J. E. Avron
When time reversal is broken the viscosity tensor can have a non vanishing odd part. In two dimensions, and only then, such odd viscosity is compatible with isotropy. Elementary and basic features of odd viscosity are examined by considering solutions of the wave and Navier-Stokes equations for hypothetical fluids where the stress is dominated by odd viscosity.
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We present variational and Hamiltonian formulations of incompressible fluid dynamics with free surface and nonvanishing odd viscosity. We show that within the variational principle the odd viscosity contribution corresponds to geometric boundary terms. These boundary terms modify Zakharov's Poisson brackets and lead to a new type of boundary dynamics. The modified boundary conditions have a natural geometric interpretation describing an additional pressure at the free surface proportional to the angular velocity of the surface itself. These boundary conditions are believed to be universal sinc…
Stokesian Dynamics is a well-established computational method for simulating dynamics of many particles suspended in a conventional passive fluid medium. Active fluids composed of self-propelling particles with broken time reversal symmetry permit the emergence of a so-called odd viscosity. In this work, we extended the conventional Stokesian Dynamics formalism to incorporate the additional hydrodynamic effects due to odd viscosity, which enables simulating collective behaviors of many particles suspended in an active fluid medium with both even viscosity and odd viscosity.
In this work, we present observable consequences of parity-violating odd viscosity term in incompressible 2+1D hydrodynamics. For boundary conditions depending on the velocity field (flow) alone we show that: (i) The fluid flow quantified by the velocity field is independent of odd viscosity, (ii) The force acting on a closed contour is independent of odd viscosity, and (iii) The odd viscosity part of torque on a closed contour is proportional to the rate of change of area enclosed by the contour with the proportionality constant being twice the odd viscosity. The last statement allows us to d…
Stability of Taylor-Couette Flow with Odd Viscosity
本文通过解析与数值方法研究奇粘性对轴对称扰动下Taylor-Couette流稳定性的影响，发现奇粘性可产生次级涡旋并通过“杠杆”效应在较大时完全抑制不稳定性，为粘度计实验提供指导。
Lorentz Reciprocal Theorem in Fluids with Odd Viscosity
本文将洛伦兹互易定理推广到具有奇数粘性的手性活性流体，通过选择奇数粘性符号相反的辅助问题实现，并证明该定理可区分两类微型游泳体，其中扭矩偶极子可产生定向运动。
Instability behavior of odd viscosity-induced viscous fluid over a vibrating bed
本文通过理论稳定性分析研究了奇数粘性对振动倾斜床面上粘性流体不稳定性的影响，识别了重力、次谐波、谐波及剪切不稳定性，并揭示了奇数粘性对各类型不稳定性的稳定或抑制作用。
Hydrodynamic flow field and frictional resistance coefficient of a disk rotating steadily in a compressible fluid layer with odd viscosity on a rigid substrate
研究了在刚性基底上旋转的盘在具有奇粘性的可压缩流体层中的流体动力学行为，发现奇粘性影响盘间相互作用并增加阻力系数。
We discuss hydrodynamic forces acting on a two-dimensional liquid domain that moves laterally within a supported fluid membrane in the presence of odd viscosity. Since active rotating proteins can accumulate inside the domain, we focus on the difference in odd viscosity between the inside and outside of the domain. Taking into account the momentum leakage from a two-dimensional incompressible fluid to the underlying substrate, we analytically obtain the fluid flow induced by the lateral domain motion, and calculate the drag and lift forces acting on the moving liquid domain. In contrast to the…
Odd Droplets: Fluids with Odd Viscosity and Highly Deformable Interfaces
本文提出具有奇偶粘度的流体模型，通过数值模拟发现奇偶粘度能破坏对称铺展，产生不对称变形和手性流动，实现液滴定向弹跳或滚动，为控制多相流和设计功能超材料提供新框架。
We numerically examine the mechanisms that describe the shock-boundary layer interactions in transonic flow past an oscillating wing section. At moderate and high angles of incidence but low amplitudes of oscillation, shock induced flow separation or shock-stall is observed accompanied by shock reversal. Even though the power input to the airfoil by the viscous forces is three orders of magnitude lower than that due to the pressure forces on the airfoil, the boundary layer manipulates the shock location and shock motion and redistributes the power input to the airfoil by the pressure forces. T…
We study the problem of flow of a neutral gas past an infinite cylinder at right angle to its axis at low Reynolds number when the fluid is characterized by broken time-reversal invariance, and hence by odd viscosity in addition to the normal even one. We solve the Oseen approximation to Navier-Stokes equation and calculate the lift force which appears due to the odd viscosity.
We develop three asymptotic models of surface waves in a non-newtonian fluid with odd viscosity. This viscosity is also known as Hall viscosity and appears in a number of applications such as quantum Hall fluids or chiral active fluids. Besides the odd viscosity effects, these models capture both gravity and capillary forces up to quadratic interactions and take the form of nonlinear and nonlocal wave equations. Two of these models describe bidirectional waves while the third PDE studies the case of unidirectional propagation. We also prove the well-posedness of these asymptotic models in spac…
Analytical solution for the hydrodynamic resistance of a disk in a compressible fluid layer with odd viscosity on a rigid substrate
本文提出在具有奇粘度的可压缩流体层中，通过解析解研究刚性圆盘的流体阻力，揭示了奇粘度对流体阻力互易性的影响。
We discuss the linear hydrodynamic response of a two-dimensional active chiral compressible fluid with odd viscosity. The viscosity coefficient represents broken time-reversal and parity symmetries in the 2D fluid and characterizes the deviation of the system from a passive fluid. Taking into account the hydrodynamic coupling to the underlying bulk fluid, we obtain the odd viscosity-dependent mobility tensor, which is responsible for the non-reciprocal hydrodynamic response to a point force. Furthermore, we consider a finite-size disk moving laterally in the 2D fluid and demonstrate that the d…
In common fluids, viscosity is associated with dissipation. However, when time-reversal-symmetry is broken a new type of non-dissipative `viscosity' may emerge. Recent theories and experiments on classical 2D systems with active spinning particles have heightened interest in odd viscosity, but a microscopic theory for it in active materials is still absent. Here we present such first-principles microscopic Hamiltonian theory, valid for both 2D and 3D, showing that odd viscosity is present in any system, equilibrium or not, with aligned spinning components. Our work substantially extends the ap…
Analytical response functions for a compressible thin fluid layer with odd viscosity
研究了具有奇粘度的可压缩薄流体层对单极和偶极奇点的流体响应，推导出精确的解析解，揭示了奇粘度对胶体颗粒和微游泳者动力学及集体行为的影响。
Thermocapillary migration of an odd viscous droplet on a uniformly heated surface: A lattice Boltzmann study
本研究通过格子玻尔兹曼方法揭示奇粘性使液滴在均匀加热表面上自发迁移，方向取决于奇粘性符号，速度受接触角和粘度比影响，且可逆重力爬升。
Odd viscosity suppresses intermittency in direct turbulent cascades
本研究通过模拟与理论发现，奇偶粘度在小尺度上抑制湍流间歇性，并构建双通道螺旋壳模型，为调控湍流间歇性提供新途径。
Traveling gravity-capillary waves with odd viscosity
本文研究了具有奇黏度的非牛顿流体表面模型中行进波的存在性，并利用非线性分岔技术给出了证明。
Odd-viscosity induced surfactant-laden shear-imposed viscous film over a slippery incline
本研究针对含不溶性表面活性剂的光滑斜面降膜，建立Orr-Sommerfeld边值问题并数值求解，分析odd黏度、剪切、滑移等因素对Yih模、Marangoni模及剪切模稳定性的影响规律。
We apply the geometric theory of swimming at low Reynolds number to the study of nearly circular swimmers in two-dimensional fluids with non-vanishing Hall, or "odd", viscosity. The Hall viscosity gives an off-diagonal contribution to the fluid stress-tensor, which results in a number of striking effects. In particular, we find that a swimmer whose area is changing will experience a torque proportional to the rate of change of the area, with the constant of proportionality given by the coefficient $η^o$ of odd viscosity. After working out the general theory of swimming in fluids with Hall visc…
Odd-viscosity-induced instability in shear flows
该研究推导了奇黏度推广的Orr--Sommerfeld--Squire方程，发现奇黏度可通过将剪切流瞬态增长转化为自持指数增长模式诱导新不稳定性，建立了瞬态增长、非正态性与非耗散力诱导不稳定性的联系。
Reversal of particle Migration for viscoelastic solution at high solvent viscosity
本文研究了粘弹性流体中溶剂粘度比 $β$ 对颗粒横向迁移的影响，发现随 $β$ 增大颗粒迁移方向发生反转，并建立了升力系数与 Weissenberg 数及旋转速度差相关的标度律。
Odd viscous flow past a sphere at low but nonzero Reynolds numbers
该研究针对低但非零雷诺数下的绕球奇黏性流动问题，用渐近匹配法和Lorentz互易定理解决相关障碍，发现轴对称条件下升力消失但会产生流动诱导的非零转矩，完善了奇黏性流体力学的相关理论。
Slip-induced odd viscous flow past a cylinder
研究通过奇粘性广义洛伦兹互易定理，揭示滑移条件下斯托克斯流中升力的产生机制，并推导低雷诺数下奥塞恩升力的主导滑移长度贡献。
Droplet Deformation and Emulsion Rheology in Two-Dimensional Odd Stokes Flow
研究二维粘性液滴在简单剪切流中变形及乳液流变学，推导奇斯托克斯流框架下的解析解，揭示奇粘性对乳液有效流变学的影响。
Nonlinear shallow-water waves with vertical odd viscosity
研究具有垂直奇粘度的三维流体中的非线性浅水波，发现奇粘性引发新的非线性效应，推导出修正的 KdV、Ostrovsky 和 KP 方程，并揭示大奇粘性下二维紧致孤波的形成。
We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken. For the case of incompressible fluids, the odd viscosity manifests itself through the free surface (no stress) boundary conditions. We first find the free surface wave solutions of hydrodynamics in the linear approximation and study the dispersion of such waves. As expected, the surface waves are chiral and even exist in the absence of gravity and vanishing…
The flow of momentum and energy in a fluid is typically associated with dissipative transport coefficients: viscosity and thermal conductivity. Fluids that break certain symmetries such as mirror symmetry and time-reversal invariance can display non-dissipative transport coefficients called odd (or Hall) viscosities and thermal conductivities. The goal of this paper is to elucidate the microscopic origin of these dissipationless transport coefficients using kinetic theory. We show that odd viscosity and odd thermal conductivity arise when the linearized collision operator is not Hermitian. Thi…
In this letter, we derive the Korteweg-de Vries (KdV) equation corresponding to the surface dynamics of a shallow depth ($h$) two-dimensional fluid with odd viscosity ($ν_o$) subject to gravity ($g$) in the long wavelength weakly nonlinear limit. In the long wavelength limit, the odd viscosity term plays the role of surface tension albeit with opposite signs for the right and left movers. We show that there exists two regimes with a sharp transition point within the applicability of the KdV dynamics, which we refer to as weak $(|ν_o|< \sqrt{gh^3}/6)$ and strong $(|ν_o|> \sqrt{gh^3}/6)$ parity-…
Ferrofluids are a synthetic magnetic colloid consisting of magnetized nanoparticles surrounded by a repulsive surfactant layer. When subjected to an external magnetic field the ferrofluid acquires a macroscopic magnetization density which leads to magnetic behavior that is intricately coupled to the ambient fluid dynamics. Ferrofluids share several features with the chiral active fluids composed of unidirectionally spinning hematite cubes, which have been shown to possess a 2D non-dissipative odd viscosity term (Nature Physics, 15, 1188-1194(2019)). In standard ferrofluid dynamics, 3D versions…
Hydrodynamics of an odd active surfer in a chiral fluid
本研究探讨线性活性微型游泳者在具有奇数粘度的可压缩薄流体层上的低雷诺数流体动力学，发现单个游泳者沿圆形路径运动且半径与奇数粘度成反比，而游泳者对则展现出依赖推进机制和初始取向的丰富两体动力学。
Force Dipole Interactions in Membranes with Odd Viscosity
研究膜中力偶相互作用与奇粘性，通过流体动力学框架推导格林张量，揭示不同动力学区域及手性响应特征。
Exact results for dissipation and steady creeping flow in three-dimensional chiral active fluids
研究了三维手性活性流体中耗散和稳态慢速流动的精确结果，通过扩展霍尔姆霍兹定理，证明了低雷诺数下流体的稳态流动场具有唯一解，并展示了奇黏性导致的能量耗散增加。
Emergent odd response in active chiral films
研究活性手性薄膜中奇响应的产生，基于经典剪切流变学，用动力学理论从微观推导其应力响应，揭示相关机制，数值解突出强剪切下的特征，确立活性手性薄膜为奇流体动力学新可控环境。
Linear odd electrophoresis of a sphere in a charged chiral active fluid
研究带奇黏度的电活性流体中带电球的电泳行为，推导出任意形状粒子在弱电场下的电泳迁移率表达式，并发现奇黏度导致电泳迁移率张量的各向异性。
We investigate the bulk hydrodynamics of the chiral vortex matter on an arbitrary closed surface, extending the ideas of [20, 41]. Placing this important example of a chiral medium onto a curved geometry reveals the geometric nature of odd viscosity. The anomalous odd viscosity of the vortex matter is associated with a special interaction of point vortices with curvature.
In simple fluids, such as water, invariance under parity and time-reversal symmetry imposes that the rotation of constituent 'atoms' are determined by the flow and that viscous stresses damp motion. Activation of the rotational degrees of freedom of a fluid by spinning its atomic building blocks breaks these constraints and has thus been the subject of fundamental theoretical interest across classical and quantum fluids. However, the creation of a model liquid which isolates chiral hydrodynamic phenomena has remained experimentally elusive. Here we report the creation of a cohesive two-dimensi…
$\mathscr{PT}$-symmetric hydrodynamics of odd viscous liquids and their oscillator counterparts
本文利用$\boldsymbol{\tilde{PT}}$对称将奇粘滞性的难测量特性转化为测量原理，构建含非线性惯性项的奇纳维-斯托克斯方程，通过$\boldsymbol{\tilde{PT}}$相变等实现奇粘滞性的高灵敏度测量，为奇输运系数测量提供多类方案。
Wave-crests around obstacles in odd viscous liquids
针对奇粘性系数未知的问题，本研究受经典液体色散面结论启发，理论确定了二维和三维奇粘性液体中运动障碍物周围的等相位波峰形状，推导出奇粘性系数需满足的参数关系，为其实验测定提供框架。
Odd slip at chiral active surfaces
本文研究手性活性表面产生的奇滑移现象，通过微扰展开分析其输运性质，发现颗粒悬浮液中的奇滑移可导致奇黏度，为奇黏度提供新机制。
Wave turbulence theory of odd fluids and solids: kinetic equations and solutions
研究奇异物与固体中波湍流的动力学方程，解析求解得到各向异性Kolmogorov-Zakharov谱，揭示正向与反向能量级联机制。
We consider an isotropic compressible non-dissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid as well as the free surface boundary conditions depend explicitly on the parity breaking non-dissipative odd viscosity term. We construct a variational principle in the form of an effective action which gives both bulk hydrodynamic equations and free surface boundary conditions. The free surface boundary conditions require an additional boundary term in the action which resemble…
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