Turbulent burning velocity and thermodiffusive instability of premixed flames.

Reported in the paper are results of unsteady three-dimensional direct numerical simulations of laminar and turbulent, lean hydrogen-air, complex-chemistry flames propagating in forced turbulence in a box. To explore the eventual influence of thermodiffusive instability of laminar flames on turbulent burning velocity, (i) a critical length scale Λ_{n} that bounds regimes of unstable and stable laminar combustion is numerically determined by gradually decreasing the width Λ of computational domain until a stable laminar flame is obtained, and (ii) simulations of turbulent flames are performed by varying the width from Λ<Λ_{n} (in this case, the instability is suppressed) to Λ>Λ_{n} (in this case, the instability may grow). Moreover, simulations are performed either using mixture-averaged transport properties (low Lewis number flames) or setting diffusivities of all species equal to heat diffusivity of the mixture (equidiffusive flames), with all other things being equal. Obtained results show a significant increase in turbulent burning velocity U_{T} when the boundary Λ=Λ_{n} is crossed in weak turbulence, but almost equal values of U_{T} are computed at Λ<Λ_{n} and Λ>Λ_{n} in moderately turbulent flames characterized by a Karlovitz number equal to 3.4 or larger. These results imply that thermodiffusive instability of laminar premixed flames substantially affects burning velocity in weak turbulence only, in line with a simple criterion proposed by Chomiak and Lipatnikov (Phys. Rev. E 107, 015102, (2023)10.1103/PhysRevE.107.015102).

Model-free forecasting of partially observable spatiotemporally chaotic systems.

Reservoir computing is a powerful tool for forecasting turbulence because its simple architecture has the computational efficiency to handle high-dimensional systems. Its implementation, however, often requires full state-vector measurements and knowledge of the system nonlinearities. We use nonlinear projector functions to expand the system measurements to a high dimensional space and then feed them to a reservoir to obtain forecasts. We demonstrate the application of such reservoir computing networks on spatiotemporally chaotic systems, which model several features of turbulence. We show that using radial basis functions as nonlinear projectors enables complex system nonlinearities to be captured robustly even with only partial observations and without knowing the governing equations. Finally, we show that when measurements are sparse or incomplete and noisy, such that even the governing equations become inaccurate, our networks can still produce reasonably accurate forecasts, thus paving the way towards model-free forecasting of practical turbulent systems.

Identifying the pattern of breakdown in a laminar-turbulent transition via binary sequence statistics and cellular-automaton simulations.

The laminar-turbulent transition induced by two-dimensional steplike roughness is investigated focusing on the pattern of breakdown. The statistics of the turbulent burst rate is found to be significantly different from the prediction of the classical theory. A systematic investigation of the pattern of breakdown is motivated by this phenomenon. It is identified with heuristic analysis that a pattern of distributed breakdown is responsible for the deviation, in contrast to the concentrated breakdown hypothesis in the classical theory. The pattern indicates that the steps probably induced a bypass transition in present experimental setup, which is different from the current understanding about the step-induced transition. Cellular-automaton simulations are carried out to validate the heuristic analysis. The influences of quasiconcentration and non-Poisson process in spot generation on the breakdown statistics are also discussed based on the simulation results.

Effect of shock waves on the statistics and scaling in compressible isotropic turbulence.

The statistics and scaling of compressible isotropic turbulence in the presence of large-scale shock waves are investigated by using numerical simulations at turbulent Mach number M_{t} ranging from 0.30 to 0.65. The spectra of the compressible velocity component, density, pressure, and temperature exhibit a k^{-2} scaling at different turbulent Mach numbers. The scaling exponents for structure functions of the compressible velocity component and thermodynamic variables are close to 1 at high orders n≥3. The probability density functions of increments of the compressible velocity component and thermodynamic variables exhibit a power-law region with the exponent -2. Models for the conditional average of increments of the compressible velocity component and thermodynamic variables are developed based on the ideal shock relations and are verified by numerical simulations. The overall statistics of the compressible velocity component and thermodynamic variables are similar to one another at different turbulent Mach numbers. It is shown that the effect of shock waves on the compressible velocity spectrum and kinetic energy transfer is different from that of acoustic waves.

Energy cascade and its locality in compressible magnetohydrodynamic turbulence.

We investigate energy transfer across scales in three-dimensional compressible magnetohydrodynamic (MHD) turbulence, a model often used to study space and astrophysical plasmas. Analysis shows that kinetic and magnetic energies cascade conservatively from large to small scales in cases with varying degrees of compression. With more compression, energy fluxes due to pressure dilation and subscale mass flux are greater, but conversion between kinetic and magnetic energy by magnetic line stretching is less efficient. Energy transfer between the same fields is dominated by local contributions regardless of compressive effects. In contrast, the conversion between kinetic and internal energy by pressure dilation is dominated by the largest scale contributions. Energy conversion between the velocity and magnetic fields is weakly local.

Intermittency, nonlinear dynamics and dissipation in the solar wind and astrophysical plasmas.

An overview is given of important properties of spatial and temporal intermittency, including evidence of its appearance in fluids, magnetofluids and plasmas, and its implications for understanding of heliospheric plasmas. Spatial intermittency is generally associated with formation of sharp gradients and coherent structures. The basic physics of structure generation is ideal, but when dissipation is present it is usually concentrated in regions of strong gradients. This essential feature of spatial intermittency in fluids has been shown recently to carry over to the realm of kinetic plasma, where the dissipation function is not known from first principles. Spatial structures produced in intermittent plasma influence dissipation, heating, and transport and acceleration of charged particles. Temporal intermittency can give rise to very long time correlations or a delayed approach to steady-state conditions, and has been associated with inverse cascade or quasi-inverse cascade systems, with possible implications for heliospheric prediction.

Is the Kelvin theorem valid for high Reynolds number turbulence?

The Kelvin-Helmholtz theorem on conservation of circulation is supposed to hold for ideal inviscid fluids and is believed to be play a crucial role in turbulent phenomena. However, this expectation does not take into account singularities in turbulent velocity fields at infinite Reynolds number. We present evidence from numerical simulations for the breakdown of the classical Kelvin theorem in the three-dimensional turbulent energy cascade. Although violated in individual realizations, we find that circulation is still conserved in some average sense. For comparison, we show that Kelvin's theorem holds for individual realizations in the two-dimensional enstrophy cascade, in agreement with theory. The turbulent "cascade of circulations" is shown to be a classical analogue of phase slip due to quantized vortices in superfluids, and various applications in geophysics and astrophysics are outlined.

Physical mechanism of the two-dimensional inverse energy cascade.

We study the physical mechanisms of the two-dimensional inverse energy cascade using theory, numerics, and experiment. Kraichnan's prediction of a -5/3 spectrum with constant, negative energy flux is verified in our simulations of 2D Navier-Stokes equations. We observe a similar but shorter range of inverse cascade in laboratory experiments. Our theory predicts, and the data confirm, that inverse cascade results mainly from turbulent stress proportional to small-scale strain rotated by 45 degrees. This "skew-Newtonian" stress is explained by the elongation and thinning of small-scale vortices by large-scale strain which weakens their velocity and transfers their energy upscale.