red. Wenexamine the cases of the combination of both types of forcing processes and find that formation of such coherentnvortices is sensitive to the mechanism of the external forcing process as well as the numerical parameters. Severalntypes of large-scale drag terms are also tested and their insignificant influence on these qualitative properties isnrevealed.