Rapidly rotating thermal convection at low Prandtl number

2001 ◽  
Vol 428 ◽  
pp. 61-80 ◽  
Author(s):  
J. H. P. DAWES
Keyword(s):  
Prandtl Number ◽  
Perturbation Expansion ◽  
Plane Layer ◽  
Interesting Case ◽  
Relative Importance ◽  
Leading Order ◽  
Amplitude Equations ◽  
Onset Of Convection ◽  
Dimensionless Groups ◽  
The Stability

Rotating Boussinesq convection in a plane layer is governed by two dimensionless groups in addition to the Rayleigh number R: the Prandtl number σ and the Taylor number Ta. Scaled equations for fully nonlinear rotating convection in the limit of rapid rotation and small Prandtl number, where the onset of convection is oscillatory, are derived by considering distinguished limits where σnTa1/2 ∼ 1 but σ → 0 and Ta → ∞, for different n > 1. In the resulting asymptotic expansion in powers of Ta−1/2 and the amplitude of convection. Three distinct asymptotic regimes are identified, distinguished by the relative importance of the subdominant buoyancy and inertial terms. For the most interesting case, n = 4, the stability of different planforms near onset is investigated using a double expansion in powers of Ta−1/8 and the amplitude of convection ε. The lack of a buoyancy term at leading order demands that the perturbation expansion be continued through six orders to derive amplitude equations determining the dynamics. The case n = 1 is also analysed. The relevance of this theory to experimental results is briefly discussed.

On the stability of thermally driven shear flow heated from below

1978 ◽  
Vol 87 (1) ◽  
pp. 65-84 ◽  
Author(s):  
J. E. Weber
Keyword(s):  
Shear Flow ◽  
Prandtl Number ◽  
Basic Flow ◽  
Uniform Heating ◽  
Onset Of Convection ◽  
Thermal Origin ◽  
Thermally Driven ◽  
Prandtl Numbers ◽  
Basic Temperature ◽  
The Stability

The onset of convection in shear flow driven by lateral heating and also uniformly heated from below is investigated numerically by Galerkin's method. Stress-free as well as rigid, perfectly conducting boundaries are considered. The analysis is valid for small and moderate Prandtl numbers. The magnitude of the lateral basic temperature gradient may be expressed by a dimensionless Grashof number G, while the uniform heating from below is represented by a Rayleigh number Ra. Depending on the values of G, Ra and the Prandtl number Pr, a variety of interesting situations arise. In particular it is demonstrated that the form of the most unstable mode, i.e. whether it is a roll with axis aligned along the basic flow (a longitudinal roll) or one with axis normal to the basic flow (a transverse roll), depends on the value of the Prandtl number. For small values of G, the marginally stable disturbances are found to be steady, while for larger values of G, oscillatory instability occurs. For all values of G considered here (G [lsim ] 3000), computations of the energy balance for the marginally stable disturbances show that the main instability mechanism is of thermal origin, while the effect of shear may be important in selecting the preferred mode of disturbance.

Asymptotic solutions of convection in rapidly rotating non-slip spheres

2007 ◽  
Vol 578 ◽  
pp. 371-380 ◽  
Author(s):  
KEKE ZHANG ◽  
XINHAO LIAO ◽  
F. H. BUSSE
Keyword(s):  
Prandtl Number ◽  
Quantitative Agreement ◽  
Wave Mode ◽  
Asymptotic Solutions ◽  
Leading Order ◽  
Slip Boundary Conditions ◽  
Onset Of Convection ◽  
Slip Boundary ◽  
Inertial Wave ◽  
Boussinesq Fluid

Asymptotic solutions describing the onset of convection in rotating, self-gravitating Boussinesq fluid spheres with no-slip boundary conditions, valid for asymptotically small Ekman numbers and for all values of the Prandtl number, are derived. Central to the asymptotic analysis is the assumption that the leading-order convection can be represented, dependent on the size of the Prandtl number, by either a single quasi-geostrophic-inertial-wave mode or by a combination of several quasi-geostrophic-inertial-wave modes, and is controlled or influenced by the effect of the oscillatory Ekman boundary layer. Comparisons between the asymptotic solutions and the corresponding fully numerical simulations show a satisfactory quantitative agreement.

scholarly journals Effect of modulation on the onset of thermal convection

1969 ◽  
Vol 35 (2) ◽  
pp. 243-254 ◽  
Author(s):  
Giulio Venezian
Keyword(s):  
Temperature Field ◽  
Applied Field ◽  
Critical Rayleigh Number ◽  
Perturbation Expansion ◽  
Horizontal Layer ◽  
Time Dependent ◽  
Steady Temperature ◽  
Onset Of Convection ◽  
Time Modulation ◽  
The Stability

The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady temperature difference between the walls of the layer, a time-dependent sinusoidal perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. The effects of the oscillating temperature field are treated by a perturbation expansion in powers of the amplitude of the applied field. The shift in the critical Rayleigh number is calculated as a function of frequency, and it is found that it is possible to advance or delay the onset of convection by time modulation of the wall temperatures.

Lack of Stability of Aggregates after Thrombin-Induced Reaggregation of Thrombin-Degranulated Platelets

1992 ◽  
Vol 67 (04) ◽  
pp. 453-457 ◽  
Author(s):  
Raelene L Kinlough-Rathbone ◽  
Marian A Packham ◽  
Dennis W Perry ◽  
J Fraser Mustard ◽  
Marco Cattaneo
Keyword(s):  
Von Willebrand Factor ◽  
Platelet Rich Plasma ◽  
Thrombus Formation ◽  
Aggregate Stability ◽  
Relative Importance ◽  
Platelet Aggregates ◽  
The Stability ◽  
Von Willebrand ◽  
Induced Aggregation ◽  
Willebrand Factor

SummaryThe stability of platelet aggregates is influenced by the extent of the release of granule contents; if release is extensive and aggregation is prolonged, deaggregation is difficult to achieve. The relative importance of the contributions of released substances to aggregate stability are not known, although stable thrombin-induced aggregates form in platelet-rich plasma from patients with barely detectable plasma or platelet fibrinogen, and ADP stabilizes thrombin-induced aggregates of platelets from patients with delta storage pool deficiency which otherwise deaggregate more readily than normal platelets. We degranulated platelets with thrombin (0.9 U/ml caused greater than 90% loss of delta and alpha granule contents) and recovered them as individual platelets in fresh medium. The degranulated platelets were reaggregated by thrombin (2 U/ml). To prevent continuing effects of thrombin, FPRCH2C1 was added when thrombin-induced aggregation of thrombin-degranulated platelets reached its maximum. EDTA (5 mM) or EGTA (5 mM) added at maximum aggregation did not deaggregate these platelets, indicating that the stability of these aggregates does not depend on Ca2+ in the medium. Whereas with control platelets a combination of PGE1 (10 μM) and chymotrypsin(10 U/ml) was required for deaggregation, with thrombin-degranulated platelets either PGE1 or chymo-trypsin alone caused extensive deaggregation. The rate and extent of deaggregation of thrombin-degranulated platelets by a combination of PGE1 and chymotrypsin was greater than with control platelets.Electron microscope gold immunocytochemistry using antihuman fibrinogen IgG, anti-von Willebrand factor and anti-fibronectin showed a) that fibrinogen in the vacuoles of degranulated platelets was visible at focal points of platelet contact in the aggregates, but that large areas of platelet contact had no fibrinogen detectable between them; and b) in comparison to fibrinogen, little fibronectin or von Willebrand factor (vWf) was detectable in the platelets.Since the linkages between thrombin-degranulated platelets reaggregated by thrombin can be disrupted either by raising cAMP (thus making glycoprotein IIb/IIIa unavailable) or by proteolysis, these linkages are less stable than those formed between normal platelets. It might therefore be expected that platelets that take part in thrombus formation and then recirculate are likely to form less stable thrombi than platelets that have not released their granule contents.

scholarly journals Steady Motion of Ice Sheets

1980 ◽  
Vol 25 (92) ◽  
pp. 229-246 ◽  
Author(s):  
L. W. Morland ◽  
I. R. Johnson
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Power Law ◽  
Perturbation Expansion ◽  
Ice Sheet ◽  
Leading Order ◽  
Plane Flow ◽  
General Law ◽  
Non Linear ◽  
Linear Differential

AbstractSteady plane flow under gravity of a symmetric ice sheet resting on a horizontal rigid bed, subject to surface accumulation and ablation, basal drainage, and basal sliding according to a shear-traction-velocity power law, is treated. The surface accumulation is taken to depend on height, and the drainage and sliding coefficient also depend on the height of overlying ice. The ice is described as a general non-linearly viscous incompressible fluid, with illustrations presented for Glen’s power law, the polynomial law of Colbeck and Evans, and a Newtonian fluid. Uniform temperature is assumed so that effects of a realistic temperature distribution on the ice response are not taken into account. In dimensionless variables a small paramter ν occurs, but the ν = 0 solution corresponds to an unbounded sheet of uniform depth. To obtain a bounded sheet, a horizontal coordinate scaling by a small factor ε(ν) is required, so that the aspect ratio ε of a steady ice sheet is determined by the ice properties, accumulation magnitude, and the magnitude of the central thickness. A perturbation expansion in ε gives simple leading-order terms for the stress and velocity components, and generates a first order non-linear differential equation for the free-surface slope, which is then integrated to determine the profile. The non-linear differential equation can be solved explicitly for a linear sliding law in the Newtonian case. For the general law it is shown that the leading-order approximation is valid both at the margin and in the central zone provided that the power and coefficient in the sliding law satisfy certain restrictions.

scholarly journals PATACSDB - The database of polyA translational attenuators in coding sequences

2015 ◽  
Author(s):  
Malgorzata Habich ◽  
Sergej Djuranovic ◽  
Pawel Szczesny
Keyword(s):  
Gene Dosage ◽  
Interesting Case ◽  
Minimal Length ◽  
Regulatory Mechanisms ◽  
Coding Sequences ◽  
Translation Apparatus ◽  
Recent Addition ◽  
Dosage Balance ◽  
The Stability ◽  
Eukaryotic Genomes

Recent addition to the repertoire of gene expression regulatory mechanisms are polyadenylate (polyA) tracks encoding for poly-lysine runs in protein sequences. Such tracks stall translation apparatus and induce frameshifting independently of the effects of charged nascent poly-lysine sequence on the ribosome exit channel. As such they substantially influence the stability of mRNA and amount of protein produced from a given transcript. Single base changes in these regions are enough to exert a measurable response on both protein and mRNA abundance, and makes each of these sequences potentially interesting case studies for effects of synonymous mutation, gene dosage balance and natural frameshifting. Here we present the PATACSDB, a resource that contain comprehensive list of polyA tracks from over 250 eukaryotic genomes. Our data is based on Ensembl genomic database of coding sequences and filtered with algorithm of 12A-1 which selects sequences of polyA tracks with a minimal length of 12 A's allowing for one mismatched base. The PATACSDB database is accesible at: http://sysbio.ibb.waw.pl/patacsdb. Source code is available for download from GitHub repository at http://github.com/habich/PATACSDB, including the scripts to recreate the database from the scratch on user's own computer.

scholarly journals The breakdown of the anelastic approximation in rotating compressible convection: implications for astrophysical systems

2015 ◽  
Vol 471 (2175) ◽  
pp. 20140689 ◽  
Author(s):  
Michael A. Calkins ◽  
Keith Julien ◽  
Philippe Marti
Keyword(s):  
Prandtl Number ◽  
Scaling Laws ◽  
Fluid Layer ◽  
Time Derivative ◽  
Density Perturbation ◽  
Plane Layer ◽  
Relative Magnitude ◽  
Critical Parameters ◽  
Anelastic Equations ◽  
Prandtl Numbers

The linear theory for rotating compressible convection in a plane layer geometry is presented for the astrophysically relevant case of low Prandtl number gases. When the rotation rate of the system is large, the flow remains geostrophically balanced for all stratification levels investigated and the classical (i.e. incompressible) asymptotic scaling laws for the critical parameters are recovered. For sufficiently small Prandtl numbers, increasing stratification tends to further destabilize the fluid layer, decrease the critical wavenumber and increase the oscillation frequency of the convective instability. In combination, these effects increase the relative magnitude of the time derivative of the density perturbation contained in the conservation of mass equation to non-negligible levels; the resulting convective instabilities occur in the form of compressional quasi-geostrophic oscillations. We find that the anelastic equations, which neglect this term, cannot capture these instabilities and possess spuriously growing eigenmodes in the rapidly rotating, low Prandtl number regime. It is shown that the Mach number for rapidly rotating compressible convection is intrinsically small for all background states, regardless of the departure from adiabaticity.

scholarly journals Inviscid spatial stability of a compressible mixing layer. Part 3. Effect of thermodynamics

1991 ◽  
Vol 224 ◽  
pp. 159-175 ◽  
Author(s):  
T. L. Jackson ◽  
C. E. Grosch
Keyword(s):  
Prandtl Number ◽  
Mixing Layer ◽  
Mean Flow ◽  
Temperature Relation ◽  
Compressible Mixing Layer ◽  
Spatial Stability ◽  
Mean Temperature ◽  
The Mean ◽  
The Difference ◽  
The Stability

We report the results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow. The models are (i) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity–temperature relation and a Prandtl number of one; (ii) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (iii) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity–temperature relation and arbitrary but constant Prandtl number. The purpose of this study was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the qualitative features of the stability characteristics are quite similar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, we show that the stability characteristics are sensitive to the value of the Prandtl number and to a particular value of the temperature ratio across the mixing layer.

scholarly journals Effect of Rotational Speed Modulation on the Weakly Nonlinear Heat Transfer in Walter-B Viscoelastic Fluid in the Highly Permeable Porous Medium

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1448
Author(s):  
Anand Kumar ◽  
Vinod K. Gupta ◽  
Neetu Meena ◽  
Ishak Hashim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Prandtl Number ◽  
Heat Transport ◽  
Viscoelastic Fluid ◽  
Rotational Speed ◽  
Weakly Nonlinear ◽  
Speed Modulation ◽  
The Stability ◽  
The Impact

In this article, a study on the stability of Walter-B viscoelastic fluid in the highly permeable porous medium under the rotational speed modulation is presented. The impact of rotational modulation on heat transport is performed through a weakly nonlinear analysis. A perturbation procedure based on the small amplitude of the perturbing parameter is used to study the combined effect of rotation and permeability on the stability through a porous medium. Rayleigh–Bénard convection with the Coriolis expression has been examined to explain the impact of rotation on the convective flow. The graphical result of different parameters like modified Prandtl number, Darcy number, Rayleigh number, and Taylor number on heat transfer have discussed. Furthermore, it is found that the modified Prandtl number decelerates the heat transport which may be due to the combined effect of elastic parameter and Taylor number.

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