Instability of Baroclinic Tidal Flow in a Stratified Fjord

2010 ◽  
Vol 40 (1) ◽  
pp. 139-154 ◽  
Author(s):  
Zhiyu Liu
Keyword(s):  
Growth Rates ◽  
Richardson Number ◽  
Tidal Flow ◽  
Maximum Amplitude ◽  
Buoyancy Frequency ◽  
Unstable Flow ◽  
Mode Structure ◽  
Turbulent Dissipation ◽  
Second Mode ◽  
The Stability

Abstract The Taylor–Goldstein equation is used to investigate the stability of a baroclinic tidal flow observed in a stratified fjord. The flow is analyzed at hourly intervals when turbulent dissipation measurements were made. The critical gradient Richardson number is often close to the Miles–Howard limit of 0.25, but sometimes it is substantially less. Although during 8 of the 24 periods examined the flow is marginally stable, it is either very stable or very unstable in others. For the unstable flow, the e-folding period of the fastest growing disturbances is 83–455 s, about 46% of the buoyancy period at the levels where the fastest growing disturbances have their maximum amplitude. These disturbances to the flows have wavelengths about 20%–72% of the water depth and have mostly a second-mode structure. Simultaneous measurements of the flow and turbulence allow for testing of the hypothesis that the growth rates of the most unstable disturbances are related to the turbulent dissipation rates. Dissipation is found to depend on the growth rates, but only to a power of about 1.2; there is a stronger (power 1.8) dependence on the buoyancy frequency.

Instability and hydraulics of turbulent stratified shear flows

2012 ◽  
Vol 695 ◽  
pp. 235-256 ◽  
Author(s):  
Zhiyu Liu ◽  
S. A. Thorpe ◽  
W. D. Smyth
Keyword(s):  
Reynolds Number ◽  
Growth Rates ◽  
Dissipation Rate ◽  
Richardson Number ◽  
Turbulent Shear ◽  
Small Scale ◽  
Buoyancy Frequency ◽  
Neutral Stability ◽  
Clyde Sea ◽  
And Diffusion

AbstractThe Taylor–Goldstein (T–G) equation is extended to include the effects of small-scale turbulence represented by non-uniform vertical and horizontal eddy viscosity and diffusion coefficients. The vertical coefficients of viscosity and diffusion, ${A}_{V} $ and ${K}_{V} $, respectively, are assumed to be equal and are expressed in terms of the buoyancy frequency of the flow, $N$, and the dissipation rate of turbulent kinetic energy per unit mass, $\varepsilon $, quantities that can be measured in the sea. The horizontal eddy coefficients, ${A}_{H} $ and ${K}_{H} $, are taken to be proportional to the dimensionally correct form, ${\varepsilon }^{1/ 3} {l}^{4/ 3} $, found appropriate in the description of horizontal dispersion of a field of passive markers of scale $l$. The extended T–G equation is applied to examine the stability and greatest growth rates in a turbulent shear flow in stratified waters near a sill, that at the entrance to the Clyde Sea in the west of Scotland. Here the main effect of turbulence is a tendency towards stabilizing the flow; the greatest growth rates of small unstable disturbances decrease, and in some cases flows that are unstable in the absence of turbulence are stabilized when its effects are included. It is conjectured that stabilization of a flow by turbulence may lead to a repeating cycle in which a flow with low levels of turbulence becomes unstable, increasing the turbulent dissipation rate and so stabilizing the flow. The collapse of turbulence then leads to a condition in which the flow may again become unstable, the cycle repeating. Two parameters are used to describe the ‘marginality’ of the observed flows. One is based on the proximity of the minimum flow Richardson number to the critical Richardson number, the other on the change in dissipation rate required to stabilize or destabilize an observed flow. The latter is related to the change needed in the flow Reynolds number to achieve zero growth rate. The unstable flows, typical of the Clyde Sea site, are relatively further from neutral stability in Reynolds number than in Richardson number. The effects of turbulence on the hydraulic state of the flow are assessed by examining the speed and propagation direction of long waves in the Clyde Sea. Results are compared to those obtained using the T–G equation without turbulent viscosity or diffusivity. Turbulence may change the state of a flow from subcritical to supercritical.

scholarly journals Unbalanced instabilities of rapidly rotating stratified shear flows

2007 ◽  
Vol 584 ◽  
pp. 373-396 ◽  
Author(s):  
J. VANNESTE ◽  
I. YAVNEH
Keyword(s):  
Couette Flow ◽  
Gravity Waves ◽  
Growth Rates ◽  
Maximum Growth ◽  
Kelvin Waves ◽  
Buoyancy Frequency ◽  
Kelvin Wave ◽  
Asymptotic Results ◽  
The Stability ◽  
Inertia Gravity Waves

The linear stability of a rotating stratified inviscid horizontal plane Couette flow in a channel is studied in the limit of strong rotation and stratification. Two dimensionless parameters characterize the flow: the Rossby number ε, defined as the ratio of the shear to the Coriolis frequency and assumed small, and the ratio s of the Coriolis frequency to the buoyancy frequency, assumed to satisfy s ≤ 1. An energy argument is used to show that unstable perturbations must have large, O(ε−1), wavenumbers. This motivates the use of a WKB-approach which, in the first instance, provides an approximation for the dispersion relation of the various waves that can propagate in the flow. These are Kelvin waves, trapped near the channel walls, and inertia–gravity waves with or without turning points.Although the waves have real phase speeds to all algebraic orders in ε, we establish that the flow is unconditionally unstable. This is the result of linear resonances between waves with oppositely signed wave momenta. Three modes of instabilities are identified, corresponding to the resonance between (i) a pair of Kelvin waves, (ii) a Kelvin wave and an inertia–gravity wave, and (iii) a pair of inertia–gravity waves. Whilst all three modes of instability are active when the Couette flow is anticyclonic, mode (iii) is the only possible instability mechanism when the flow is cyclonic.We derive asymptotic estimates for the instability growth rates. These are exponentially small in ε, i.e. of the form Im ω = a exp(-Ψ/ε) for some positive constants a and Ψ. For the Kelvin-wave instabilities (i), we obtain analytic expressions for a and Ψ; the maximum growth rate, in particular, corresponds to Ψ = 2. For the other types of instabilities, we make the simplifying assumption s ≪ 1 and find that the maximum growth rates correspond to Ψ=2.80 for (ii) and Ψ= π for (iii). The asymptotic results are confirmed by numerical computations. These reveal, in particular, that the instabilities (iii) have much smaller growth rates in cyclonic flows than in anticyclonic flows, even though Ψ = π in both cases.Our results highlight the limitations of the so-called balanced models, widely used in geophysical fluid dynamics, which filter out Kelvin and inertia–gravity waves and hence predict the stability of Couette flow. They are also relevant to the stability of Taylor–Couette flows and of astrophysical accretion disks.

Analyzing the current effectiveness of the Russian economy's design

2020 ◽  
Vol 8 (8) ◽  
pp. 1476-1496
Author(s):  
V.V. Smirnov
Keyword(s):  
Economic Growth ◽  
Sustainable Development ◽  
Growth Rates ◽  
Systems Approach ◽  
Mineral Resources ◽  
Cash Flows ◽  
Moscow Oblast ◽  
Structural Balance ◽  
Russian Economy ◽  
The Stability

Subject. The article discusses Russia’s economy and analyzes its effectiveness. Objectives. The study attempts to determine to what extent Russia’s economy is effective. Methods. The study is based on the systems approach and the statistical analysis. Results. I discovered significant fluctuations of the structural balance due to changing growth rates of the total gross national debt denominated in the national currency, and the stability of growth rates of governmental revenue. Changes in the RUB exchange rate and an additional growth in GDP are the main stabilizers of the structural balance, as they depend on hydrocarbon export. As a result of the analysis of cash flows, I found that the exports slowed down. Financial resources are strongly centralized, since Moscow and the Moscow Oblast are incrementing their share in the export of mineral resources, oil and refining products and import of electrical machines and equipment. Conclusions and Relevance. The fact that the Russian economy has been effectively organized is proved with the centralization of the economic power and the limits through the cross-regional corporation, such as Moscow and the Moscow Oblast, which is resilient to any regional difficulties ensuring the economic growth and sustainable development. The findings would be valuable for the political and economic community to outline and substantiate actions to keep rates of the economic growth and sustainable development of the Russian economy.

scholarly journals Barrier-Free Wheelchair with a Mechanical Transmission

2021 ◽  
Vol 11 (11) ◽  
pp. 5280
Author(s):  
Jongseok Lee ◽  
Wonhyeong Jeong ◽  
Jaeoh Han ◽  
Taesu Kim ◽  
Sehoon Oh
Keyword(s):  
The Elderly ◽  
Transmission System ◽  
Motor Drives ◽  
Mechanical Transmission ◽  
Link Structure ◽  
Second Mode ◽  
Important Means ◽  
The Stability ◽  
Flat Ground ◽  
Climbing Stairs

Wheelchairs are an important means of transportation for the elderly and disabled. However, the movement of wheelchairs on long curbs and stairs is restricted. In this study, a wheelchair for climbing stairs was developed based on a mechanical transmission system that rotates the entire driving part through a link structure and an actuator to change the speed. The first mode drives the caterpillar, and the second mode drives the wheels. When driving on flat ground, it uses landing gears and wheels, and when climbing stairs, it uses the caterpillar; accordingly, a stable driving is possible. The stability of the transmission is confirmed through stress analysis. The method used in our study makes it is possible to manufacture lightweight wheelchairs because a single motor drives both the wheel and caterpillar through the transmission system.

Entrainment and mixing in stratified shear flows

2001 ◽  
Vol 428 ◽  
pp. 349-386 ◽  
Author(s):  
E. J. STRANG ◽  
H. J. S. FERNANDO
Keyword(s):  
Internal Waves ◽  
Richardson Number ◽  
Transition Period ◽  
Lower Layer ◽  
Buoyancy Flux ◽  
Shear Instability ◽  
Mixing Efficiency ◽  
Buoyancy Frequency ◽  
Entrainment Rate ◽  
Turbulent Eddies

The results of a laboratory experiment designed to study turbulent entrainment at sheared density interfaces are described. A stratified shear layer, across which a velocity difference ΔU and buoyancy difference Δb is imposed, separates a lighter upper turbulent layer of depth D from a quiescent, deep lower layer which is either homogeneous (two-layer case) or linearly stratified with a buoyancy frequency N (linearly stratified case). In the parameter ranges investigated the flow is mainly determined by two parameters: the bulk Richardson number RiB = ΔbD/ΔU2 and the frequency ratio fN = ND=ΔU.When RiB > 1.5, there is a growing significance of buoyancy effects upon the entrainment process; it is observed that interfacial instabilities locally mix heavy and light fluid layers, and thus facilitate the less energetic mixed-layer turbulent eddies in scouring the interface and lifting partially mixed fluid. The nature of the instability is dependent on RiB, or a related parameter, the local gradient Richardson number Rig = N2L/ (∂u/∂z)2, where NL is the local buoyancy frequency, u is the local streamwise velocity and z is the vertical coordinate. The transition from the Kelvin–Helmholtz (K-H) instability dominated regime to a second shear instability, namely growing Hölmböe waves, occurs through a transitional regime 3.2 < RiB < 5.8. The K-H activity completely subsided beyond RiB ∼ 5 or Rig ∼ 1. The transition period 3.2 < RiB < 5 was characterized by the presence of both K-H billows and wave-like features, interacting with each other while breaking and causing intense mixing. The flux Richardson number Rif or the mixing efficiency peaked during this transition period, with a maximum of Rif ∼ 0.4 at RiB ∼ 5 or Rig ∼ 1. The interface at 5 < RiB < 5.8 was dominated by ‘asymmetric’ interfacial waves, which gradually transitioned to (symmetric) Hölmböe waves at RiB > 5:8.Laser-induced fluorescence measurements of both the interfacial buoyancy flux and the entrainment rate showed a large disparity (as large as 50%) between the two-layer and the linearly stratified cases in the range 1.5 < RiB < 5. In particular, the buoyancy flux (and the entrainment rate) was higher when internal waves were not permitted to propagate into the deep layer, in which case more energy was available for interfacial mixing. When the lower layer was linearly stratified, the internal waves appeared to be excited by an ‘interfacial swelling’ phenomenon, characterized by the recurrence of groups or packets of K-H billows, their degeneration into turbulence and subsequent mixing, interfacial thickening and scouring of the thickened interface by turbulent eddies.Estimation of the turbulent kinetic energy (TKE) budget in the interfacial zone for the two-layer case based on the parameter α, where α = (−B + ε)/P, indicated an approximate balance (α ∼ 1) between the shear production P, buoyancy flux B and the dissipation rate ε, except in the range RiB < 5 where K-H driven mixing was active.

scholarly journals On the stability of ocean overflows

2008 ◽  
Vol 602 ◽  
pp. 241-266 ◽  
Author(s):  
LARRY J. PRATT ◽  
KARL R. HELFRICH ◽  
DAVID LEEN
Keyword(s):  
Potential Vorticity ◽  
Growth Rates ◽  
Deep Ocean ◽  
Basic Flow ◽  
Necessary Condition ◽  
Zero Energy ◽  
Coriolis Parameter ◽  
Hydraulic Behaviour ◽  
Zero Potential ◽  
The Stability

The stability of a hydraulically driven sill flow in a rotating channel with smoothly varying cross-section is considered. The smooth topography forces the thickness of the moving layer to vanish at its two edges. The basic flow is assumed to have zero potential vorticity, as is the case in elementary models of the hydraulic behaviour of deep ocean straits. Such flows are found to always satisfy Ripa's necessary condition for instability. Direct calculation of the linear growth rates and numerical simulation of finite-amplitude behaviour suggests that the flows are, in fact, always unstable. The growth rates and nonlinear evolution depend largely on the dimensionless channel curvature κ=2αg′/f2, where 2α is the dimensional curvature, g′ is the reduced gravity, and f is the Coriolis parameter. Very small positive (or negative) values of κ correspond to dynamically wide channels and are associated with strong instability and the breakup of the basic flow into a train of eddies. For moderate or large values of κ, the instability widens the flow and increases its potential vorticity but does not destroy its character as a coherent stream. Ripa's condition for stability suggests a theory for the final width and potential vorticity that works moderately well. The observed and predicted growth in these quantities are minimal for κ≥1, suggesting that the zero-potential-vorticity approximation holds when the channel is narrower than a Rossby radius based on the initial maximum depth. The instability results from a resonant interaction between two waves trapped on opposite edges of the stream. Interactions can occur between two Kelvin-like frontal waves, between two inertia–gravity waves, or between one wave of each type. The growing disturbance has zero energy and extracts zero energy from the mean. At the same time, there is an overall conversion of kinetic energy to potential energy for κ>0, with the reverse occurring for κ<0. When it acts on a hydraulically controlled basic state, the instability tends to eliminate the band of counterflow that is predicted by hydraulic theory and that confounds hydraulic-based estimates of volume fluxes in the field. Eddy generation downstream of the controlling sill occurs if the downstream value of κ is sufficiently small.

scholarly journals Host-Directed Evolution of a Novel Lactate Oxidase in Streptococcus iniae Isolates from Barramundi (Lates calcarifer)

2009 ◽  
Vol 75 (9) ◽  
pp. 2908-2919 ◽  
Author(s):  
Roslina A. Nawawi ◽  
Justice C. F. Baiano ◽  
E. Charlotte E. Kvennefors ◽  
Andrew C. Barnes
Keyword(s):  
Molecular Weight ◽  
Growth Rates ◽  
Tidal Flow ◽  
The United States ◽  
Flavin Mononucleotide ◽  
Streptococcus Iniae ◽  
The Novel ◽  
Lactate Oxidase ◽  
Oxidase Gene

ABSTRACT In Streptococcus iniae, lactate metabolism is dependent upon two proteins, lactate permease that mediates uptake and lactate oxidase, a flavin mononucleotide-dependent enzyme that catalyzes oxidation of α-hydroxyacids. A novel variant of the lactate oxidase gene, lctO, in Australian isolates of S. iniae from diseased barramundi was found during a diagnostic screen using LOX-1 and LOX-2 primers, yielding amplicons of 920 bp instead of the expected 869 bp. Sequencing of the novel gene variant (type 2) revealed a 51-nucleotide insertion in lctO, resulting in a 17-amino-acid repeat in the gene product, and three-dimensional modeling indicated formation of an extra loop in the monomeric protein structure. The activities of the lactate oxidase enzyme variants expressed in Escherichia coli were examined, indicating that the higher-molecular-weight type 2 enzyme exhibited higher activity. Growth rates of S. iniae expressing the novel type 2 enzyme were not reduced at lactate concentrations of 0.3% and 0.5%, whereas a strain expressing the type 1 enzyme exhibited reduced growth rates at these lactate concentrations. During a retrospective screen of 105 isolates of S. iniae from Australia, the United States, Canada, Israel, Réunion Island, and Thailand, the type 2 variant arose only in isolates from a single marine farm with unusually high tidal flow in the Northern Territory, Australia. Elevated plasma lactate levels in the fish, resulting from the effort of swimming in tidal flows of up to 3 knots, may exert sufficient selective pressure to maintain the novel, high-molecular-weight enzyme variant.

scholarly journals Non-axisymmetric Instabilities in Shocked Accretion Flows

2003 ◽  
Vol 214 ◽  
pp. 95-96
Author(s):  
Wei-Min Gu ◽  
Thierry Foglizzo
Keyword(s):  
Black Hole ◽  
Numerical Integration ◽  
Recent Work ◽  
Growth Rates ◽  
Linearized Equations ◽  
X Ray ◽  
Accretion Flows ◽  
The Stability ◽  
X Ray Binaries ◽  
Axisymmetric Perturbations

We investigate the stability of shocked inviscid isothermal accretion flows onto a black hole. Of the two possible shock positions, the outer one is known to be stable to axisymmetric perturbations, while the inner one is unstable. Our recent work, however, shows that the outer shock is generally linearly unstable to non-axisymmetric perturbations. Eigenmodes and growth rates are obtained by numerical integration of the linearized equations. These results offer new perspectives to interpret the variability of X-ray binaries.

scholarly journals Instability Through Anisotropy in Spherical Stellar Systems

1987 ◽  
Vol 127 ◽  
pp. 515-516
Author(s):  
P.L. Palmer ◽  
J. Papaloizou
Keyword(s):  
Growth Rate ◽  
Eigenvalue Problem ◽  
Growth Rates ◽  
Stellar Systems ◽  
Matrix Eigenvalue Problem ◽  
Simple Method ◽  
Anisotropic Models ◽  
Poisson Equations ◽  
Degree Of Anisotropy ◽  
The Stability

We consider the linear stability of spherical stellar systems by solving the Vlasov and Poisson equations which yield a matrix eigenvalue problem to determine the growth rate. We consider this for purely growing modes in the limit of vanishing growth rate. We show that a large class of anisotropic models are unstable and derive growth rates for the particular example of generalized polytropic models. We present a simple method for testing the stability of general anisotropic models. Our anlysis shows that instability occurs even when the degree of anisotropy is very slight.

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