In this note, we propose a new idea by analyzing the basic disturbance equations, and give starting equations for understanding the instability phenomena of laminar flows and transition to turbulence. It is considered that there is an interaction between the disturbance and the base flow in the process of disturbance amplification. The transition to turbulence is the result of this interaction. The linearity of the disturbance in linear theory is oversimplified the problem. It is pointed out that the development of disturbance is subjected to the influence of the base flow, and these effects must be included in the governing equations of the disturbance.
We derive the flow field disturbance produced by point viscosity variations in a heterogeneous fluid when subject to a background flow while neglecting fluid inertia. The disturbance flow field is found to be identical to that generated by a force-dipole called stresslet. Using a combination of theory and numerical simulations, we show how the hydrodynamics of an active rigid particle is altered due to the presence of point viscosity variations, and how this can be exploited to manipulate and steer them in microfluidic environments.
We show possibility of the Plane Couette (PC) flow instability for Reynolds number Re>Reth=140. This new result of the linear hydrodynamic stability theory is obtained on the base of refusal from the traditionally used assumption on longitudinal periodicity of the disturbances along the direction of the fluid flow. We found that earlier existing understanding on the linear stability of this flow for any arbitrary large Reynolds number is directly related with an assumption on the separation of the variables of the spatial variability for the disturbance field and their periodicity in linear th…
We examine the response of an inertia-less viscoelastic channel flow to localized perturbations. A simplified model shows that the non-linear interaction between the velocity and elastic stress fields can split an initial pulsed disturbance into two separate pulses if the initial disturbance and the base elastic stress are sufficiently high. In accordance, we demonstrate that a transition to a pulse-splitting regime can be achieved experimentally. These results suggest a possible new direction for studying the elastic instability of viscoelastic channel flows at high elasticity through the gro…
Laminar flows through pipes driven at steady, pulsatile or oscillatory rates undergo a sub-critical transition to turbulence. We carry out an extensive linear non-modal stability analysis of these flows and show that for sufficiently high pulsation amplitudes the stream-wise vortices of the classic lift-up mechanism are outperformed by helical disturbances exhibiting an Orr-like mechanism. In oscillatory flow, the energy amplification depends solely on the Reynolds number based on the Stokes-layer thickness and for sufficiently high oscillation frequency and Reynolds number, axisymmetric distu…
A general, two-way coupled, point-particle formulation that accounts for the disturbance created by the dispersed particles in obtaining the undisturbed fluid flow field needed for accurate computation of the force closure models is presented. Specifically, equations for the disturbance field created by the presence of particles are first derived based on the inter-phase momentum coupling force in a finite-volume formulation. Solution to the disturbance field is obtained using two approaches: (i) direct computation of the disturbance velocity and pressure using the reaction force due to partic…
In this article the stability loss of the Hartmann flow are investigated by applying the equations for disturbances. The velocity and electric potential quasi-static MHD model is used. The equations allow us to calculate time-dependent disturbance fields using a base flow and an initial disturbance. Two type of initial perturbations are considered: the eigenfunction of the linearized MHD equations and a fluid injection into the flow. These two approaches lead to identical stability results. However, we found a significant difference in the practical implementation of the two approaches. Dealin…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the associated eigenproblem. The neutral stability boundary and the corresponding critical wave number are obtained for liquid - liquid and air - water systems. Depending on the problem parameters, the instability sets in owing to short, intermediate, of long wave most unstable perturbations. Patterns of the most unstable disturbances are reported and discussed…
We consider a full set of harmonics for the Stokes wave in deep water in the absence of viscosity, and examine the role that higher harmonics play in modifying the classical Benjamin-Feir instability. Using a representation of the wave coefficients due to Wilton, a perturbation analysis shows that the Stokes wave may become unbounded due to interactions between the $N^{th}$ harmonic of the primary wave train and a set of harmonics of a disturbance. If the frequency of the $n^{th}$ harmonic is denoted $ ω_{n} =ω\left( {1 \pm δ} \right)$ then instability will occur if $$ 0<δ<\frac{\sqrt 2\ k\,n^…
Ongoing development of fuel storage and delivery systems for space probes, interplanetary vehicles, satellites and orbital platforms continues to drive interest in propellant management systems that utilize surface tension to retain, channel and control flow in microgravity environments. Although it has been known for decades that capillary flows offer an ideal method of fuel management, there has been little research devoted to the general stability properties of such flows. In this work, we demonstrate theoretically why capillary flows which channel wetting liquids in slender open triangular…
For decades, transition to turbulence in viscoelastic parallel shear flows was believed to require nonlinear instabilities. We provide numerical evidences for a new wall-mode linear instability that directly triggers the transition to elastoinertial turbulence in channel flow. The instability is 2D but 3D features become important as nonlinear effects grow. With larger disturbances, direct transition to nonlinear instabilities, leading to turbulent states of both inertial and elastoinertial natures, are observed.
We explore the laminar to turbulence transition of round jets at low Reynolds number (Re < 1000) using a novel experimental setup and linear stability theory (LST). The setup has a large domain and a low disturbance environment which increases the critical Re to approximately 500, permitting the appearance of a hitherto unknown puff-like instability (PFI). The instability is identified in the self-similar region of the jet through clean flow visualizations (FV) and further corroborated by particle image velocimetry (PIV) measurements. For 400< Re <700, the flow exhibits PFI embedded in a puff-…
In this paper, the physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. For the first time, a model derived strictly from physics is proposed to show that the flow instability under finite amplitude disturbance leads to turbulent transition. The proposed model is named as "energy gradient method." It is demonstrated that it is the transverse energy gradient that leads to the disturbance amplification while the disturbance is damped by the energy loss due to visc…
We study the stability of Stokes waves on a free surface of an ideal fluid of infinite depth. For small steepness the modulational instability dominates the dynamics, but its growth rate is vastly surpassed for steeper waves by an instability due to disturbances localized at the wave crest, explaining why long propagating ocean swell consists of small-amplitude waves. The dominant localized disturbances are either co-periodic with the Stokes wave, or have twice its period. The nonlinear stage of instability for steep wave evolution reveals the formation of a plunging breaker.
In the theory of hydrodynamic stability, the procedure to decompose an incompressible flow field into its basic motion and disturbances is imprecise and problematic because the disturbances, infinitesimal or finite, are ill-defined quantities in analysis. The linearised equations contravene the first principles of classical mechanics while the disturbance-driven non-linear formulation can hardly be considered as exact science. The notion that unstable and amplified disturbances precipitating the early stages of laminar-turbulent transition is vague, speculative or fundamentally flawed. Similar…
Negative viscosity seems to be an impossible parameter for any thermodynamic system. But for some special boundary conditions the viscosity of a fluid has apparently become negative, like for secondary flow of a fluid or in a plasma flow interacting with a dominant magnetic field. This work studied the effect of negative viscosity for a fluid flow over a cylinder. Four different viscosities are considered, in which the positive viscosities of Air and CO2 has been considered at 300 K temperature and their negative pair of viscosities are considered in this work. The results show a vast differen…
Passive aerodynamic robustness reduces disturbance amplification in flight
J. C. Wu Center for Aerodynamics, School of Aeronautics and Astronautics, Shanghai Jiao Tong University（上海交通大学航空航天学院空气动力学中心）；Commercial Aircraft Corporation of China, Ltd.（中国商用飞机有限责任公司）
This study aims to investigate the possible sources of non-axisymmetric disturbances and their propagation mechanism in Taylor Couette flow (TCF) for wide gap problems using direct numerical simulation with a radius ratio of 0.5 and Reynolds number (Re) ranging from 60 to 650. Here, attention is focused on the viscous layer (VL) thickness in near-wall regions and its spatial distribution along the axial direction to gain an insight into the origin and propagation of non-axisymmetric disturbances. The results show that an axisymmetric Taylor-vortex flow occurs when Re is between 68 and 425. Abo…
The linear evolution of disturbances due to a ribbon vibrating at frequency $ω_0$ in plane Poiseuille flow is computed by solving the associated initial boundary value problem in the Fourier-Laplace plane, followed by inversion. A novel algorithm for identifying the temporal modes of the Orr-Sommerfeld equation (OSE) in the complex wavenumber plane, which are required in the inversion, is presented. Unlike in many prior studies, the performance of the Laplace integral first, not only avoids complicated causality arguments and confusion, in locating upstream and downstream modes, that is preval…
Instability of stratified multi-phase flow in a rotating platform becomes important because of a potential role in micro-mixing and micro-machines. Centrifugal actuation can play an important role in driving the flow and Coriolis force can enhance the mixing in a short span by destabilizing the flow. In this study, we focus on the impact of the Coriolis force on a rotating viscosity-stratified flow with a thin diffusive mixed layer between two fluid layers. Modal stability analysis is used to estimate the critical parameters, namely Rotation number, Reynolds number, and wave number, which are …
We study the stability of multi-layer radial flows in porous media within the Hele-Shaw model. We perform a linear stability analysis for radial flows consisting of an arbitrary number of fluid layers with interfaces separating fluids of constant viscosity and with positive viscosity jump at each interface in the direction of flow. Several different time-dependent injection strategies are analyzed including the maximal injection rate that maintains a stable flow. We find numerically that flows with more fluid layers can be stable with faster time-dependent injection rates than comparable flows…
In this paper, the instability of layered two-phase flows caused by the presence of a soluble surfactant (or a surface active solute) is studied. The fluids have different viscosities, but are density matched to focus on Marangoni effects. The fluids flow between two flat plates, which are maintained at different solute concentrations. This establishes a constant flux of solute from one fluid to the other in the base state. A linear stability analysis is performed, using a combination of asymptotic and numerical methods. In the creeping flow regime, Marangoni stresses destabilize the flow, pro…
The instability of ideal non-divergent zonal flows on the sphere is determined numerically by the instability criterion of Arnol'd (1966) for the sectional curvature. Zonal flows are unstable for all perturbations besides for a small set which are in approximate resonance. The sectional curvature scales with $m/\ell$ for large total and zonal wave numbers $\ell$ and $m$ of the perturbations. The planetary rotation is stable and the presence of rotation reduces the instability of perturbations.
In this article we consider the linear stability of the two-dimensional flow induced by the linear stretching of a surface in the streamwise direction. The basic flow is a rare example of an exact analytical solution of the Navier-Stokes equations. Using results from a large Reynolds number asymptotic study and a highly accurate spectral numerical method we show that this flow is linearly unstable to disturbances in the form of Tollmien-Schlichting waves. Previous studies have shown this flow is linearly stable. However, our results show that this is only true for Görtler-type disturbances.
Direct numerical simulation (DNS) was conducted to investigate the evolution of a straight vortex tube based on Hon & Walker's model, which was originally proposed for a symmetric hairpin vortex tube (Hon,T.L. & Walker, J.D.A, Computers & Fluids, 20(3), pp. 343-358, 1991), under the shear of a laminar boundary-layer flow and its response of the near-wall flows. Here, the streamwise vortex tube is a lifted streamwise vortex. The circulation and angle-to-wall of the vortex tube are varied. Circulation above a threshold produces multiple hairpin vortices that align in the streamwise direction ove…
We investigate the large-scale influence of numerical noises as tiny artificial stochastic disturbances on a sustained turbulence. Using the two-dimensional (2D) turbulent Rayleigh-Bénard (RB) convection as an example, we numerically solve the NS equations, separately, by means of a traditional algorithm with double precision (marked by RKwD) and the so-called clean numerical simulation (CNS). The numerical simulation given by the RKwD is a mixture of the "true" physical solution and the "false" numerical noises that is random and can be regarded as a kind of artificial stochastic disturbances…
In the context of transition analysis, linear input-output analysis determines worst-case disturbances to a laminar base flow based on a generic right-hand-side volumetric/boundary forcing term. The worst-case forcing is not physically realizable, and, to our knowledge, a generic framework for posing physically-realizable worst-case disturbance problems is lacking. In natural receptivity analysis, disturbances are forced by matching (typically local) solutions within the boundary layer to outer solutions consisting of free-stream vortical, entropic, and acoustic disturbances. We pose a scatter…
Dissimilar heat transfer enhancement in spatially developing flow between parallel perforated plates by inducing a streamwise travelling-wave disturbance
Center for Research on Innovative Simulation Software, Institute of Industrial Science, The University of Tokyo（东京大学工业科学研究所创新模拟软件研究中心）
A parametric numerical study of three-dimensional instability of steady flows in a helical pipe of arbitrary curvature and torsion is carried out. The computations are performed by a numerical approach verified against independent experimental and numerical results in a previous study. The results are reported as dependences of the critical Reynolds number, critical wavenumber and the critical frequency on the dimensionless pipe curvature and torsion. A multiplicity of different disturbance modes becoming most unstable at different values of the governing parameters, is observed. Patterns of t…
We report experimental results on elastic instability in a viscoelastic channel shear flow due to only a natural non-smoothed inlet and small holes along the channel for pressure measurements. We show that non-normal mode instability results in elastic waves and chaotic flow self-organized into periodically cycled stream-wise streaks synchronized by elastic wave frequency. The chaotic flow persists above the transition with increasing $Wi$ further into elastic turbulence and drag reduction regimes. Thus, we resolve the recent puzzle whether strong prearranged perturbations are necessary to get…
The Tayler instability is a kink-type flow instability which occurs when the electrical current through a conducting fluid exceeds a certain critical value. Originally studied in the astrophysical context, the instability was recently shown to be also a limiting factor for the upward scalability of liquid metal batteries. In this paper, we continue our efforts to simulate this instability for liquid metals within the framework of an integro-differential equation approach. The original solver is enhanced by multi-domain support with Dirichlet-Neumann partitioning for the static boundaries. Part…
