Stratified Shear Layer Research Articles

Optimal excitation of two dimensional Holmboe instabilities

Highly stratified shear layers are rendered unstable even at high stratifications by Holmboe instabilities when the density stratification is concentrated in a small region of the shear layer. These instabilities may cause mixing in highly stratified environments. However, these instabilities occur in limited bands in the parameter space. We perform Generalized Stability analysis of the two dimensional perturbation dynamics of an inviscid Boussinesq stratified shear layer and show that Holmboe instabilities at high Richardson numbers can be excited by their adjoints at amplitudes that are orders of magnitude larger than by introducing initially the unstable mode itself. We also determine the optimal growth that is obtained for parameters for which there is no instability. We find that there is potential for large transient growth regardless of whether the background flow is exponentially stable or not and that the characteristic structure of the Holmboe instability asymptotically emerges as a persistent quasi-mode for parameter values for which the flow is stable.

RETRACTED: The development of autonomous low-cost biped mobile surveillance robot by intelligent bricks

RETRACTED: The development of autonomous low-cost biped mobile surveillance robot by intelligent bricks

RETRACTED: Stability analysis of community and ecosystem hierarchies using the Lyapunov method

RETRACTED: Stability analysis of community and ecosystem hierarchies using the Lyapunov method

RETRACTED: Identification and monitoring of bridge health from ambient vibration data

Many bridges in Taiwan have been in use from the period that Taiwan was governed by the Japanese, over 50 years ago, which is the average ultimate usable lifetime of such structures. Three-quarters of the bridges on major highways have been in use for more than 20 years and numerous bridges on country roads have also been in use for more than 20 years. In other words, most of the bridges in Taiwan are aging and may require repair or replacement. Ambient vibration tests are utilized to measure the response of old bridges, which are difficult to equip with accelerometers. The Fourier transform method is traditionally used to gain important information about ambient vibration records. However, the development of information technology over the last 20 years has meant that there are more kinds of signal management technologies, including the wavelet and Hilbert—Huang transform (HHT) methods. In this study we investigate the characteristics of aging bridges by comparison with their structural properties. We analyze their ambient vibration, and discuss the possible influence of the frequency function. Long-term environmental impacts create many structural problems, but with traditional methods examination of bridge health is difficult. Therefore, in our HHT management system, we examine destroyed bridges. The characteristics and behavior of bridges subjected to random loading can be understood by analysis with the random decrement technique and the frequency response function method.

RETRACTED: A case study of damage detection in benchmark buildings using a Hilbert-Huang Transform-based method

In this study we investigate the feasibility of detecting structural damage using the Hilbert--Huang Transform (HHT) method. A damage detection index, which we call the ratio of equivalent damping ratio (RED), is proposed. The damage detection index is evaluated using the HHT and the Fast Fourier Transform (FFT) methods for the analysis of shaking table test data obtained for benchmark models based upon the Kobe and El Centro earthquakes. The results indicate that, when the response of the structure is in the elastic region, the RED value changes only slightly in both the HHT and the FFT spectra. In addition, when the structural response is nonlinear (i.e., member yielding occurs), the RED and peak ground acceleration curves indicate the incremental change in the HHT spectra. However, the same phenomena cannot be found in the FFT spectra. Moreover, there is greater change in the value of the RED for the top floor than for the other floors. Furthermore, structural damage is detected only when acceleration response data from the top floor is used. Therefore, the RED estimated from the smoothed HHT spectra is an effective and sensitive index for detecting structural damage. The proposed RED strategy will be used to establish an on-line health monitoring scheme for detecting structural damage in steel structures right after the occurrence of ground motion.

RETRACTED: Fuzzy Lyapunov Stability Analysis and NN Modeling for Tension Leg Platform Systems

RETRACTED: Fuzzy Lyapunov Stability Analysis and NN Modeling for Tension Leg Platform Systems

Identifying unstable modes in stratified shear layers

One interpretation of the mechanism of instability in stratified shear flows is based on the idea that two independently propagating waves may interact to cause mutual growth in one another. This theory is used in the present study to develop a diagnostic that can be used to identify different types of unstable modes. We focus on stratified shear layers that are susceptible to both the Kelvin–Helmholtz (KH) and Holmboe (H) modes of instability—though the formulation is more general. The diagnostic is found to be useful in differentiating between KH and H modes in the symmetric stratified shear layer (where the center of the shear layer and the density interface coincide). The asymmetric stratified shear layer is also examined since there is no clear distinction between KH- and H-type modes in this flow. The KH mechanism of growth is predicted to extend to stronger stratifications (i.e., larger bulk Richardson numbers) than in the symmetric case, in qualitative agreement with nonlinear numerical results. However, the transition is found to be a gradual one in which the KH mechanism gives way to the H as the bulk Richardson number is increased. In order to demonstrate the utility of the method, we apply it to instability observed in the Fraser River estuary.

RETRACTED: The Development of Half-circle Fuzzy Numbers and Application in Fuzzy Control

RETRACTED: The Development of Half-circle Fuzzy Numbers and Application in Fuzzy Control

Transport and mixing of density in a continuously stratified shear layer

Scalar transport and mixing by active turbulence in a high Reynolds number inhomogeneous stratified shear layer are investigated using three-dimensional Direct Numerical Simulation. Two density profiles are considered: (i) two layers of homogenous fluid with different density, namely the two-layer case, and (ii) a continuously stratified background ambient, namely the Jd case. The evolution of the mixing layer includes shear instability, formation of Kelvin–Helmholtz rollers, transition to turbulence, fully developed active turbulence, and, finally, decay toward a laminar state. In the Jd case, internal gravity waves carrying momentum and energy are observed to propagate away from the shear layer. Although different during the initial evolution, the eddy diffusivity and mixing efficiency when plotted as a function of buoyancy, Reynolds number takes similar values between the two cases later in time during the stage when turbulence decays. During this stage, the mixing efficiency computed based on the buoy...

Interactions between magnetohydrodynamic shear instabilities and convective flows in the solar interior

Motivated by the interface model for the solar dynamo, this paper explores the complex magnetohydrodynamic interactions between convective flows and shear-driven instabilities. Initially, we consider the dynamics of a forced shear flow across a convectively-stable polytropic layer, in the presence of a vertical magnetic field. When the imposed magnetic field is weak, the dynamics are dominated by a shear flow (Kelvin-Helmholtz type) instability. For stronger fields, a magnetic buoyancy instability is preferred. If this stably stratified shear layer lies below a convectively unstable region, these two regions can interact. Once again, when the imposed field is very weak, the dynamical effects of the magnetic field are negligible and the interactions between the shear layer and the convective layer are relatively minor. However, if the magnetic field is strong enough to favour magnetic buoyancy instabilities in the shear layer, extended magnetic flux concentrations form and rise into the convective layer. These magnetic structures have a highly disruptive effect upon the convective motions in the upper layer.

Dynamics of a stratified shear layer above a region of uniform stratification

Direct numerical simulations (DNS) are performed to investigate the behaviour of a weakly stratified shear layer in the presence of a strongly stratified region beneath it. Both, coherent Kelvin–Helmholtz (KH) rollers and small-scale turbulence, are observed during the evolution of the shear layer. The deep stratification measured by the Richardson number Jd is varied to study its effect on the dynamics. In all cases, a pycnocline is found to develop at the edges of the shear layer. The region of maximum shear shifts downward with increasing time. Internal waves are excited, initially by KH rollers, and later by small-scale turbulence. The wave field generated by the KH rollers is narrowband and of stronger amplitude than the broadband wave field generated by turbulence. Linear theory based on Doppler-shifted frequency of the KH mode is able to predict the angle of the internal wave phase lines during the direct generation of internal waves by KH rollers. Waves generated by turbulence are relatively weaker with a broader range of excitation angles which, in the deep region, tend towards a narrower band. The linear theory that works for the internal waves excited by KH rollers does not work for the turbulence generated waves. The momentum transported by the internal waves into the interior can be large, about 10% of the initial momentum in the shear layer, when Jd ≃ 0.25. Integration of the turbulent kinetic energy budget in time and over the shear layer thickness shows that the energy flux can be up to 17% of the turbulent production, 33% of the turbulent dissipation rate and 75% of the buoyancy flux. These numbers quantify the dynamical importance of internal waves. In contrast to linear theory where the effect of deep stratification on the shear layer instabilities has been found to be weak, the present nonlinear simulations show that the evolution of the shear layer is significantly altered because of the significant momentum and energy carried away by the internal waves.

Image analysis applied to the study of mixing in a stably stratified shear layer

The development and breaking of Kelvin–Helmholtz waves is one of the primary causes of mixing in many geophysical and engineering flows with layers of fluids having different densities and horizontal velocities. Although this phenomenon was extensively studied in the field, a complete description can be experimentally obtained only by the use of image analysis techniques that are applicable only in laboratory experiments. The particular nature of the flow, especially before the development of the waves when the flow is parallel but in opposite direction, makes the application of the classical image velocimetry techniques non-trivial. With this in mind, a stably stratified shear flow was reproduced in the laboratory by means of a tilting tank. The velocity and density fields were measured simultaneously with multipoint time-resolved techniques during the formation and development of the Kelvin–Helmholtz waves. A novel particle tracking procedure is proposed that includes the stretching of the acquired images in the direction orthogonal to the main motion. Tests on synthetic images show a meaningful improvement in the effectiveness of particle tracking when using the proposed technique. Laser-Induced Fluorescence (LIF) data have been acquired by a second camera, equipped with a band-pass filter in order to measure only the fluoresced light. Particle Tracking Velocimetry (PTV) and LIF data have been referenced to the same frame by a registration procedure based on an affine transformation. In the range of the parameters investigated during the experiments, the evolution of the interface thickness and sharpness scales with the advective time scale. The analysis of the space–time evolution of the longitudinal statistics gives a comprehensive picture of the development and breaking of the waves.

Evolution of an initially turbulent stratified shear layer

Direct numerical simulations of a stratified shear layer are performed for several different values of Reynolds, bulk Richardson, and Prandtl numbers. Unlike previous numerical studies, the initial perturbations are turbulent. These initial broadband perturbations do not allow the formation of distinct coherent structures such as Kelvin-Helmholtz rollers and streamwise vortices found in previous studies. In the absence of stratification, the shear layer thickness grows linearly and fully developed turbulence is achieved with mean velocities, turbulence intensities, and turbulent kinetic energy budgets that agree well with previous experimental and numerical data. When buoyancy is included, the shear layer grows to an asymptotic thickness, and the corresponding bulk Richardson number, Rib, is within the range, 0.32±0.06, found in previous studies. The apparent scatter in the evolution of Rib is shown to have a systematic dependence on Reynolds and Prandtl numbers. A detailed description of buoyancy effects on turbulence energetics, transport, and mixing is presented. The Reynolds shear stress, ⟨u1′u3′⟩, is significantly reduced by buoyancy, thus decreasing the shear production of turbulence. Owing to buoyancy, gradients in the vertical direction tend to be larger than other gradients in the fluctuating velocity and density fields. However, this anisotropy of the gradients is lower when the Reynolds number increases. Coherent finger-like structures are identified in the density field at late time and their vertical extent obtained by a scaling analysis.

Mixing properties of a stably stratified parallel shear layer

The results of a laboratory investigation on turbulent mixing of mass and momentum associated with the collapse of Kelvin-Helmholtz waves which develop in a stably stratified parallel shear layer with O(103) Schmidt number are presented. The waves were generated in a stratified, tilting tank using a denser fluid underlying a lighter fluid with a velocity shear between the layers. Detailed velocity and density measurements were conducted simultaneously using particle tracking velocimetry and laser-induced fluorescence techniques. Estimation of the efficiency of mixing, the ratio between the diffusive flux of density responsible for mixing, to the turbulent kinetic energy dissipation rate, suggest it is independent of the initial values of the Reynolds and the bulk Richardson numbers. The measurements of the eddy diffusivities of mass and momentum showed a reasonable agreement with other laboratory-based predictions of turbulent mixing and observational data in atmospheric stably stratified flows.

Evolution and mixing of asymmetric Holmboe instabilities

When a stably stratified density interface is embedded in a region of strong velocity shear, hydrodynamic instabilities result. Here we generalize the stratified shear layer to allow an offset between the centre of the shear layer and the density interface. By including this asymmetry, and keeping the density interface thin with respect to the shear layer, the asymmetric Holmboe (AH) instability emerges. This study examines the evolution and mixing behaviour of AH instabilities, and compares the results to the well-known Kelvin–Helmholtz (KH) and Holmboe instabilities. This is done by performing a series of direct numerical simulations (DNS). The simulation results show that there are two different mixing mechanisms present. The first is a feature of KH instabilities and leads to the mixing and production of intermediate density fluid. The second mixing mechanism is found in AH and Holmboe instabilities and consists of regions of mixing and turbulence production that are located on one or both sides of the density interface. Since the Holmboe-type instabilities do not generate a large-scale overturning of the central isopycnal, the density interface is able to retain its identity throughout the mixing event. The amount of mixing that takes place is found to be strongly dependent on the degree of asymmetry in the flow.

Evolution of a forced stratified mixing layer

Laboratory measurements were carried out in a spatially developing stably stratified shear layer generated downstream of a splitter plate. The instabilities were controlled using a flapper spanning the entire shear layer, with the flapper forced at the fastest growing frequency of the primary [Kelvin-Helmholtz (KH)] instability. The measurements were taken as the KH instabilities roll up, break down, and degenerate into stratified turbulence. Both stratified and homogeneous shear layers were considered, the latter acting as the “baseline” case. The measurements included the streamwise and vertical velocities (made using X-wire hot film probes), which allowed calculation of the mean and rms velocities, turbulent kinetic energy (TKE) dissipation, and TKE production. The density and its gradients were measured using miniature conductivity probes. The measurements and flow visualization elicited interesting features of KH evolution, namely that KH billows may be turbulent from the onset, the TKE dissipation is largest at early stages of evolution, the production of TKE is a maximum at the breakdown of billows, the decay of turbulence to fossilized motions and concomitant formation of fine (layered) structure occur rapidly after the breakdown of billows, and episodic rebirth of (zombie) turbulence develops before a final permanently fossilized state is achieved.

Instability and Diapycnal Momentum Transport in a Double-Diffusive, Stratified Shear Layer

Abstract The linear stability of a double-diffusively stratified, inflectional shear flow is investigated. Double-diffusive stratification has little effect on shear instability except when the density ratio Rρ is close to unity. Double-diffusive instabilities have significant growth rates and can represent the fastest-growing mode even in the presence of inflectionally unstable shear with a low Richardson number. In the linear regime, background shear has no effect on double-diffusive modes except to select the orientation of the wave vector. The converse is not true: double-diffusive modes modify the mean shear via momentum fluxes. The momentum flux driven by salt sheets is parameterized in terms of a Schmidt number (ratio of eddy viscosity to saline diffusivity) Scs. In the oceanic parameter regime, Scs is less than unity and can be approximated as Scs = 0.08 ln[Rρ/(Rρ − 1)]. Enhanced molecular dissipation by unstable motions is quantified in terms of the dissipation ratio Γ, and the results are compared with observations. Corresponding results are given for diffusive convection in an inflectional shear flow, though linear theory is expected to give a less accurate description of this mechanism.

Dynamics of a stratified shear layer with horizontal shear

The evolution of a stratified shear layer with mean shear in the horizontal direction, orthogonal to gravity, is numerically investigated with focus on the structural organization of the vorticity and density fields. Although the Reynolds number of the flow increases with time, facilitating instabilities and turbulence, the bulk Richardson number signifying the level of stratification also increases. Remarkably rich dynamics is found: turbulence; the emergence of coherent core/braid regions from turbulence; formation of a lattice of dislocated vortex cores connected by thin horizontal sheets of collapsed density and vorticity; density-driven intrusions at the edges of the shear layer; and internal wave generation and propagation. Stratification introduces significant vertical variability although it inhibits the vertical velocity. The molecular dissipation of turbulent kinetic energy and of turbulent potential energy are both found to be substantial even in the case with highest stratification, and primarily concentrated in thin horizontal sheets. The simulation data are used to help explain how buoyancy induces the emergence of columnar vortex cores from turbulence and then dislocates these cores to eventually form a lattice of ‘pancake’ eddies connected by thin sheets with large vertical shear (horizontal vorticity) and density gradient.

Turbulent mixing and transport of collisionless plasmas across a stratified velocity shear layer

Two‐dimensional simulations of the Kelvin‐Helmholtz (K‐H) instability in a nonuniform density medium and with the transverse magnetic field show the strong development of turbulence through nonlinear instabilities. Ideal MHD simulation results have indicated that the difference in density between two media plays a crucial role on the fast turbulent mixing and transport. The onset of the turbulence is triggered not only by the secondary K‐H instability but also by the Rayleigh‐Taylor (R‐T) instability at the density interface inside the normal K‐H vortex. The secondary R‐T instability alters macroscopic structure by transporting dense fluids to tenuous region, while the secondary K‐H instability is just a seed for the turbulence. Full particle simulations are also conducted and reproduces the similar result of the ideal MHDs, except that the strong electrostatic field caused by the secondary R‐T instability scatters ions and deforms the electron density interface. As a result, the mixing area increases anomalously fast and extends spatially as compared to the result in the uniform density case.

The instability and breaking of long internal waves

Laboratory experiments are carried out to determine the nature of internal wave breaking and the limiting wave steepness for progressive, periodic, lowest-mode internal waves in a two-layer, miscible density stratification. Shoaling effects are not considered. The waves investigated here are long relative to the thickness of the density interface separating the two fluid layers. Planar laser-induced fluoresence (PLIF) flow visualization shows that wave breaking most closely resembles a Kelvin–Helmholtz shear instability originating in the high-shear wave crest and trough regions. However, this instability is strongly temporally and spatially modified by the oscillations of the driving wave shear. Unlike a steady stratified shear layer, the wave instability discussed here is not governed by the canonical stability limit. Instead, the wave time scale (the time scale of the destabilizing shear) imposes an additional constraint on instability, lowering the critical Richardson number below 1/4. Experiments were carried out to quantify this instability threshold, and show that, for the range of wavenumbers considered in this study, the critical wave steepness at which the wave breaking occurs is wavenumber-dependent (unlike surface waves). The corresponding critical wave Richardson numbers at incipient wave breaking are well below 1/4, in consonance with a modified instability analysis based on results from stratified shear flow instability theory.