Resonant interactions in rotating homogeneous three-dimensional turbulence.

*(English)*Zbl 1097.76033The purpose is to investigate the limit of rapidly rotating three-dimensional turbulence, where resonant interactions dominate at leading order and two-dimensional turbulence will be achieved. The authors present numerical simulations of forced homogeneous rotating turbulence to explore quantitatively the long-time effects of resonant interactions on the two-dimensionalization as \(Ro\to \infty,\) \(Ro\) being the Rossby number.

The first section is an introduction concerning the large-scale flows which are greatly affected by rotations, the resonant wave theory, and the characterization of turbulent flows under rapid rotation from the point of view of Reynolds number and Rossby number, respectively. The second section represents a review of the resonant wave theory of rapidly rotating fluids, including the rigorous mathematical results.

Section three concerns numerical simulations and analysis for rotating Navier-Stokes equations in a \(128^3\) periodic box with a forcing given by \(f_i(k,t)=\varepsilon_{k,i}/\widehat u_i(k,t)^*\), where \(\widehat u_i(k,t)^*\) is the conjugate of Fourier component \(\widehat u_i(k,t),\) \(\varepsilon_{k,i}\) are the energy input rates and \(k\) is the wavenumber vector. This section is divided into three sub-sections. The first one focuses on the energy spectra and transfer, the second is related to the dynamics of slow modes, and the last one is devoted to fast mode interactions. The authors discuss numerical schemes and present the simulation results to investigate the mechanism of two-dimensionalization in rotating turbulence and to study the role of resonant triads.

Section four presents conclusions of the work.

The first section is an introduction concerning the large-scale flows which are greatly affected by rotations, the resonant wave theory, and the characterization of turbulent flows under rapid rotation from the point of view of Reynolds number and Rossby number, respectively. The second section represents a review of the resonant wave theory of rapidly rotating fluids, including the rigorous mathematical results.

Section three concerns numerical simulations and analysis for rotating Navier-Stokes equations in a \(128^3\) periodic box with a forcing given by \(f_i(k,t)=\varepsilon_{k,i}/\widehat u_i(k,t)^*\), where \(\widehat u_i(k,t)^*\) is the conjugate of Fourier component \(\widehat u_i(k,t),\) \(\varepsilon_{k,i}\) are the energy input rates and \(k\) is the wavenumber vector. This section is divided into three sub-sections. The first one focuses on the energy spectra and transfer, the second is related to the dynamics of slow modes, and the last one is devoted to fast mode interactions. The authors discuss numerical schemes and present the simulation results to investigate the mechanism of two-dimensionalization in rotating turbulence and to study the role of resonant triads.

Section four presents conclusions of the work.

Reviewer: R. Militaru (Craiova)