TY - JOUR
T1 - Split energy–helicity cascades in three-dimensional homogeneous and isotropic turbulence
AU - Biferale, L.
AU - Musacchio, S.
AU - Toschi, F.
PY - 2013
Y1 - 2013
N2 - We investigate the transfer properties of energy and helicity fluctuations in fully developed homogeneous and isotropic turbulence by changing the nature of the nonlinear Navier–Stokes terms. We perform a surgery of all possible interactions, by keeping only those triads that have sign-definite helicity content. In order to do this, we apply an exact decomposition of the velocity field in a helical Fourier basis, as first proposed by Constantin & Majda (Commun. Math. Phys, vol. 115, 1988, p. 435) and exploited in great detail by Waleffe (Phys. Fluids A, vol. 4, 1992, p. 350), and we evolve the Navier–Stokes dynamics keeping only those velocity components carrying a well-defined (positive or negative) helicity. The resulting dynamics preserves translational and rotational symmetries but not mirror invariance. We give clear evidence that this three-dimensional homogeneous and isotropic chiral turbulence is characterized by a stationary inverse energy cascade with a spectrum Eback(k)~k-5/3 and by a direct helicity cascade with a spectrum Eforw(k)~k-7/3. Our results are important to highlight the dynamics and statistics of those subsets of all possible Navier–Stokes interactions responsible for reversal events in the energy-flux properties, and demonstrate that the presence of an inverse energy cascade is not necessarily connected to a two-dimensionalization of the flow. We further comment on the possible relevance of such findings to flows of geophysical interest under rotations and in thin layers. Finally we propose other innovative numerical experiments that can be achieved by using a similar decimation of degrees of freedom.
AB - We investigate the transfer properties of energy and helicity fluctuations in fully developed homogeneous and isotropic turbulence by changing the nature of the nonlinear Navier–Stokes terms. We perform a surgery of all possible interactions, by keeping only those triads that have sign-definite helicity content. In order to do this, we apply an exact decomposition of the velocity field in a helical Fourier basis, as first proposed by Constantin & Majda (Commun. Math. Phys, vol. 115, 1988, p. 435) and exploited in great detail by Waleffe (Phys. Fluids A, vol. 4, 1992, p. 350), and we evolve the Navier–Stokes dynamics keeping only those velocity components carrying a well-defined (positive or negative) helicity. The resulting dynamics preserves translational and rotational symmetries but not mirror invariance. We give clear evidence that this three-dimensional homogeneous and isotropic chiral turbulence is characterized by a stationary inverse energy cascade with a spectrum Eback(k)~k-5/3 and by a direct helicity cascade with a spectrum Eforw(k)~k-7/3. Our results are important to highlight the dynamics and statistics of those subsets of all possible Navier–Stokes interactions responsible for reversal events in the energy-flux properties, and demonstrate that the presence of an inverse energy cascade is not necessarily connected to a two-dimensionalization of the flow. We further comment on the possible relevance of such findings to flows of geophysical interest under rotations and in thin layers. Finally we propose other innovative numerical experiments that can be achieved by using a similar decimation of degrees of freedom.
U2 - 10.1017/jfm.2013.349
DO - 10.1017/jfm.2013.349
M3 - Article
SN - 0022-1120
VL - 730
SP - 309
EP - 327
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -