Effects of helicity on dissipation in homogeneous box turbulence

The dimensionless dissipation coefficient $\beta=\varepsilon L/U^3$ is an important characteristic of statistically stationary homogeneous turbulence. In studies of $\beta$, the external force is typically isotropic and large-scale, and its helicity $H_f$ either zero or not measured. Here, we study the dependence of $\beta$ on $H_f$ and find that it decreases $\beta$ by up to 10$\%$ for both isotropic forces and shear flows. The numerical finding is supported by static and dynamical upper bound theory. Both show a relative reduction similar to the numerical results. That is, the qualitative and quantitative dependence of $\beta$ on the helicity of the force is well captured by upper bound theory. Consequences for the value of the Kolmogorov constant and theoretical aspects of turbulence control and modelling are discussed in connection with the properties of the external force. In particular, the eddy viscosity in large eddy simulations of homogeneous turbulence should be decreased by about 10$\%$ in case of strongly helical forcing.Comment: postprint versio

Dynamic feedback control through wall suction in shear flows

Flow control is of interest in many open and wall-bounded shear flows in order to reduce drag or to avoid sudden large fluctuations that may lead to material failure. An established means of control is the application of suction through a porous wall. Here, we combine suction with a feedback strategy whereby the suction velocity is adjusted in response to either the kinetic energy or the shear stress at the bottom wall. The control procedure is then used in an attempt to stabilize invariant solutions and to carry out direct numerical simulations with a prescribed value of the friction coefficient.Comment: Proceedings in Applied Mathematics and Mechanics (in press

Linear stability analysis of purely elastic travelling wave solutions in pressure driven channel flows

Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a sub-critical bifurcation from infinity. These travelling-wave solutions were suggested to organise the phase-space dynamics of purely elastic and elasto-inertial chaotic channel flows. Here, we consider a wide range of parameters, covering the purely-elastic and elasto-inertial cases, and demonstrate that the two-dimensional travelling-wave solutions are unstable when embedded in sufficiently wide three-dimensional domains. Our work demonstrates that studies of purely elastic and elasto-inertial turbulence in straight channels require three-dimensional simulations, and no reliable conclusions can be drawn from studying strictly two-dimensional channel flows.Comment: 10 pages, 5 page

Nonuniversal transition to condensate formation in two-dimensional turbulence

The occurrence of system-scale coherent structures, so-called condensates, is a well-known phenomenon in two-dimensional turbulence. Here, the transition to condensate formation is investigated as a function of the magnitude of the force and for different types of forcing. Random forces with constant mean energy input lead to a supercritical transition, while forcing through a small-scale linear instability results in a subcritical transition with bistability and hysteresis. That is, the transition to condensate formation in two-dimensional turbulence is nonuniversal. For the supercritical case we quantify the effect of large-scale friction on the value of the critical exponent and the location of the critical point

Self-organisation processes in (magneto)hydrodynamic turbulence

Self-organising processes occurring in isotropic turbulence and homogeneous magnetohydrodynamic (MHD) turbulence are investigated in relation to the stability of helical flow structures. A stability analysis of helical triad interactions shows that compared to hydrodynamics, equilibria of the triadic evolution equations have more instabilities with respect to perturbations on scales larger than the characteristic scale of the system. Some of these instabilities can be mapped to Stretch-Twist-Fold dynamo action and others to the inverse cascade of magnetic helicity. High levels of cross-helicity are found to constrain small-scale instabilities more than large scale instabilities and are thus expected to have an asymmetric damping effect on forward and inverse energy transfer. Results from a numerical investigation into the influence of helicity on energy transfer and dissipation are consistent with this observation. The numerical work also confirms the predictions of an approximate method describing the Reynolds number dependence of the dimensionless dissipation coefficient for MHD turbulence. These predictions are complemented by the derivation of mathematically rigorous upper bounds on the dissipation rates of total energy and cross-helicity in terms of applied external forces. Large-scale helical flows are also found to emerge in relaminarisation events in direct numerical simulations of isotropic hydrodynamic turbulence at low Reynolds number, where the turbulent fluctuations suddenly collapse in favour of a large-scale helical flow, which was identified as a phase-shifted ABC-flow. A statistical investigation shows similarities to relaminarisation of localised turbulence in wall-bounded parallel shear flows. The turbulent states have an exponential survival probability indicating a memoryless process with a characteristic lifetime, which is found to depend super-exponentially on Reynolds number akin to well-established results for pipe and plane Couette flow. These and further similarites suggest that the phase space dynamics of isotropic turbulence and wall-bounded shear flows are qualitatively similar and that the relaminarisation of isotropic turbulence can also be explained by the escape from a chaotic saddle

Effects of Forcing Mechanisms on the Multiscale Properties of Magnetohydrodynamics

We performed numerical simulations to study the response of magnetohydrodynamics (MHD) to large-scale stochastic forcing mechanisms parametrized by one parameter, $0 \le a \le1$, going from direct injection on the velocity field ($a = 1$) to stirring acts on the magnetic field only ($a = 0$). We study the multi-scale properties of the energy transfer, by splitting the total flux in channels mediated by (i) the kinetic non-linear advection, (ii) the Lorentz force, (iii) the magnetic advection and (iv) magnetic stretching term. We further decompose the fluxes in two sub-channels given by heterochiral and homochiral components in order to distinguish forward, inverse and flux-loop cascades. We show that there exists a quasi-singular role of the magnetic forcing mechanism for $a \sim 1$: a small injection on the magnetic field $a < 1$ can strongly deplete the mean flux of kinetic energy transfer throughout the kinetic non-linear advection channel. We also show that this negligible mean flux is the result of a flux-loop balance between heterochiral (direct) and homochiral (inverse) transfers. Conversely, both homochiral and heterochiral channels transfer energy forward for the other three channels. Cross exchange between velocity and the magnetic field is reversed around $a = 0.4$ and except when $a \sim 1$ we always observe that heterochiral mixed velocity-magnetic energy triads tend to move energy from magnetic to velocity fields. Our study is an attempt to further characterize the multi-scale nature of MHD dynamics, by disentangling different properties of the total energy transfer mechanisms, which can be useful for improving sub-grid-modelling

Sudden Relaminarization and Lifetimes in Forced Isotropic Turbulence

We demonstrate an unexpected connection between isotropic turbulence and wall-bounded shear flows. We perform direct numerical simulations of isotropic turbulence forced at large scales at moderate Reynolds numbers and observe sudden transitions from a chaotic dynamics to a spatially simple flow, analogous to the laminar state in wall bounded shear flows. We find that the survival probabilities of turbulence are exponential and the typical lifetimes increase superexponentially with the Reynolds number. Our results suggest that both isotropic turbulence and wall-bounded shear flows qualitatively share the same phase-space dynamics.Comment: 6 pages, 8 figures including supplementary materia