The energy cascade as the origin of intense events in small-scale turbulence

Abstract

This work presents evidence of the relation between the dynamics of intense events in the dissipative range of turbulence and the energy cascade. The generalised (Hölder) means are used to construct signals that track the temporal evolution of intense enstrophy and dissipation events in direct numerical simulations of isotropic turbulence. These signals are remarkably time-correlated with the average dissipation signal, and with its large-scale surrogate, despite describing only a small fraction of the flow domain, and they precede the dissipation signal with a temporal advancement that grows with their intensity and that scales in integral time units. Interpreted from a causal perspective, these results point to the energy cascade as the driver of the intense events in the dissipative range. Moreover, it is shown that the temporal advancements of the generalised means are consistent with a local energy cascade, whereby eddies cascade in a time proportional to their turnover time, causing intense eddies to reach the dissipative scales before weak eddies. These results shed light on the dynamics of intense and extreme events in small-scale turbulence, and provide empirical support to the phenomenological foundations of a broad class of intermittency models based on the turbulence cascade.

Characterizing the Role of Non‐Linear Interactions in the Transition to Submesoscale Dynamics at a Dense Filament

“…For example, the rate of change of vorticity in an adiabatic system is $$$\frac{D\zeta }{Dt}=-f\delta -\delta \zeta -{w}_{x}{v}_{z}+{w}_{y}{u}_{z}.$$$ Only the first term on the right hand side, which does not involve a feedback, is present in a quasigeostrophic system. In addition, at the submesoscale the inertial term in the equations of motion ( u ⋅∇ u ∼ U 2 / L ) is of the same order as the Coriolis term ( uf ∼ Uf ), facilitating cross‐scale kinetic energy transfers (Johnson, 2020; Vela‐Martín, 2022).…”

“…Only the first term on the right hand side, which does not involve a feedback, is present in a quasigeostrophic system. In addition, at the submesoscale the inertial term in the equations of motion (u ⋅∇u ∼ U 2 /L) is of the same order as the Coriolis term (uf ∼ Uf), facilitating cross-scale kinetic energy transfers (Johnson, 2020;Vela-Martín, 2022).…”

Development of a multi-layer network model for characterizing energy cascade behavior on turbulent mixing

“…The partial differential equation is employed in the prototype model to investigate the irreversibility of the energy cascade, and the nonstationary interaction is introduced in it with the application of the nonlinear term [Josserand et al (2017)]. The generalized Holder means are used to study the relationship between the energy cascade and the strong burst events in the dissipative range [Vela-Martin (2022)]. The multifractal method is utilized to assess the dependence of energy cascade with dissipation in the Northwest Atlantic Ocean [Isern-Fontanet and Turiel (2021)].…”

“…Properties of the ECMN and weighted singlelayer network (WSLN) allow the exploration of multi-scale interaction in the energy cascade. Researches have supported the relationship between dissipation and energy cascade [Cardesa et al (2015); Cardesa et al (2017); Ballouz et al (2020); Vela-Martin (2022)]. Therefore, a network structure coefficient k based on topological framework is proposed to estimate the energy transfer strength in turbulent mixing and to validate the effectiveness of ECMN.…”

Turbulence via intermolecular potential: Uncovering the origin

“…Subsequently, numerous attempts to explain the physical nature of turbulence have been made throughout the twentieth century (for a detailed bibliography, refer, for example, to the books by Chorin [2] or Frisch [3]), yet, the reason for such a spontaneous manifestation of turbulence in an initially laminar flow remained unknown thus far. In practice, turbulent-like motions in numerically simulated flows are created via deliberate perturbations even in relatively recent works [4][5][6][7]. Such a notorious inability of the conventional equations of fluid mechanics to produce spontaneous turbulent solutions at high Reynolds numbers suggests that a key physical effect, which is responsible for the development of turbulence, is missing from them.…”