Single-scale two-dimensional-three-component generalized-Beltrami-flow solutions of incompressible Navier-Stokes equations

Chai, Jin; Wu, Tong; Fang, Le

doi:10.1016/j.physleta.2020.126857

Cited by 7 publications

(3 citation statements)

References 33 publications

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“…In particular, a triad phase, φ 1 ( p) + φ 1 ( q) − φ 1 ( k), is explicitly represented on the right-hand side, indicating the link between S k and the phase of velocities (see Refs. [11,[38][39][40] for more discussions). This expression explicitly illustrates that both the amplitudes and the phases can affect the evolution of S k .…”

Section: Discussionmentioning

confidence: 99%

“…For example, a Gaussian random field yields null S k ; an incompressible isotropic two-dimensional turbulence also leads to null S k (see Refs. [8,9] for discussions); and in some typical initial conditions the energy transfer is suppressed in a very short time period [10,11], while S k is accordingly near zero. We also observed positive S k when reversing the velocities in a fully developed three-dimensional turbulence [12,13], which leads to a strong nonequilibrium procedure afterwards [14][15][16].…”

Section: Introductionmentioning

confidence: 98%

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Existence of positive skewness of velocity gradient in early transition

et al. 2021

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The present study uses direct numerical simulations to calculate two different transitional flows from laminar flow to turbulence, that is, the two-scale wake flow and the two-dimensional Reyleigh-Taylor unstable flow, respectively. Both results show that the skewness of the longitudinal velocity gradient, S k , can become positive in the early transition stage, which is beyond our expectation since the turbulent equilibrium state always implies negative values of S k . These phenomena are explained analytically by considering only two dominant Fourier modes with harmonic relations. It is illustrated that the sign of S k is not only affected by the amplitudes of the perturbation velocities, but also related to their phases. We expect that the present results will be helpful for understanding the formation of turbulent equilibrium state and for constructing a new measurable criterion of the transition onset.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Existence of positive skewness of velocity gradient in early transition

et al. 2021

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“…This idealisation admits a direct analytical study of the impact of energy input through its impact on various explicit flows. Indeed, explicit flows are frequently used as a tool for benchmarking analytical and numerical studies in this and other contexts, e.g., [3,5,6,11,12,16], and also for turbulence studies, e.g. [7,10,13].…”

Section: Introductionmentioning

confidence: 99%

Geophysical fluid models with simple energy backscatter: explicit flows and unbounded exponential growth

Prugger,

Rademacher,

Yang

2021

Preprint

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Motivated by numerical schemes for large scale geophysical flow, we consider the rotating shallow water and Boussinesq equations on the whole space with horizontal kinetic energy backscatter source terms built from constant negative viscosity and stabilising hyperviscosity. We study the impact of this energy input through various explicit flows, which are simultaneously solving the nonlinear equations and the linear equations that arise upon dropping the transport nonlinearity, i.e., the linearisation in the zero state. These include barotropic, parallel and Kolmogorov flows as well as monochromatic inertia gravity waves. With focus on stable stratification we find that the backscatter generates numerous solutions of this type that grow exponentially and unboundedly, also with vertical structure. This signifies the possibility of undesired energy concentration into specific modes due to the backscatter. Families of steady state flows of this type arise as well and superposition principles in the nonlinear equations provide explicit sufficient conditions for instability of some of these. For certain steady barotropic flows of this type we provide numerical evidence of eigenmodes whose growth rates are proportional to the amplitude factor. For all other arising steady solutions we prove this is not possible.

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Exact time scale of energy exchange in triad interactions of homogeneous isotropic turbulence

Fang

Wang

2021

Physics of Fluids

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We solve analytically the period of a single triad interaction of homogeneous isotropic turbulence. Comparing with the traditional concept of the timescale of energy transfer, we found that this period is a timescale of energy exchange among the three wave vectors of a triad. Quantitatively, the timescale of energy exchange is usually longer if the equilibrium dissipation law is satisfied; however, when energy transfer is suppressed, the energy exchange becomes dominant. We extract the periods in typical numerical experiments of triad interactions and show that they are in good agreement with theoretical predictions. This picture implies that energy exchange corresponds to oscillation, while energy transfer corresponds to damping, and the damping rate is correlated with the oscillation. The present results of the timescale of energy transfer are expected to be applied in nonequilibrium turbulent flows.

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Single-scale two-dimensional-three-component generalized-Beltrami-flow solutions of incompressible Navier-Stokes equations

Cited by 7 publications

References 33 publications

Existence of positive skewness of velocity gradient in early transition

Existence of positive skewness of velocity gradient in early transition

Geophysical fluid models with simple energy backscatter: explicit flows and unbounded exponential growth

Exact time scale of energy exchange in triad interactions of homogeneous isotropic turbulence

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