We report on the observation of surface gravity wave turbulence at scales larger than the forcing ones in a large basin. In addition to the downscale transfer usually reported in gravity wave turbulence, an upscale transfer is observed, interpreted as the inverse cascade of weak turbulence theory. A steady state is achieved when the inverse cascade reaches a scale in between the forcing wavelength and the basin size, but far from the latter. This inverse cascade saturation, which depends on the wave steepness, is probably due to the emergence of nonlinear dissipative structures such as sharp-crested waves.
This investigation presents evidence of the relation between the dynamics of intense events in small-scale turbulence and the energy cascade. We use the generalised (Hölder) means to track the temporal evolution of intense events of the enstrophy and the dissipation in direct numerical simulations of isotropic turbulence. We show that these events are modulated by large-scale fluctuations, and that their evolution is consistent with a local multiplicative cascade, as hypothesised by a broad class of intermittency models of turbulence.
This paper analyses the turbulent energy cascade from the perspective of statistical mechanics, and relates inter-scale energy fluxes to statistical irreversibility and information-entropy production. The microscopical reversibility of the energy cascade is tested by constructing a reversible 3D turbulent system using a dynamic model for the sub-grid stresses. This system, when reversed in time, develops a sustained inverse cascade towards the large scales, evidencing that the characterisation of the inertial energy cascade must consider the possibility of an inverse regime. This experiment is…
Vortex annihilation and inverse cascades in two dimensional superfluid turbulence
我们研究了二维超流湍流，采用有效的描述有效的极限超流涡的密度是参数小。在足够低的温度下，有效的描述产生逆级联与柯尔莫哥洛夫能谱$E(k) \sim k^{-5/3}$。用$N(t)$表示涡的数目作为时间的函数，我们发现，涡的湮灭率的标度类似于$\dot N \sim N^{5/3}$的状态与反级联和$\dot N \sim N^2$的层流。
We investigate three-dimensional quantum turbulence as described by the Gross-Pitaevskii model using the analytical method exploited in the Onsager "ideal turbulence" theory. We derive the scale-independence of the scale-to-scale kinetic energy flux and establish a double-cascade scenario: at scales much larger than the mean intervortex $\ell_i$, the Richardson cascade becomes dominant, whereas at scales much smaller than $\ell_i$, another type of cascade is induced by quantum stress. We then evaluate the corresponding velocity power spectrum using a phenomenological argument. The relation bet…
We investigate a quite strong turbulence in a supercritical fluid near a gas-liquid critical point. Specifically, we consider a case in which the Kolmogorov scale is much smaller than the equilibrium correlation length $ξ$. Although equilibrium critical fluctuations are destroyed by turbulence, $ξ$ still provides a crossover length scale between two types of energy cascade. At scales much larger than $ξ$, the Richardson cascade becomes dominant, whereas at scales much smaller than $ξ$, another type of cascade, which we call the van der Waals cascade, is induced by density fluctuations. Experim…
We refute the criticism expressed in a Comment by Krstulovic, L'vov, and Nazarenko [arXiv:2107.10598] on our paper [Phys. Rev. E 103, 023106 (2021)]. We first show that quantization of circulation is not ignored in our analysis. Then, we propose a more sophisticated analysis to avoid a subtle problem with the regularity of the velocity field. We thus defend the main results of our paper, which predicts the double-cascade scenario where the quantum stress cascade follows the Richardson cascade. We also provide a conjecture on the relation between the Kelvin-wave cascade and the quantum stress c…
In this paper, we present an experimental investigation of the turbulent saturation of the flow driven by parametric resonance of inertial waves in a rotating fluid. In our set-up, a half-meter wide ellipsoid filled with water is brought to solid body rotation, and then undergoes sustained harmonic modulation of its rotation rate. This triggers the exponential growth of a pair of inertial waves via a mechanism called the libration-driven elliptical instability. Once the saturation of this instability is reached, we observe a turbulent state for which energy is injected into the resonant inerti…
We study the statistics of free-surface turbulence at large Reynolds numbers produced by direct numerical simulations in a fluid layer at different thickness with fixed characteristic forcing scale. We observe the production of a transient inverse cascade, with a duration which depends on the thickness of the layer, followed by a transition to three-dimensional turbulence initially produced close to the bottom, no-slip boundary. By switching off the forcing, we study the decaying turbulent regime and we find that it cannot be described by an exponential law. Our results show that boundary cond…
We study forced, rapildy rotating and stably stratified turbulence in an elongated domain using an asymptotic expansion at simultaneously low Rossby number $Ro\ll1$ and large domain height compared to the energy injection scale, $h=H/\ell_{in}\gg1$. The resulting equations depend on the parameter $λ=(h Ro )^{-1}$ and the Froude number $Fr$. An extensive set of direct numerical simulations (DNS) is performed to explore the parameter space $(λ,Fr)$. We show that a forward energy cascade occurs in one region of this space, and a split energy cascade outside it. At weak stratification (large $Fr$)…
Finite-temperature quantum turbulence is often described in terms of two immiscible fluids that can flow with a non-zero mean relative velocity. Such out-of-equilibrium state is known as counterflow superfluid turbulence. We report here the emergence of a counterflow-induced inverse energy cascade in three-dimensional superfluid flows by performing extensive numerical simulations of the Hall-Vinen-Bekarevich-Khalatnikov model. As the intensity of the mean counterflow is increased, an abrupt transition, from a fully three-dimensional turbulent flow to a quasi two-dimensional system exhibiting a…
In a recent paper [T. Tanogami Phys. Rev. E 103, 023106 ] proposes a scenario for quantum turbulence where the energy spectrum at scales smaller than the inter-vortex distance is dominated by a quantum stress cascade, in opposition to Kelvin wave cascade predictions. The purpose of the present comment is to highlight some physical issues in the derivation of the quantum stress cascade, in particular to stress that quantization of circulation has been ignored.
We performed numerical simulations of decaying quantum turbulence by using a generalized Gross-Pitaevskii equation, that includes a beyond mean field correction and a nonlocal interaction potential. The nonlocal potential is chosen in order to mimic He II by introducing a roton minimum in the excitation spectrum. We observe that at large scales the statistical behavior of the flow is independent of the interaction potential, but at scales smaller than the intervortex distance a Kelvin wave cascade is enhanced in the generalized model. In this range, the incompressible kinetic energy spectrum o…
A $p$-adic hydrodynamic type equation with two integrals of motion is proposed. It can be considered as a model cascade equation for energy dissipation in fully developed turbulence. Some of special cases of the proposed equation are detailed and it is shown that for a specific choice of parametrs they have stationary solutions that correspond to the 2/3 Kolmogorov-Obukhov law. Possible further studies of the proposed model are discussed.
A recent discovery about the inertial range of homogeneous and isotropic turbulence is the saturation of the scaling exponents $ζ_n$ for large $n$, defined via structure functions of order $n$ as $S_{n}(r)=\overline{(δ_r u)^{n}}=A(n)r^{ζ_{n}}$. We focus on longitudinal structure functions for $δ_r u$ between two positions that are $r$ apart in the same direction. In a previous paper (Phys.\ Rev.\ Fluids 6, 104604, 2021), we developed a theory for $ζ_n$, which agrees with measurements for all $n$ for which reliable data are available, and shows saturation for large $n$. Here, we derive expressi…
