Sagar Chakraborty
We use the more intuitive approach due to Kolmogorov (and subsequently, Landau in his text on fluid dynamics) to calculate some third-order structure functions for quasi-geostrophic turbulence for the forward cascade of pseudo-potential enstrophy and the inverse energy cascade in quasi-geostrophic turbulence.
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Rotating turbulence is commonly known for being dominated by geostrophic vortices that are invariant along the rotation axis and undergo inverse cascade. Yet, it has recently been shown to sustain fully three-dimensional states with a downscale energy cascade. In this letter, we investigate the statistical properties of three-dimensional rotating turbulence by the means of direct numerical simulations in a triply periodic box where geostrophic vortices are specifically damped. The resulting turbulent flow is an inertial wave turbulence that verifies the Zakharov-Kolmogorov spectrum derived ana…
The effect of domain anisotropy on the inverse cascade occurring within the geostrophic turbulence regime of rapidly rotating Rayleigh-Bénard convection (RRBC) is investigated. In periodic domains with square cross-section in the horizontal a domain-filling dipole state is present. For rectangular periodic domains a Kolmogorov-like flow consisting of a periodic array of alternating unidirectional jets with embedded vortices is observed, together with an underlying weak meandering transverse jet. Similar transitions occurring in weakly dissipative two-dimensional flows driven by externally impo…
We look at various correlation functions, which include those that involve both the velocity and the vorticity fields, in 2-D isotropic homogeneous decaying turbulence.We adopt the more intuitive approach due to Kolmogorov (and subsequently, Landau in his text on fluid dynamics) and show that how the 2-D turbulence results, obtainable using other methods, may be established in a simpler way.Also, some experimentally verifiable correlation functions in the dissipation range have been derived for the same system.The paper also showcases the inability of the Kolmogorov-Landau approach to get the …
We consider a 2-layer quasi-geostrophic ocean model where the upper layer is forced by a steady Kolmogorov wind stress in a periodic channel domain, which allows to mathematically study the nonlinear development of the resulting flow. The model supports a steady parallel shear flow as a response to the wind stress. As the maximal velocity of the shear flow (equivalently the maximal amplitude of the wind forcing) exceeds a critical threshold, the zonal jet destabilizes due to baroclinic instability and we numerically demonstrate that a first transition occurs. We obtain reduced equations of the…
The properties of rotating turbulence driven by precession are studied using direct numerical simulations and analysis of the underlying dynamical processes in Fourier space. The study is carried out in the local rotating coordinate frame, where precession gives rise to a background shear flow, which becomes linearly unstable and breaks down into turbulence. We observe that this precession-driven turbulence is in general characterized by coexisting two dimensional (2D) columnar vortices and three dimensional (3D) inertial waves, whose relative energies depend on the precession parameter $Po$. …
A phenomenological theory is proposed to analyze the asymptotic dynamics of perturbed inviscid Kolmogorov shear flows in two dimensions. The phase diagram provided by the theory is in qualitative agreement with numerical observations, which include three phases depending on the aspect ratio of the domain and the size of the perturbation: a steady shear flow, a stationary dipole, and four traveling vortices. The theory is based on a precise study of the inviscid damping of the linearized equation and on an analysis of nonlinear effects. In particular, we show that the dominant Landau pole contr…
Kolmogorov's theory for turbulence in 1941 is based on a hypothesis that small-scale statistics are uniquely determined by the kinematic viscosity and the mean rate of energy dissipation. Landau remarked that the local rate of energy dissipation should fluctuate in space over large scales and hence should affect small-scale statistics. Experimentally, we confirm the significance of this large-scale fluctuation, which is comparable to the mean rate of energy dissipation at the typical scale for energy-containing eddies. The significance is independent of the Reynolds number and the configuratio…
In Kolmogorov's phenomenological theory of turbulence, the energy spectrum in the inertial range scales with the wave number $k$ as $k^{-5/3}$ and extends up to a dissipation wave number $k_ν$, which is given in terms of the energy dissipation rate $ε$ and viscosity $ν$ by $k_ν\propto(ε/ν^3)^{1/4}$. This result leads to Landau's heuristic estimate for the number of degrees of freedom that scales as $\Re^{9/4}$, where $\Re$ is the Reynolds number. Here we consider the possibility of establishing a quantitative basis for these results from first principles. In particular, we examine the extent t…
A framework is developed to describe the two-point statistics of potential vorticity in rotating and stratified turbulence as described by the Boussinesq equations. The Karman-Howarth equation for the dynamics of the two-point correlation function of potential vorticity reveals the possibility of inertial-range dynamics in certain regimes in the Rossby, Froude, Prandtl and Reynolds number parameters. For the case of large Rossby and Froude numbers, and for the case of quasi-geostrophic dynamics, a linear scaling law with 2/3 prefactor is derived for the third-order mixed correlation between po…
We look at various correlation functions, which include those that involve both the velocity and the vorticity fields, in two-dimensional (2D) isotropic homogeneous unforced turbulence. We adopt the more intuitive approach due to Kolmogorov (and subsequently, Landau in his text on fluid dynamics) and show that how the 2D turbulence's results, obtainable using other methods, may be established in a simpler way. Same method is used to calculate some third-order structure functions for quasi-geostrophic (QG) turbulence for the forward cascade of pseudo-potential enstrophy and the inverse energy c…
Spectral Reconstruction for Under-Resolved Turbulence Measurements Using a Variational Cutoff Dissipation Model
本文提出一种变分截断耗散模型，用于解决低分辨率湍流测量中湍流动能低估问题，通过硬性能量截断实现频谱重建，提升流体诊断的准确性。
We revisit the issue of whether thermal fluctuations are relevant for incompressible fluid turbulence, and estimate the scale at which they become important. As anticipated by Betchov in a prescient series of works more than six decades ago, this scale is about equal to the Kolmogorov length, even though that is several orders of magnitude above the mean free path. This result implies that the deterministic version of the incompressible Navier-Stokes equation is inadequate to describe the dissipation range of turbulence in molecular fluids. Within this range, the fluctuating hydrodynamics equa…
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