On the Formulation of Lagrangian Stochastic Models for Geophysical Turbulent Flows

On the Well-Mixed Quasi-One-Dimensional Formulation of Lagrangian Stochastic Models for Turbulent Relative Dispersion

This paper has been withdrawn by the author due to a crucial error in the formulation.

Turbulent fluxes of entropy and internal energy in temperature stratified flows

We derive equations for the mean entropy and the mean internal energy in the low-Mach-number temperature stratified turbulence (i.e., for turbulent convection or stably stratified turbulence), and show that turbulent flux of entropy is given by ${\bf F}_s=\overlineρ \, \overline{{\bf u} s}$, where $\overlineρ$ is the mean fluid density, $s$ are fluctuations of entropy and overbars denote averaging over an ensemble of turbulent velocity field, ${\bf u}$. We demonstrate that the turbulent flux of entropy is different from the turbulent convective flux, ${\bf F}_c=\overline{T} \, \overlineρ \, \o…

Role of Coherent Eddies in Potential Vorticity Transport in Two-layer Quasigeostrophic Turbulence

The transport by materially coherent eddies is studied in a two-layer quasigeostrophic model of geophysical turbulence. The coherent eddies are identified by closed contours of the Lagrangian-averaged vorticity deviation obtained from Lagrangian particles advected by the flow. A series of flow regimes with different bottom friction strengths are considered---it is found that coherent eddies become more prevalent and longer-lasting as the strength of the bottom drag increases. These coherent eddies, with average core radius close to the deformation radius, propagate zonally with speeds close to…

Lagrangian views on turbulent mixing of passive scalars

The Lagrangian view of passive scalar turbulence has recently produced interesting results and interpretations. Innovations in theory, experiments, simulations and data analysis of Lagrangian turbulence are reviewed here in brief. Part of the review is closely related to the so-called Kraichnan model for the advection of the passive scalar in synthetic turbulence. Possible implications for a better understanding of the passive scalar mixing in Navier-Stokes turbulence are also discussed.

Geophysical turbulence and the duality of the energy flow across scales

The ocean and the atmosphere, and hence the climate, are governed at large scale by interactions between pressure gradient, Coriolis and buoyancy forces. This leads to a quasi-geostrophic balance in which, in a two-dimensional-like fashion, the energy injected by solar radiation, winds or tides goes to large scales in what is known as an inverse cascade. Yet, except for Ekman friction, energy dissipation and turbulent mixing occur at small scale implying the formation of such scales associated with breaking of geostrophic dynamics through wave-eddy interactions \cite{ledwell_00, vanneste_13} o…

极端垂直气流作为稳定分层湍流中拉格朗日扩散的驱动因素

Extreme vertical drafts as drivers of Lagrangian dispersion in stably stratified turbulent flows

本研究利用数值模拟探讨了极端垂直气流对稳定分层湍流中拉格朗日粒子对相对扩散的加速作用，并量化了其与经典Richardson标度的偏差，对大气海洋混合及污染物输运具有重要意义。

Finite-time Lagrangian transport analysis: Stable and unstable manifolds of hyperbolic trajectories and finite-time Lyapunov exponents

We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval. A major motivation for the consideration of this problem arises from the desire to study transport and mixing problems in geophysical flows where the flow is obtained from a numerical solution, on a finite space-time grid, of an appropriate partial differential equation model for the velocity field. Of particular interest is the characterisation, location, and evolution of "transport barriers" in the flow, i.e…

直接拉格朗日跟踪模拟垂直发展湍流云中液滴生长

Direct Lagrangian tracking simulation of droplet growth in vertically-developing turbulent cloud

本文基于直接数值模拟与拉格朗日粒子跟踪开发了新的云微物理模型，研究湍流对液滴生长的影响，揭示了湍流促进碰撞合并及降水形成的作用。

Deep learning for Lagrangian drift simulation at the sea surface

We address Lagrangian drift simulation in geophysical dynamics and explore deep learning approaches to overcome known limitations of state-of-the-art model-based and Markovian approaches in terms of computational complexity and error propagation. We introduce a novel architecture, referred to as DriftNet, inspired from the Eulerian Fokker-Planck representation of Lagrangian dynamics. Numerical experiments for Lagrangian drift simulation at the sea surface demonstrates the relevance of DriftNet w.r.t. state-of-the-art schemes. Benefiting from the fully-convolutional nature of Drift-Net, we expl…

Interaction of a monopole vortex with an isolated topographic feature in a three-layer geophysical flow

In the frame of a three-layer quasi-geostrophic analytical model of a $f$-plane geophysical flow, Lagrangian advection being induced by the interaction of a monopole vortex with an isolated topographic feature is addressed. Two different cases when the monopole locates either within the upper or the middle layer are of our interest. In the bottom layer, there is a delta function topographic feature, which generates a closed recirculation region in its vicinity due to the background flow. This recirculation region extends to the middle and upper layers, and it plays the role of a topographic vo…

Disperse two-phase flows, with applications to geophysical problems

In this paper we study the motion of a fluid with several dispersed particles whose concentration is very small (smaller than $10^{-3}$), with possible applications to problems coming from geophysics, meteorology, and oceanography. We consider a very dilute suspension of heavy particles in a quasi-incompressible fluid (low Mach number). In our case the Stokes number is small and --as pointed out in the theory of multiphase turbulence-- we can use an Eulerian model instead of a Lagrangian one. The assumption of low concentration allows us to disregard particle--particle interactions, but we tak…

通过粗粒化表征大规模间歇性分层湍流中的局部能量传递

Characterization of local energy transfer in large-scale intermittent stratified turbulent flows via coarse graining

该研究针对大气海洋中分层湍流的大规模间歇性问题，改进空间滤波程序分析极端垂直气流的影响，发现其能触发跨尺度能量传递并加强特定尺度下动能与势能的耦合。

Drift wave-zonal flow dynamics

A remarkable phenomenon in turbulent flows is the spontaneous emergence of coherent large spatial scale zonal jets. Geophysical examples of this phenomenon include the Jovian banded winds and the Earth's polar front jet. In this work a comprehensive theory for the interaction of jets with turbulence, Stochastic Structural Stability Theory, is applied to the problem of understanding the formation and maintenance of the zonal jets that are crucial for enhancing plasma confinement in fusion devices.

Point vortex dynamics in three-dimensional ageostrophic balanced flows

Geophysical turbulent flows, characterized by rapid rotation, quantified by small Rossby number, and stable stratification, often self-organize into a collection of coherent vortices, referred to as a vortex gas. The lowest order asymptotic expansion in Rossby number is quasigeostrophy which has purely horizontal velocities and cyclone-anticylone antisymmetry. Ageostrophic effects are important components of many geophysical flows and, as such, these phenomena are not well-modeled by quasigeostrophy. The next order correction in Rossby number, which includes ageostrohpic affects, is so-called …

基于条件扩散模型的间隙拉格朗日湍流信号的随机重建

Stochastic Reconstruction of Gappy Lagrangian Turbulent Signals by Conditional Diffusion Models

提出基于条件生成扩散模型的随机方法，重建湍流被动平流物体轨迹缺失数据，保留非高斯间歇特性，精度优于高斯过程回归，适用于多物理场景。