Frontal instabilities and waves in a differentially rotating fluid

2011 ◽  
Vol 685 ◽  
pp. 532-542 ◽  
Author(s):  
J.-B. Flór ◽  
H. Scolan ◽  
J. Gula
Keyword(s):  
Baroclinic Instability ◽  
Phase Speed ◽  
Small Scale ◽  
Immiscible Fluid ◽  
Mean Flow ◽  
Disk Rotation ◽  
Fluid Layers ◽  
The Stability ◽  
Almost All ◽  
Instability Regime

AbstractWe present an experimental investigation of the stability of a baroclinic front in a rotating two-layer salt-stratified fluid. A front is generated by the spin-up of a differentially rotating lid at the fluid surface. In the parameter space set by rotational Froude number, $F$, dissipation number, $d$ (i.e. the ratio between disk rotation time and Ekman spin-down time) and flow Rossby number, a new instability is observed that occurs for Burger numbers larger than the critical Burger number for baroclinic instability. This instability has a much smaller wavelength than the baroclinic instability, and saturates at a relatively small amplitude. The experimental results for the instability regime and the phase speed show overall a reasonable agreement with the numerical results of Gula, Zeitlin & Plougonven (J. Fluid Mech., vol. 638, 2009, pp. 27–47), suggesting that this instability is the Rossby–Kelvin instability that is due to the resonance between Rossby and Kelvin waves. Comparison with the results of Williams, Haines & Read (J. Fluid Mech., vol. 528, 2005, pp. 1–22) and Hart (Geophys. Fluid Dyn., vol. 3, 1972, pp. 181–209) for immiscible fluid layers in a small experimental configuration shows continuity in stability regimes in $(F, d)$ space, but the baroclinic instability occurs at a higher Burger number than predicted according to linear theory. Small-scale perturbations are observed in almost all regimes, either locally or globally. Their non-zero phase speed with respect to the mean flow, cusped-shaped appearance in the density field and the high values of the Richardson number for the observed wavelengths suggest that these perturbations are in many cases due to Hölmböe instability.

Planetary Wave Response to Surface Forcing and Instability in the Presence of Mean Flow and Topography

2007 ◽  
Vol 37 (5) ◽  
pp. 1297-1320 ◽  
Author(s):  
Peter D. Killworth ◽  
Jeffrey R. Blundell
Keyword(s):  
Baroclinic Instability ◽  
Phase Speed ◽  
Linear Growth Rate ◽  
Ekman Pumping ◽  
Mean Flow ◽  
Small Surface ◽  
Random Forcing ◽  
Ocean Response ◽  
Almost Everywhere ◽  
Almost All

Abstract The local response of an ocean with slowly varying mean flow, stratification, and topography to two sources of disturbance is examined, concentrating on whether the resulting surface elevations are observable. The first is the ocean response to surface forcing (Ekman pumping or buoyancy forcing). For typical amplitudes of random forcing, while much of the ocean response is small (surface elevations less than 1 mm), there are sufficient near resonances (or pseudoresonances involving a critical layer) to produce elevations of 1 cm or more in much of the ocean. The second source is baroclinic instability. The fastest linear growth rate, as well as those for specific wavelengths, is computed globally. Almost all of the ocean is baroclinically unstable, and the most unstable waves are found to possess a small wavelength (often less than 10 km) with a disturbance concentrated near the surface: e-folding times O(20 days) are frequently found. However, the phase speed for the disturbances is almost everywhere slower westward than free planetary waves with mean flow and topography. Since the free waves propagate at speeds similar to observations, instability may be a good source of variability but is probably not responsible directly for observed wave propagation.

Inertia–gravity waves in a liquid-filled, differentially heated, rotating annulus

2015 ◽  
Vol 782 ◽  
pp. 144-177 ◽  
Author(s):  
Anthony Randriamampianina ◽  
Emilia Crespo del Arco
Keyword(s):  
Prandtl Number ◽  
Gravity Waves ◽  
Large Scale ◽  
Baroclinic Instability ◽  
Zonal Flow ◽  
Small Scale ◽  
Mean Flow ◽  
Baroclinic Waves ◽  
Fluid Properties ◽  
Spatio Temporal

Direct numerical simulations based on high-resolution pseudospectral methods are carried out for detailed investigation into the instabilities arising in a differentially heated, rotating annulus, the baroclinic cavity. Following previous works using air (Randriamampianina et al., J. Fluid Mech., vol. 561, 2006, pp. 359–389), a liquid defined by Prandtl number $Pr=16$ is considered in order to better understand, via the Prandtl number, the effects of fluid properties on the onset of gravity waves. The computations are particularly aimed at identifying and characterizing the spontaneously emitted small-scale fluctuations occurring simultaneously with the baroclinic waves. These features have been observed as soon as the baroclinic instability sets in. A three-term decomposition is introduced to isolate the fluctuation field from the large-scale baroclinic waves and the time-averaged mean flow. Even though these fluctuations are found to propagate as packets, they remain attached to the background baroclinic waves, locally triggering spatio-temporal chaos, a behaviour not observed with the air-filled cavity. The properties of these features are analysed and discussed in the context of linear theory. Based on the Richardson number criterion, the characteristics of the generation mechanism are consistent with a localized instability of the shear zonal flow, invoking resonant over-reflection.

Ageostrophic instabilities of fronts in a channel in a stratified rotating fluid

2009 ◽  
Vol 627 ◽  
pp. 485-507 ◽  
Author(s):  
J. GULA ◽  
R. PLOUGONVEN ◽  
V. ZEITLIN
Keyword(s):  
Baroclinic Instability ◽  
Water Model ◽  
Small Scale ◽  
Rotating Fluid ◽  
Shallow Water Model ◽  
Mean Flow ◽  
Nonlinear Saturation ◽  
The Mean ◽  
Rotating Shallow Water ◽  
Stability Results

It is known that for finite Rossby numbers geostrophically balanced flows develop specific ageostrophic instabilities. We undertake a detailed study of the Rossby–Kelvin (RK) instability, previously studied by Sakai (J. Fluid Mech., vol. 202, 1989, pp. 149–176) in a two-layer rotating shallow-water model. First, we benchmark our method by reproducing the linear stability results obtained by Sakai (1989) and extend them to more general configurations. Second, in order to determine the relevance of RK instability in more realistic flows, simulations of the evolution of a front in a continuously stratified fluid are carried out. They confirm the presence of RK instability with characteristics comparable to those found in the two-layer case. Finally, these simulations are used to study the nonlinear saturation of the RK modes. It is shown that saturation is achieved through the development of small-scale instabilities along the front which modify the mean flow so as to stabilize the RK mode. Remarkably, the developing instability leads to conversion of kinetic energy of the basic flow to potential energy, contrary to classical baroclinic instability.

Laboratory Observations of Gravity Wave, Critical Layer Flows Using Single and Double Wave Forcing

1994 ◽  
Vol 47 (6S) ◽  
pp. S113-S117
Author(s):  
Donald P. Delisi ◽  
Timothy J. Dunkerton
Keyword(s):  
Gravity Wave ◽  
Wave Breaking ◽  
Critical Level ◽  
Phase Speed ◽  
Vertical Shear ◽  
Critical Layer ◽  
Small Scale ◽  
Mean Flow ◽  
Wave Forcing ◽  
Internal Mixing

Laboratory measurements of gravity wave, critical layer flows are presented. The measurements are obtained in a salt-stratified annular tank, with a vertical shear profile. Internal gravity waves are generated at the floor of the tank and propagate vertically upward into the fluid. At a depth where the phase speed of the wave equals the mean flow speed, defined as a critical level, the waves break down, under the right forcing conditions, generating small scale turbulence. Two cases are presented. In the first case, the wave forcing is a single, monochromatic wave. In this case, the early wave breaking is characterized as Kelvin-Helmholtz breaking at depths below the critical level. Later wave breaking is characterized by weak overturning in the upper part of the tank and regular, internal mixing regions in the lower part of the tank. In the second case, the wave forcing is two monochromatic waves, each propagating with a different phase speed. In this case, the early wave breaking is again Kelvin-Helmholtz in nature, but later wave breaking is characterized by sustained overturning in the upper part of the tank with internal mixing regions in the lower part of the tank. Mean velocity profiles are obtained both before and during the experiments.

scholarly journals Barotropic Instability at Minimal Resolution

2006 ◽  
Vol 134 (10) ◽  
pp. 2943-2950 ◽  
Author(s):  
Joseph Egger
Keyword(s):  
Initial Conditions ◽  
Baroclinic Instability ◽  
Plane Channel ◽  
Necessary Condition ◽  
Barotropic Instability ◽  
Mean Flow ◽  
Linear Shear ◽  
The Stability ◽  
Basic Features ◽  
Plane Channel Flow

Abstract Two linear minimum-resolution models of β-plane channel flow are presented in analogy to the well-known two-layer model of baroclinic instability in order to see if basic features of barotropic instability can be demonstrated using similarly simple models. Two models are discussed within this pedagogical framework. A spectral model with two wave modes is applied to a cosine jet. Necessary conditions for instability are derived. The stability analysis shows that this simple model captures the shortwave cutoff and the asymmetry of the instability with respect to the direction of the jet quite well. It is demonstrated that the cutoff follows from Fjörtoft’s theorem for wave triads. A gridpoint model with two points in the interior of the channel is discussed as well. An analog to the classical necessary condition for instability is derived. A stability problem in a nonrotating system is discussed where the mean flow velocity is constant near the walls and a linear shear flow is assumed near the channel’s axis. In this case, the stability characteristics of the low-order model come close to those of the full problem where a simple analytic solution is available. Addition of the β term stabilizes the flow. A proper choice of the initial conditions always enables short-term growth of the perturbation energy for stable mean flows. A qualitative interpretation of the instability mechanism is presented for both models, which exploits the fact that the locations of corresponding extrema of streamfunction and vorticity need not coincide. It is concluded that low-resolution models are well suited for a discussion of the basic features of barotropic instability.

Wave breakdown in stratified shear flows

1977 ◽  
Vol 79 (3) ◽  
pp. 481-497 ◽  
Author(s):  
M. T. Landahl ◽  
W. O. Criminale
Keyword(s):  
Shear Flows ◽  
Flow Instability ◽  
Stability Boundary ◽  
Small Scale ◽  
Mean Flow ◽  
Order Unity ◽  
Stable Regime ◽  
Density Interface ◽  
Density Interfaces ◽  
The Stability

The wave-mechanical condition (Landahl 1972) for breakdown of an unsteady laminar flow into strong small-scale secondary instabilities is applied to some simple stratified inviscid shear flows. The cases considered have one or two discrete density interfaces and simple discontinuous or continuous velocity profiles. A primary wavelike disturbance to such a flow produces a perturbation velocity that is discontinuous at a density interface. The resulting instantaneous system, defined as the sum of the mean flow and the primary oscillation, develops a local secondary shear-flow instability that has a group velocity equal to the arithmetic mean of the instantaneous velocities on the two sides of the interface. According to the breakdown criterion, the disturbed flow will become critical whenever this velocity reaches a value equal to the phase velocity of the primary wave. The calculations show that for a single density interface breakdown may occur for low to moderate wave amplitudes in a fairly narrow range of Richardson numbers on the stable side of the stability boundary. On the other hand, in the unstable regime maximum wave slopes of order unity may be reached before breakdown occurs; this conclusion is in qualitative agreement with experiments. When the system includes two density interfaces, it is found that there exists a range of high Richardson numbers far into the stable regime for which breakdown may take place even for very small and zero wave interface deflexions.

Resistance of cherry varieties to spring return frozes in the conditions of Astrakhan region

2020 ◽  
Author(s):  
A.A. Dronic A.A. ◽  
Keyword(s):  
Weather Conditions ◽  
Damage Score ◽  
The Stability ◽  
Almost All ◽  
Total Damage ◽  
Continental Climate ◽  
Unfavorable Weather

The article presents an assessment of the stability of introduced cherry varieties to spring return frosts in 2020 in the conditions of the sharply continental climate of the Astrakhan region. As a result of unfavorable weather conditions, the total damage score of all varieties was 2-5 points. Almost all the studied varieties showed an insufficient level of resistance to recurrent frosts.

Unit-Wise Ranking of Inventory Control Techniques Used in Small Scale Cement Enterprises: A Small Scale Entrepreneurial Perspective

2015 ◽  
Vol 3 (2) ◽  
Author(s):  
Vipul Chalotra
Keyword(s):  
Inventory Control ◽  
Economic Order Quantity ◽  
Economic Order ◽  
Small Scale ◽  
Just In Time ◽  
Order Quantity ◽  
Control Techniques ◽  
Material Requirement Planning ◽  
Material Requirement ◽  
Almost All

The present research divulges the different inventory control techniques used small scale cements enterprises operated by small scale entrepreneurs through the assistance of primary data collected from eight small scale cement enterprises operating in SIDCO & SICOP, under DIC (District Industries Center) in District Udhampur of Jammu & Kashmir State. The various inventory control techniques identified and quested for in the research were: Always Better Control (ABC), Economic Order Quantity (EOQ), Material Requirement Planning (MRP), and Just-in-Time (JIT). The results of the ranking table quoted that Economic Order Quantity (EOQ) was awarded first rank by almost all the units representing overall mean score of 1.71, Always Better Control (ABC) was denoted by rank two repressing overall mean value as 2.00, Material Requirement Planning (MRP) was quoted rank three as depicted by its mean ranking (2.25), and Just-in-time (JIT) was accorded rank four (3.71) by almost all the small scale cements entrepreneurs/owners.

Studies on Polyaniline: Polyethyleneterephthalate Films

2006 ◽  
Vol 111 ◽  
pp. 99-102 ◽  
Author(s):  
A.A. Ahmed ◽  
Faiz Mohammad
Keyword(s):  
Electrical Conductivity ◽  
Electrical Properties ◽  
Arrhenius Equation ◽  
Great Increase ◽  
Thermooxidative Stability ◽  
Ambient Conditions ◽  
Dc Electrical Conductivity ◽  
The Stability ◽  
Almost All ◽  
Conductivity Retention

The films of polyaniline:polyethyleneterephthalate films were prepared by polymerizing aniline soaked in polyethyleneterephthalate films of different thicknesses. The films were characterized by FTIR as well as for their electrical properties. The electrical properties of the films were observed to be of good quality as almost all the films showed a great increase in their electrical conductivity from insulator to semiconductor region after doping with hydrochloric acid. All the films in their doped state follow the Arrhenius equation for the temperature dependence of electrical conductivity from 35 to 115oC. The thermooxidative stability was studied by thermogravimetry and differential thermal analysis. The stability in terms of dc electrical conductivity retention was also studied under ambient conditions by two slightly different techniques viz. isothermal and cyclic techniques. The dc electrical conductivity of the films was found to be stable below 90oC for all the films under ambient conditions.

Turbulent flow between counter-rotating concentric cylinders: a direct numerical simulation study

2008 ◽  
Vol 615 ◽  
pp. 371-399 ◽  
Author(s):  
S. DONG
Keyword(s):  
Turbulent Flow ◽  
Large Scale ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Small Scale ◽  
Mean Flow ◽  
Concentric Cylinders ◽  
High Reynolds

We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

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