arXiv subjects

Jin-Han Xie

Publications and source records attributed to Jin-Han Xie.

At least 19 recordsLinked to original sources

arXiv2026

Area and Perimeter Rules of Velocity Circulation in Two-Dimensional Turbulence with Large-scale Absolute Equilibrium

We demonstrate that the area rule of velocity circulation -- traditionally associated with the turbulent inertial range but shown not to be exact -- is strictly satisfied in the large-scale absolute equilibrium of two-dimensional (2D) homogeneous isotropic turbulence under enstrophy equipartition. We also derive a novel perimeter rule from the 2D inviscid loop equation, which posits that the probability distribution function (PDF) of velocity circulation depends solely on the loop perimeter rather than its area. This perimeter rule holds strictly in the large-scale absolute equilibrium characterized by energy equipartition. At the intermediate states determined by both enstrophy and energy, these two regimes are separated by a characteristic equilibrium scale $l_\text{eq}$: the area rule governs loop statistics when $l\ll l_\text{eq}$, while the perimeter rule emerges for $l\gg l_\text{eq}$. These statistical laws remain robust even for loops with extreme aspect ratios as low as $0.03$, a value that inertial-range studies never achieved. Our findings provide a new steady-state solution to the 2D loop equation and suggest additional solutions, paving the way for exploring previously undiscovered geometric invariants of turbulence.

physics.flu-dyn↗

arXiv2026

Wave-mean decomposition of scale-dependent kinetic energy from surface drifters

Separating waves and mean flows is a fundamental challenge in ocean dynamics. Lagrangian filtering of passive-tracer time series into high-frequency wave and low-frequency mean-flow components provides a practical route, as the relevant time scales are often cleanly split in the Lagrangian frame. Here we show that Lagrangian filtering can be applied to surface drifter observations, providing a powerful approach to quantify wave and mean-flow contributions to surface kinetic energy statistics. A key methodological choice is to implement the filtering in a generalized Lagrangian mean (GLM) framework, attributing filtered velocities to mean rather than particle trajectories; this produces more physically interpretable diagnostics. Using Gulf of Mexico drifter data, we compute second-order velocity structure functions (SF2s) for waves and mean flow components across spatial scales. With these filtered SF2s as a benchmark, we illustrate that Helmholtz decomposition of unfiltered SF2s alone should not be interpreted as a dynamical wave-mean decomposition. Applying Helmholtz decomposition to the filtered SF2s further illuminates seasonal dynamics. Mean-flow surface kinetic energy is rotationally dominated at scales larger than O(1) km, while at and below O(1) km, divergent and rotational contributions are approximately equipartitioned in both summer and winter, suggesting low-frequency divergent motions and possible associated vertical exchange. Winter mean flows are more active than summer mean flows over 500 m-10 km. Super-inertial motions are broadly consistent with linear waves. In winter, wave kinetic energy is concentrated at smaller spatial scales than in summer, possibly reflecting enhanced downscale transfer by stronger submesoscale mean flows.

physics.flu-dyn↗

arXiv2026

Area rule of velocity circulation in two-dimensional instability-driven turbulence beyond the inertial range

The velocity statistics reveal non-universality in both three-dimensional (3-D) and two-dimensional (2-D) turbulence, despite both prototype systems containing an energy inertial range with constant energy flux. Recently, statistics of scale-dependent velocity circulation exhibit universal bifractal behavior in 2-D and 3-D hydrodynamic turbulence and quantum turbulence, where the circulation scale is defined as the square root of the minimum area enclosed by the loop. This loop-shape independent definition of scale bases on the area rule of circulation first proposed by Migdal: the probability density function (PDF) of circulation is only a function of the minimal surface area enclosed by the loop but not the shape of the loop. This paper demonstrates that the derivation of the circulation area rule can be generalized to all scales in 2-D instability-driven turbulence, not limited to the inertial range. However, the area rule is not the only solution to the loop equation, so it may not be observed. Another necessary condition for the validity of the area rule is that the second-order momentum of circulation is loop-shape independent. By deriving the relationship between the second-order moment of circulation on a rectangular loop and the energy spectrum, we prove that the area rule cannot be satisfied in the classic inertial-range turbulence with -5/3 or -3 spectral scalings. As in the 3-D case, the second-order moment of circulation is size-dependent. Compared with the circulation PDFs, the PDFs normalized by the second-order moment of circulation exhibit significantly weaker dependence on loop shape.

physics.flu-dyn↗

arXiv2024

Multi-range fractional model for convective atmospheric surface-layer turbulence

We develop a multi-range fractional (MRF) model to capture the turbulent spectrum consisting of multiple self-similar ranges impacted by multiple effects. The MRF model is validated using long-term observational atmospheric surface layer data from Qingtu lake with extreme Reynolds numbers up to Re$_τ\sim O(10^6)$. The spectral exponent in each range and the transition scales between different ranges are solo parameters in the MRF model and are identified for streamwise velocity, vertical velocity, and temperature, and they update the quantifications in the multi-point Monin-Obukhov theory. Therefore, based on the MRF model and considering the consistency between the turbulent spectrum and variance, we propose an expression for the vertical dependence of the streamwise velocity variance that is inadequately described by the Monin-Obukhov similarity theory. The MRF model provides a new method to analyze and quantify turbulent data, and as a time-series model, it enables the generation of synthetic turbulent data.

physics.flu-dyn↗

arXiv2024

Energy spectrum of two-dimensional isotropic rapidly rotating turbulence

We study a two-dimensional isotropic rotating system and obtain both theoretically and numerically a $K^{-2}$ energy spectrum under the rapidly rotating condition ($Ro\ll 1$), which was initially obtained by Zeman (1994) and Zhou (1995). In rotating turbulence, the $K^{-2}$ energy spectrum was proposed under the assumption of isotropy, however, the direction selectivity of rotation breaks isotropy, making this $K^{-2}$ spectrum not easily observable. To fill the gap between theoretical assumptions and realizability, we study the turbulence of inertial waves in an artificial two-dimensional isotropic rotating turbulence system. In the limit of a small Rossby number, we asymptotically derive a nonlinear amplitude equation for inertial waves, which gives the $K^{-2}$ spectrum using a strong turbulence argument. This scaling is justified by numerical simulations of both the amplitude equation and the original system.

physics.flu-dyn↗

arXiv2024

Hall effect on the joint cascades of magnetic energy and helicity in helical magnetohydrodynamic turbulence

Helical magnetohydrodynamic turbulence with Hall effects is ubiquitous in heliophysics and plasma physics, such as star formation and solar activities, and its intrinsic mechanisms are still not clearly explained. Direct numerical simulations reveal that when the forcing scale is comparable to the ion inertial scale, Hall effects induce remarkable cross helicity. It then suppresses the inverse cascade efficiency, leading to the accumulation of large-scale magnetic energy and helicity. The process is accompanied by the breaking of current sheets via filaments along magnetic fields. Using the Ulysses data, the numerical findings are separately confirmed. These results suggest a novel mechanism wherein small-scale Hall effects could strongly affect large-scale magnetic fields through cross helicity.

physics.plasm-ph↗

arXiv2023

Spectral condensation in quasi-geostrophic turbulence above small-scale topography

Sea-floor topography is essential for oceanic fluid dynamics in many perspectives, and it is believed to enhance energy dissipation to oceanic flows. This study numerically examines the impact of small-scale topography on the dynamic of quasi-geostrophic barotropic flows and finds that small-amplitude topography enhances upscale energy flux and leads to condensation, which contradicts the common understanding. Topography-induced dissipation only happens when its amplitude is stronger than the first critical value. And there exists a second critical topography magnitude, corresponding to a second-order phase transition. When the topography magnitude lies between the two critical values, energy simultaneously transfers to both large and small scales. When the topography magnitude exceeds the second critical value, energy only transfers downscale. The discovery of counterintuitive topography-enhanced energy flux and the critical phenomenon brings new challenges to topography parameterization in ocean models.

physics.flu-dyn↗

arXiv2023

Non-Hermitian topological wall modes in rotating Rayleigh-Benard convection

We show that the rotating Rayleigh-Benard convection, where a rotating fluid is heated from below, exhibits non-Hermitian topological states. Recently, Favier and Knobloch (JFM 2020) hypothesized that the robust wall modes in rapidly rotating convection are topologically protected. We study the linear problem around the conduction profile, and by considering a Berry curvature defined in the complex wavenumber space, particularly, by introducing a complex vertical wavenumber, we find that these modes can be characterized by a non-zero integer Chern number, indicating their topological nature. The eigenvalue problem is intrinsically non-Hermitian, therefore the definition of Berry curvature generalizes that of the stably stratified problem. Moreover, the three-dimensional setup naturally regularizes the eigenvector at the infinite horizontal wavenumber. Under the hydrostatic approximation, it recovers a two-dimensional analogue of the one which explains the topological origin of the equatorial Kelvin and Yanai waves. The existence of the tenacious wall modes relies only on rotation when the fluid is stratified, no matter whether it is stable or unstable. However, the neutrally stratified system does not support a topological edge state. In addition, we define a winding number to visualize the topological nature of the fluid.

physics.flu-dyn↗

arXiv2023

Departure from the statistical equilibrium of large scales in three-dimensional hydrodynamic turbulence

We study the statistically steady states of the forced dissipative three-dimensional homogeneous isotropic turbulence at scales larger than the forcing scale in real separation space. The probability density functions (PDFs) of longitudinal velocity difference at large separations are close to but deviate from Gaussian, measured by their non-zero odd parts. Under the assumption that forcing controls the large-scale dynamics, we propose a conjugate regime to Kolmogorov's inertial range, independent of the forcing scale, to capture the odd parts of PDFs. The analytical expressions of the third-order longitudinal structure functions derived from the Kármán-Howarth-Monin equation prove that the odd-part PDFs of velocity differences at large separations are small but non-zero, and show that the odd-order longitudinal structure functions have a universal power-law decay with exponent $-2$ as the separation tends to infinity regardless of the particular forcing form, implying a significant coupling between large and small scales. Thus, dynamics of large scales depart from the absolute equilibrium, and we can partially recover small-scale information without explicitly resolving small-scale dynamics. The departure from the statistical equilibrium is quantified and found to be viscosity independent. Even though this departure is small, it is significant and should be considered when studying the large scales of the forced three-dimensional homogeneous isotropic turbulence.

physics.flu-dyn↗

arXiv2022

Spatial-temporal structure functions in Burgers turbulence driven by an Ornstein-Uhlenbeck process

We explore the spatial-temporal structure functions of Burgers turbulence driven by a temporal Ornstein-Uhlenbeck (OU) process, where the characteristic time scale of the OU process is much larger than that of the energy flux across spatial scales. Based on the Kármán-Howarth-Monin equation, we obtain an expression for the third-order spatial-temporal structure function away from the dissipation scale. This expression combines Kolmogorov's exact result of spatial structure function and the exponential temporal decay of the external force. We numerically justify this expression and find that the high-order structure functions also decay exponentially, however, the dependence of decay rates on order is different for the odd- and even-order structure functions. Comparing the OU-driven Burgers turbulence with that driven by temporal white noise, their spatial structure functions are identical when the energy injection rates are the same, which justifies Kolmogorov's theory, but these two systems' temporal structure functions differ. Also, the velocity pdf in the OU-driven Burgers turbulence shows a bimodal distribution, contradicting the near-Gaussian distribution in white-noise-driven turbulence.

physics.flu-dyn↗

arXiv2022

Direct observational evidence of an oceanic dual kinetic energy cascade and its seasonality

The Ocean's turbulent energy cycle has a paradox; large-scale eddies under the control of Earth's rotation primarily transfer kinetic energy (KE) to larger scales via an inverse cascade, while a transfer to smaller scales is needed to accomplish dissipation. It has been argued, using numerical simulations, that fronts, waves and other turbulent structures can produce a forward cascade of KE toward dissipation scales. However, this forward cascade and its coexistence with known inverse cascade were not confirmed in observations. Here we present the first evidence of a dual KE cascade in the Ocean by analyzing velocity measurements from surface drifters released in the Gulf of Mexico. Our results show that KE is injected at two dominant scales and transferred to both large and small scales, with the downscale flux dominating at scales smaller than ~1-10km. The cascade rates are modulated seasonally, with stronger KE injection and forward transfer during winter.

physics.ao-ph↗

arXiv2021

Global expressions for high-order structure functions in Burgers turbulence

Since the famous work by Kolmogorov on incompressible turbulence, the structure-function theory has been a key foundation of modern turbulence study. Due to the simplicity of Burgers turbulence, structure functions are calculated to arbitrary orders, which provides numerous implications for other compressible turbulent systems. We present the derivation of exact forcing-scale resolving expressions for high-order structure functions of the burgers turbulence. Compared with the previous theories where the structure functions are calculated in the inertial range based on the statistics of shocks, our expressions link high-order structure functions in different orders without extra information on the flow structure and are valid beyond the inertial range, therefore they are easily checked by numerical simulations.

physics.flu-dyn↗

arXiv2020

Phase transition of the energy flux in the near-inertial wave--mesoscale eddy coupled turbulence

Wind forcing injects energy into the mesoscale eddies and near-inertial waves (NIWs) in the ocean, and the NIW is believed to solve the puzzle of mesoscale energy budget by absorbing energy from mesoscale eddies followed by a forward cascade of NIW energy which finally dissipates at the ocean interior. This work studies the turbulent energy transfer in the NIW--quasigeostrophic mean mesoscale eddy coupled system based on a previously derived two-dimensional model which has a Hamiltonian structure and inherits conserved quantities in the Boussinesq equations (Xie \& Vanneste, \textit{J. Fluid Mech.}, vol. 774, 2015, pp. 147--169). Based on the conservation of energy, potential enstrophy and wave action, we propose a heuristic argument predicting the existence of phase transition with changing the relative strength between NIW and mean flow. By running forced-dissipative numerical simulations with varying parameter $R$, the ratio of the magnitude of NIW and mean-flow forcing, we justify the existence of phase transition, which is found to be second-order, around critical value $R_c$. When $0 R_c$, energy transfers downscale, wave action transfers bidirectionally, and vortex filaments are dominant. We find the catalytic wave induction (CWI) mechanism where the NIW induces a downscale energy flux of the mean flow. The CWI mechanism differs from the stimulated loss of balance by the absence of energy conversion from the mesoscale eddy to NIW, and it is found to be effective in the toy-model study, making it potentially important for ocean energetics.

physics.flu-dyn↗

arXiv2019

Third-order structure functions for isotropic turbulence with bidirectional energy transfer

We derive and test a new heuristic theory for third-order structure functions that resolve the forcing scale in the scenario of simultaneous spectral energy transfer to both small and large scales, which can occur naturally in rotating stratified turbulence or magnetohydrodynamical~(MHD) turbulence, for example. The theory has three parameters, namely the upscale/downscale energy transfer rates and the forcing scale, and it includes the classic inertial range theories as local limits. When applied to measured data, our global-in-scale theory can deduce the energy transfer rates using the full range of data, therefore it has broader applications compared with the local theories, especially in the situations where the data is imperfect. In addition, because of the resolution of forcing scales, the new theory can detect the scales of energy input, which was impossible before. We test our new theory with a two-dimensional simulation of MHD turbulence.

physics.flu-dyn↗

arXiv2017

Interaction between mountain waves and shear flow in an inertial layer

Mountain-generated inertia-gravity waves (IGWs) affect the dynamics of both the atmosphere and the ocean through the mean force they exert as they interact with the flow. A key to this interaction is the presence of critical-level singularities or, when planetary rotation is taken into account, inertial-level singularities, where the Doppler-shifted wave frequency matches the local Coriolis frequency. We examine the role of the latter singularities by studying the steady wavepacket generated by a multiscale mountain in a rotating linear shear flow at low Rossby number. Using a combination of WKB and saddle-point approximations, we provide an explicit description of the form of the wavepacket, of the mean forcing it induces, and of the mean-flow response. We identify two distinguished regimes of wave propagation: Regime I applies far enough from a dominant inertial level for the standard ray-tracing approximation to be valid; Regime II applies to a thin region where the wavepacket structure is controlled by the inertial-level singularities. The wave--mean-flow interaction is governed by the change in Eliassen--Palm (or pseudomomentum) flux. This change is localised in a thin inertial layer where the wavepacket takes a limiting form of that found in Regime II. We solve a quasi-geostrophic potential-vorticity equation forced by the divergence of the Eliassen--Palm flux to compute the wave-induced mean flow. Our results, obtained in an inviscid limit, show that the wavepacket reaches a large-but-finite distance downstream of the mountain (specifically, a distance of order $k_*^{1/2} Δ^{3/2}$, where $k_*^{-1}$ and $Δ$ measure the wave and envelope scales of the mountain) and extends horizontally over a similar scale.

physics.flu-dyn↗

arXiv2016

A reduced model for salt-finger convection in the small diffusivity ratio limit

A simple model of nonlinear salt-finger convection in two dimensions is derived and studied. The model is valid in the limit of small solute to heat diffusivity ratio and large density ratio, which is relevant to both oceanographic and astrophysical applications. Two limits distinguished by the magnitude of the Schmidt number are found. For order one Schmidt numbers, appropriate for astrophysical applications, a modified Rayleigh-Bénard system with large-scale damping due to a stabilizing temperature is obtained. For large Schmidt numbers, appropriate for the oceanic setting, the model combines a prognostic equation for the solute field and a diagnostic equation for inertia-free momentum dynamics. Two distinct saturation regimes are identified for the second model: The weakly driven regime is characterized by a large-scale flow associated with a balance between advection and linear instability, while the strongly driven regime produces multiscale structures, resulting in a balance between the energy input through linear instability and the energy transfer between scales. For both regimes, we analytically predict and numerically confirm the dependence of the kinetic energy and salinity fluxes on the ratio between solute and heat Rayleigh numbers. The spectra and probability density functions are also computed.

physics.flu-dyn↗

arXiv2015

A generalised-Lagrangian-mean model of the interactions between near-inertial waves and mean flow

Wind forcing of the ocean generates a spectrum of inertia-gravity waves that is sharply peaked near the local inertial (or Coriolis) frequency. The corresponding near-inertial waves (NIWs) are highly energetic and play a significant role in the slow, large-scale dynamics of the ocean. To analyse this role, we develop a new model of the nondissipative interactions between NIWs and balanced motion. The model is derived using the generalised-Lagrangian-mean (GLM) framework (specifically, the glm variant of Soward & Roberts (2010)), taking advantage of the time-scale separation between the two types of motion to average over the short NIW period. We combine Salmon's (2013) variational formulation of GLM with Whitham averaging to obtain a system of equations governing the joint evolution of NIWs and mean flow. Assuming that the mean flow is geostrophically balanced reduces this system to a simple model coupling Young & Ben Jelloul's (1997) equation for NIWs with a modified quasi-geostrophic equation. In this coupled model, the mean flow affects the NIWs through advection and refraction; conversely, the NIWs affect the mean flow by modifying the potential-vorticity inversion - the relation between advected potential vorticity and advecting mean velocity - through a quadratic wave term, consistent with the GLM results of Buhler & McIntyre (1998). The coupled model is Hamiltonian and its conservation laws, for wave action and energy in particular, prove illuminating: on their basis, we identify a new interaction mechanism whereby NIWs forced at large scales extract energy from the balanced flow as their horizontal scale is reduced by differential advection and refraction so that their potential energy increases. A rough estimate suggests that this mechanism could provide a significant sink of energy for mesoscale motion and play a part in the global energetics of the ocean.

physics.flu-dyn↗

arXiv2014

Dynamics of a spherical particle in an acoustic field: a multiscale approach

A rigid spherical particle in an acoustic wave field oscillates at the wave period but has also a mean motion on a longer time scale. The dynamics of this mean motion is crucial for numerous applications of acoustic microfluidics, including particle manipulation and flow visualisation. It is controlled by four physical effects: acoustic (radiation) pressure, streaming, inertia and viscous drag. In this paper, we carry out a systematic multiscale analysis of the problem in order to assess the relative importance of these effects depending on the parameters of the system that include wave amplitude, wavelength, sound speed, sphere radius, and viscosity. We identify two distinguished regimes characterised by a balance among three of the four effects, and we derive the equations that govern the mean particle motion in each regime. This recovers and organises classical results by King, Gor'kov and Doinikov, clarifies the range of validity of these results, and reveals a new nonlinear dynamical regime. In this regime, the mean motion of the particle remains intimately coupled to that of the surrounding fluid, and while viscosity affects the fluid motion, it plays no part in the acoustic pressure. Simplified equations, valid when only two physical effects control the particle motion, are also derived. They are used to obtain sufficient conditions for the particle to behave as a passive tracer of the Lagrangian-mean fluid motion.

physics.flu-dyn↗