Shear Flow Instability Research Articles

Linear instability of viscous parallel shear flows: revisiting the perturbation no-slip condition

Linear stability analysis currently fails to predict turbulence transition in canonical viscous flows. We show that two alternative models of the boundary condition for incipient perturbations at solid walls produce linear instabilities that could be sufficient to explain turbulence transition. In many cases, the near-wall behaviour of the discovered instabilities is empirically indistinguishable from the classical no-slip condition. The ability of these alternative boundary conditions to predict linear instabilities that are consistent with turbulence transition suggests that the no-slip condition may be an overly simplified model of fluid–solid interface physics, particularly as a description of the flow perturbations that lead to turbulence transition in wall-bounded flows.

Free surface water waves generated by instability of an exponential shear flow in arbitrary depth

The stability of an exponential current in water to infinitesimal perturbations in the presence of gravity and capillarity is revisited and reformulated using the Weber and Froude numbers. Some new results on the generation of gravity-capillary waves are presented, which supplement the previous works of Morland et al. [“Waves generated by shear layer instabilities,” Proc. Math. Phys. Sci. 433, 441–450 (1991)] and Young and Wolfe [“Generation of surface waves by shear-flow instability,” J. Fluid Mech. 739, 276–307 (2014)] on finite depth. To consider perturbations at much larger scales, special attention is given to the stability of exponential currents only in the presence of gravity. More precisely, the present investigation reveals significant insights into the stability of exponential shear currents under different environmental conditions. Notably, we have identified that the dimensionless growth rate increases with the Froude number, providing a deeper understanding of the interplay between shear layer thickness and surface velocity. Furthermore, our analysis elucidates the dimensional wavelength of the most unstable mode, emphasizing its relevance to the characteristic shear layer thickness. Additionally, within the realm of gravity-capillary instabilities, we have established a sufficient condition for the stability of exponential currents based on the Weber number. Our findings are supported by stability diagrams at finite depth, showing how the size of stable domains correlates with the characteristic thickness of the shear layer. Moreover, we have explored the stability of a thin film of liquid in an exponential shearing flow, further enriching our understanding of the complex dynamics involved in such systems.

Evolution of wind-induced wave groups in water of finite depth

The generation of water waves by wind is a fundamental and much-studied problem of scientific and operational concern. One mechanism that has obtained a wide degree of acceptance and use is the Miles air shear flow instability theory in which water waves grow due to energy transfer from the air at a critical level where the wave phase speed matches the wind speed. In this paper we revisit and extend this theory by examining how the predicted wave growth rate depends on the water depth and the wind shear parameters. At the same time we include frictional effects due to water bottom stress and at the water surface, and add an additional driving term due to wave stress in the air near the sea surface, using a turbulent parametrisation. The theory is developed using a frictional modification of the usual potential flow theory for water waves, the modified Euler equations, coupled to linearised air-flow equations. To assist our analysis we develop a long-wave approximation for the key Miles growth parameter, which explicitly shows how this depends on the water depth and the wind shear parameters. Since our focus is on the development of wave groups, we present a forced nonlinear Schrödinger equation in which the forcing term describes wave growth or decay. For very shallow water the modified Euler equations are reduced to their shallow-water counterpart, which are briefly discussed using Riemann invariants.

A polynomial-correction Navier-Stokes characteristic boundary condition

In an effort to assess the efficacy of different non-reflecting boundary conditions (NRBCs) in high-order solvers, several NRBCs have been implemented in the context of the discontinuous Galerkin (DG) discretization. The methods considered are based on buffer zone techniques and boundary-imposed conditions. The former mainly utilizes the sponge layer (SL), the perfectly matched layer (PML) and the supersonic layer (SSL), while the latter uses a Riemann extrapolation (RE) technique and a novel polynomial-correction Navier-Stokes characteristic boundary condition (PC-NSCBC). The developed PC-NSCBC method reconstructs an explicit boundary state, instead of modifying the equations on the boundary or specifying ad hoc compatibility conditions on corners and edges. This property pairs well with a Riemann solver, as is typical in a DG method. Moreover, the boundary state can be assembled either from a one-dimensional perspective (NSCBC1D) or using partial knowledge of multi-dimensional effects (NSCBC3D).Four different benchmark problems are considered: a 1D linear acoustic pulse in a quiescent flow, a 2D non-linear pressure pulse in a quiescent flow, an isentropic vortex and a shear-flow vortex shedding instability. Results imply that mainly the PML performs better than most other approaches. This is especially true for acoustically-dominated flows. Alternatively, for flow conditions predominantly less acoustic in nature and strongly non-linear, instabilities in the PML may arise. The SL and SSL both suggest that a larger layer is required to deliver comparable results to the PML. The proposed (PC-)NSCBC methods demonstrate reasonable success with no instabilities reported, which is impressive given the comparatively less computational effort required. Partial inclusion of the transverse terms in the NSCBC3D noticeably enhances the output of the NSCBC1D, albeit further investigation is required to determine an optimal, universal expression for its transverse tuning coefficient.

Connecting shear flow and vortex array instabilities in annular atomic superfluids

Connecting shear flow and vortex array instabilities in annular atomic superfluids

Long-wave instabilities of sloping stratified exchange flows

We investigate the linear instability of two-layer stratified shear flows in a sloping two-dimensional channel, subject to non-zero longitudinal gravitational forces. We reveal three previously unknown instabilities, distinct from the well-known Kelvin–Helmholtz instability and Holmboe wave instability, in that they have longer wavelengths (of the order of 10 to $10^3$ shear-layer depths) and often slower growth rates. Importantly, they can grow in background flows with gradient Richardson number $\gg 1$ , which offers a new mechanism to sustain turbulence and mixing in strongly stratified flows. These instabilities are shown to be generic and relatively insensitive to Reynolds number, Prandtl number, base flow profile and boundary conditions. The nonlinear evolution of these instabilities is investigated through a forced direct numerical simulation, in which the background momentum and density are sustained. The growth of long unstable waves in background flows initially stable to short wave causes a decrease in the local gradient Richardson number. This leads to local nonlinear processes that result in small-scale overturns resembling Kelvin–Helmholtz billows. Our results establish a new energy exchange pathway, where the mean kinetic energy of a strongly stratified flow is extracted by primary unstable long waves and secondary short waves, and subsequently dissipated into internal energy.

Instability of adiabatic shear flows in a channel

The combined forced and free convection flow of a Newtonian fluid in a horizontal plane-parallel channel is examined. The boundary walls are considered as adiabatic, so that the only thermal effect acting in the fluid is the viscous dissipation due to the nonzero shear flow. As the shear flow may be caused by either an imposed horizontal pressure gradient or an imposed velocity difference between the bounding walls, one may envisage two scenarios where the stationary basic flow is Poiseuille-like or Couette-like, respectively. Both cases are surveyed with a special focus on practically significant cases where the Gebhart number is considered as very small, though nonzero. Furthermore, the Prandtl number is assumed as extremely large, thus pinpointing a scenario of creeping buoyant flow with a fluid having a very large viscosity. Within such a framework, the instability of the basic flow is analysed versus small-amplitude perturbations.

Vorticity wave interaction, Krein collision, and exceptional points in shear flow instabilities.

We relate the model of vorticity wave interaction to Krein collision, PT-symmetry breaking, and the formation of exceptional points in shear flow instabilities. We show that the dynamical system of coupled vorticity waves is a pseudo-Hermitian system with nonreciprocal coupling terms. Krein signatures of the eigenvalues are illustrated as the signs of the action of the vorticity waves. Interaction between positive-action and negative-action vorticity waves then corresponds to the Krein collision between eigenvalues with opposite Krein signatures, the spontaneous breaking of PT symmetry, and the formation of exceptional points. The control parameter of the PT-symmetry-breaking bifurcation is the ratio between frequency detuning and coupling strength of the vorticity waves. The critical behavior near the exceptional points is described as a transition between phase-locking and phase-slip dynamics of the vorticity waves. The phase-slip dynamics correspond to nonmodal, transient growth of perturbations in the regime of unbroken PT symmetry, and the phase-slip frequency Ω∝|k-k_{c}|^{1/2} shares the same critical exponent with the phase rigidity of system eigenvectors.

Constraints on the Alfvénicity of Switchbacks

Switchbacks (SBs) are localized structures in the solar wind containing deflections of the magnetic field direction relative to the background solar wind magnetic field. The amplitudes of the magnetic field deflection angles (θ) for different SBs vary from ∼40° to ∼160°–170°. Alignment of the perturbations of the magnetic field (Δ B ) and the bulk solar wind velocity (Δ V ) is observed inside SBs so that Δ V ∼ Δ B when the background magnetic field is directed toward the Sun (if the background solar wind magnetic field direction is anti-sunward then Δ V ∼ − Δ B , supporting anti-sunward propagation in the background solar wind frame). This causes spiky enhancements of the radial bulk velocity inside SBs. We have investigated the deviations of SB perturbations from Alfvénicity by evaluating the distribution of the parameter α, defined as the ratio of the parallel to Δ B component of Δ V to Δ V A = Δ B /4π n i m i inside SBs, i.e., α = V ∣∣/∣Δ V A∣ (α = ∣Δ V ∣/∣Δ V A∣ when Δ V ∼ Δ B ), which quantifies the deviation of the perturbation from an Alfvénic one. Based on Parker Solar Probe (PSP) observations, we show that α inside SBs has systematically lower values than it has in the pristine solar wind: α inside SBs observed during PSP Encounter 1 were distributed in a range from ∼0.2 to ∼0.9. The upper limit on α is constrained by the requirement that the jump in velocity across the switchback boundary be less than the local Alfvén speed. This prevents the onset of shear flow instabilities. The consequence of this limitation is that the perturbation of the proton bulk velocity in SBs with θ > π/3 cannot reach α = 1 (the Alfvénicity condition) and the highest possible α for an SB with θ = π is 0.5. These results have consequences for the interpretation of switchbacks as large amplitude Alfvén waves.

Generation of Subion Scale Magnetic Holes from Electron Shear Flow Instabilities in Plasma Turbulence

Magnetic holes (MHs) are coherent structures associated with strong magnetic field depressions in magnetized plasmas. They are observed in many astrophysical environments at a wide range of scales, but their origin is still under debate. In this work, we investigate the formation of subion scale MHs using a fully kinetic 2D simulation of plasma turbulence initialized with parameters typical of the Earth’s magnetosheath. Our analysis shows that the turbulence is capable of generating subion scale MHs from large scale fluctuations via the following mechanism: first, the nonlinear large scale dynamics spontaneously leads to the development of thin and elongated electron velocity shears; these structures then become unstable to the electron Kelvin–Helmholtz instability and break up into small scale electron vortices; the electric current carried by these vortices locally reduces the magnetic field, inducing the formation of subion scale MHs. The MHs thus produced exhibit features consistent with satellite observations and with previous numerical studies. We finally discuss the kinetic properties of the observed subion scale MHs, showing that they are characterized by complex non-Maxwellian electron velocity distributions exhibiting anisotropic and agyrotropic features.

Three-dimensional shear-flow instability saturation via stable modes

Turbulence in three dimensions (3D) supports vortex stretching that has long been known to accomplish energy transfer to small scales. Moreover, net energy transfer from large-scale, forced, unstable flow-gradients to smaller scales is achieved by gradient-flattening instability. Despite such enforcement of energy transfer to small scales, it is shown here that the shear-flow-instability-supplied 3D-fluctuation energy is largely inverse-transferred from the fluctuation to the mean-flow gradient, and such inverse transfer is more efficient for turbulent fluctuations in 3D than in two dimensions (2D). The transfer is due to linearly stable eigenmodes that are excited nonlinearly. The stable modes, thus, reduce both the nonlinear energy cascade to small scales and the viscous dissipation rate. The vortex-tube stretching is also suppressed. Up-gradient momentum transport by the stable modes counters the instability-driven down-gradient transport, which also is more effective in 3D than in 2D (≈70% vs ≈50%). From unstable modes, these stable modes nonlinearly receive energy via zero-frequency fluctuations that vary only in the direction orthogonal to the plane of 2D shear flow. The more widely occurring 3D turbulence is thus inherently different from the commonly studied 2D turbulence, despite both saturating via stable modes.

Tripolar vortices in inhomogeneous magnetoplasmas in the presence of non-Maxwellian electron distributions

Nonlinear equations governing the characteristics of tripolar vortices (TPVs) are investigated in an inhomogeneous magnetoplasma having inertialess non-Maxwellian electrons that obey the Cairns, kappa, and (r, q)-distributions. Analytical and numerical solutions of the nonlinear equations are presented for various possible cases. In this regard, the dispersion relation for the drift ion-acoustic waves (IAWs) is derived, and the condition describing the shear flow instability is discussed. It is realized that enhancing the impact of non-Maxwellian electrons in the aforementioned three distributions modifies the size and formation of TPVs. It is found that the increase in the electron concentration in the regions of low-phase space density leads to enhancement in the size of TPVs and the perturbation potential as compared to the effect of increasing concentration of electrons in the regions of high phase space density. The riveting interplay of low and high-energy electrons with spiky distribution and the resulting novel effects on the propagation of vortex structures are also discussed in detail. The present study is useful to understand the (non)linear propagation characteristics of the drift IAWs in space plasmas with special reference to the F-region of the ionosphere and also in laboratory experiments where the nonthermal distribution functions are usually found.

Modeling the Day‐To‐Day Variability of Midnight Equatorial Plasma Bubbles With SAMI3/SD‐WACCM‐X

AbstractIt is well‐known that equatorial plasma bubbles (EPBs) are highly correlated to the post‐sunset rise of the ionosphere on a climatological basis. However, when proceeding to the daily EPB development, what controls the day‐to‐day/longitudinal variability of EPBs remains a puzzle. In this study, we investigate the underlying physics responsible for the day‐to‐day/longitudinal variability of EPBs using the Sami3 is A Model of the Ionosphere (SAMI3) and the Specified Dynamics Whole Atmosphere Community Climate Model with thermosphere‐ionosphere eXtension (SD‐WACCM‐X). Simulation results on October 20, 22, and 24, 2020 were presented. SAMI3/SD‐WACCM‐X self‐consistently generated midnight EPBs on October 20 and 24, displaying irregular and regular spatial distributions, respectively. However, EPBs are absent on October 22. We investigate the role of gravity waves on upwelling growth and EPB development and discuss how gravity waves contribute to the distributions of EPBs. We found the westward wind associated with solar terminator waves and gravity waves induces polarization electric fields that map to the equatorial ionosphere from higher latitudes, resulting in midnight vertical drift enhancement and retrograde plasma flow. The upward vertical drift and retrograde flow further lead to shear flow instability and midnight plasma vortex, creating background conditions identical to the post‐sunset ionosphere. This provides conditions favorable for the upwelling growth and EPB development. The converging and diverging winds associated with solar terminator waves and midnight temperature maximum also affect the longitudinal distribution of EPBs. The absence of EPBs on October 22 is related to the weak westward wind associated with solar terminator waves.

Non-ideal instabilities in sinusoidal shear flows with a streamwise magnetic field

We investigate the linear stability of a sinusoidal shear flow with an initially uniform streamwise magnetic field in the framework of incompressible magnetohydrodynamics (MHD) with finite resistivity and viscosity. This flow is known to be unstable to the Kelvin–Helmholtz instability in the hydrodynamic case. The same is true in ideal MHD, where dissipation is neglected, provided the magnetic field strength does not exceed a critical threshold beyond which magnetic tension stabilizes the flow. Here, we demonstrate that including viscosity and resistivity introduces two new modes of instability. One of these modes, which we refer to as an Alfvénic Dubrulle–Frisch instability, exists for any non-zero magnetic field strength as long as the magnetic Prandtl number ${{{Pm}}} < 1$ . We present a reduced model for this instability that reveals its excitation mechanism to be the negative eddy viscosity of periodic shear flows described by Dubrulle & Frisch (Phys. Rev. A, vol. 43, 1991, pp. 5355–5364). Finally, we demonstrate numerically that this mode saturates in a quasi-stationary state dominated by counter-propagating solitons.

Baroclinic Instability of a Time-Dependent Zonal Shear Flow

In the real atmosphere, the development of large-scale motion is often related to the baroclinic properties of the atmosphere. So, it is necessary to discuss the stability condition of baroclinic flow. It is advantageous to use a layered model to discuss baroclinic instability, not only to apply the potential vortex equation directly, but also to deal with shear of basic flow. The stability and oscillatory shear ability of Rossby waves are studied based on the two-layer Phillips model in the β plane; then, we summarize the baroclinic instability of time-dependent zonal shear flows. The multiscale method is used to eliminate some terms of natural frequency oscillations of nonlinear operators in the third-order expansion, thus generating an equation about the amplitude of the lowest-order Rossby wave in the long-time variable. The large amplitude perturbation begins to decrease, which produces the desired behavior. After the amplitude decreases for some time, the amplitude of Rossby waves can still be found to oscillate periodically with the time variable.

Critical-layer instability of shallow-water magnetohydrodynamic shear flows

In this paper, the instability of shallow-water shear flow with a sheared parallel magnetic field is studied. Waves propagating in such magnetic shear flows encounter critical levels where the phase velocity relative to the basic flow,$c-U(y)$, matches the Alfvén wave velocities$\pm B(y)/\sqrt {\mu \rho }$, based on the local magnetic field$B(y)$, the magnetic permeability$\mu$, and the mass density of the fluid$\rho$. It is shown that when the two critical levels are close to each other, the critical layer can generate an instability. The instability problem is solved, combining asymptotic solutions at large wavenumbers and numerical solutions, and the mechanism of instability explained using the conservation of momentum. For the shallow-water magnetohydrodynamic system, the paper gives the general form of the local differential equation governing such coalescing critical layers for any generic field and flow profiles, and determines precisely how the magnetic field modifies the purely hydrodynamic stability criterion based on the potential vorticity gradient in the critical layer. The curvature of the magnetic field profile, or equivalently the electric current gradient$J' = - B''/\mu$in the critical layer, is found to play a complementary role in the instability.

Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers

The recently discovered centre-mode instability of rectilinear viscoelastic shear flow (Garget al.,Phys. Rev. Lett., vol. 121, 2018, 024502) has offered an explanation for the origin of elasto-inertial turbulence that occurs at lower Weissenberg numbers ($Wi$). In support of this, we show using weakly nonlinear analysis that the subcriticality found in Pageet al.(Phys. Rev. Lett., vol. 125, 2020, 154501) is generic across the neutral curve with the instability becoming supercritical only at low Reynolds numbers ($Re$) and high$Wi$. We demonstrate that the instability can be viewed as purely elastic in origin, even for$Re=O(10^3)$, rather than ‘elasto-inertial’, as the underlying shear doesnotfeed the kinetic energy of the instability. It is also found that the introduction of a realistic maximum polymer extension length,$L_{max}$, in the FENE-P model moves the neutral curve closer to the inertialess$Re=0$limit at a fixed ratio of solvent-to-solution viscosities,$\beta$. At$Re=0$and in the dilute limit ($\beta \rightarrow 1$) with$L_{max} =O(100)$, the linear instability can be brought down to more physically relevant$Wi\gtrsim 110$at$\beta =0.98$, compared with the threshold$Wi=O(10^3)$at$\beta =0.994$reported recently by Khalidet al.(Phys. Rev. Lett., vol. 127, 2021, 134502) for an Oldroyd-B fluid. Again, the instability is subcritical, implying that inertialess rectilinear viscoelastic shear flow is nonlinearly unstable – i.e. unstable to finite-amplitude disturbances – for even lower$Wi$.

Influence of grid resolution of large-eddy simulations on foehn-cold pool interaction.

Numerical simulations are performed to assess the influence of horizontal and vertical model resolution on the turbulent erosion of a cold-air pool (CAP) by foehn winds in an Alpine valley near Innsbruck, Austria. Strong wind shear in the transition zone from the CAP to the overlying foehn generates turbulence by shear-flow instability and contributes to the CAP erosion. The sensitivity of this process to grid resolution in the "grey zone" of turbulence is studied with the Weather Research and Forecasting model in large-eddy simulation (LES) mode with a horizontal grid spacing of 200, 40, and 13.33 m and in mesoscale mode with a grid spacing of 1 km. Moreover, two different vertical resolutions are tested. The mesoscale simulation exhibits deficiencies in the CAP development and is neither able to resolve nor parametrize the effect of Kelvin-Helmholtz (K-H) instability. In contrast, the LES with the coarsest horizontal grid spacing begins to explicitly permit K-H instability, albeit individual K-H waves are not completely resolved, and thereby greatly improves the stability and wind profile of the foehn. Refining the LES grid spacing leads to a more explicit and realistic representation of turbulence, but surprisingly has little impact on mean quantities. An increase in the vertical resolution shows the greatest benefit in the turbulent upper part of the foehn jet, whereas an increase in the horizontal resolution improves the turbulence characteristics, especially at the foehn-CAP interface. However, spectral analysis indicates that even a horizontal grid spacing of 40 m does not fully capture the energy cascade in the inertial subrange. Eddies remain too large and foehn-CAP interaction is too vigorous compared with the simulation with 13.33 m grid spacing. Nevertheless, results illustrate the potential benefit of an (100 m) model resolution for improving numerical weather predictions in complex terrain.

Excitation of Initial Waves by Wind: A Theoretical Model and Its Experimental Verification.

We present a theory of evolution of wind waves in time and space under abruptly applied wind forcing that is experimentally validated in a laboratory wind-wave tank. The model describes qualitatively and quantitatively the complex wave field development from the initial smooth surface to the finite state. The stochastic nature of wind waves is treated by considering an ensemble of coexisting unstable harmonics that grow due to shear flow instability. Breaking limits the wave growth initially; the process is then controlled by fetch-limited growth duration.

Mushroom-instability-driven Magnetic Reconnections in Collisionless Relativistic Jets

Abstract We study the kinetic plasma dynamics in collisionless relativistic jets with velocity shear, by carrying out particle-in-cell simulations in the transverse plane of a jet. It is discovered that intermittent magnetic reconnections (MRs) are driven by mushroom instability (MI), which is an important kinetic-scale plasma instability in the plasma shear flows with relativistic bulk speed. We refer to this sequence of kinetic plasma phenomena as “MI-driven MR.” The MI-driven MRs intermittently occur with moving the location of the reconnection points from the vicinity of the initial velocity-shear surface toward the center of the jet. As a consequence, the number density of high-energy electrons that are accelerated by MI-driven MRs increases with time in the region inside the initial velocity-shear surface with the accompanying generation and subsequent amplification of magnetic fields by MI. The maximum Lorentz factor of electrons increases with initial bulk Lorentz factor of the jet. A possible relation of MI-driven MR to the bright synchrotron emission in the jet spine of an active galactic nucleus jet is also discussed.