The effect of a shear flow on convection in a layer heated non-uniformly from below

1985 ◽  
Vol 154 ◽  
pp. 303-319 ◽  
Author(s):  
I. C. Walton
Keyword(s):  
Boundary Layer ◽  
Shear Flow ◽  
Fluid Layer ◽  
Heated Layer ◽  
Vertical Temperature ◽  
Onset Of Convection ◽  
A Value ◽  
Blasius Boundary Layer ◽  
Convection Problem

In an earlier paper (Walton 1982) we showed that, when a fluid layer is heated non-uniformly from below in such a way that the vertical temperature difference maintained across the layer is a slowly varying monotonic function of a horizontal coordinate x, then convection occurs for x > xc, where xc is the point where the local Rayleigh number is equal to the critical value for a uniformly heated layer. Furthermore, the amplitude of the convection increases smoothly from exponentially small values for x [Lt ] xc and asymptotes to a value given by Stuart–Watson theory for x [Gt ] xc.At the present time no solutions of this kind are available for a class of problems in which the onset of instability is heavily influenced by a shear flow (e.g. Görtler vortices in a boundary layer on a curved wall, convection in a heated Blasius boundary layer). In a first step to bridge the gap between these problems and in order to elucidate the difficulties associated with the presence of a shear flow, we investigate the effect of a (weak) shear flow on our earlier convection problem. We show that the onset of convection is delayed and that it appears more suddenly, but still smoothly. The role of horizontal diffusion is shown to be of paramount importance in enabling a solution of this kind to be found, and the implications of these results for instabilities in higher-speed shear flows are discussed.

scholarly journals Numerical analysis of the chemical kinetic mechanisms of ozone depletion and halogen release in the polar troposphere

2013 ◽  
Vol 13 (9) ◽  
pp. 24171-24222 ◽  
Author(s):  
L. Cao ◽  
H. Sihler ◽  
U. Platt ◽  
E. Gutheil
Keyword(s):  
Boundary Layer ◽  
Surface Area ◽  
Ozone Depletion ◽  
Reaction Rates ◽  
The Arctic ◽  
Strong Impact ◽  
Reactive Surface ◽  
A Value ◽  
Halogen Species

Abstract. In recent years, the role of halogen species (e.g. Br, Cl) in the troposphere of polar regions is investigated after the discovery of their importance for boundary layer ozone destruction in the polar spring. Halogen species take part in an auto-catalytic chemical cycle including key self reactions. In this study, several chemical reaction schemes are investigated, and the importance of specific reactions and their rate constants is identified by a sensitivity analysis. A category of heterogeneous reactions related to HOBr activate halogen ions from sea salt aerosols, fresh sea ice or snow pack, driving the "bromine explosion". In the Arctic, a small amount of NOx may exist, which comes from nitrate contained in the snow, and this NOx may have a strong impact on ozone depletion. The heterogeneous reaction rates are parameterized by considering the aerodynamic resistance, a reactive surface ratio, β, i.e. ratio of reactive surface area to total ground surface area, and the boundary layer height, Lmix. It is found that for β = 1, the ozone depletion process starts after five days and lasts for 40 h for Lmix = 200 m. Ozone depletion duration becomes independent of the height of the boundary layer for about β≥20, and it approaches a value of two days for β=100. The role of nitrogen and chlorine containing species on the ozone depletion rate is studied. The calculation of the time integrated bromine and chlorine atom concentrations suggests a value in the order of 103 for the [Br] / [Cl] ratio, which reveals that atomic chlorine radicals have minor direct influence on the ozone depletion. The NOx concentrations are influenced by different chemical cycles over different time periods. During ozone depletion, the reaction cycle involving the BrONO2 hydrolysis is dominant. A critical value of 0.002 of the uptake coefficient of the BrONO2 hydrolysis reaction at the aerosol and saline surfaces is identified, beyond which the existence of NOx species accelerate the ozone depletion event – for lower values, deceleration occurs.

Onset of convection in a near-critical binary fluid mixture driven by concentration gradient

2018 ◽  
Vol 848 ◽  
pp. 1098-1126 ◽  
Author(s):  
Zhan-Chao Hu ◽  
Xin-Rong Zhang
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Concentration Gradient ◽  
Fluid Layer ◽  
Initial Density ◽  
Onset Of Convection ◽  
Fluid Mixture ◽  
Concentration Boundary ◽  
Binary Fluid ◽  
Theoretical Criterion

A linear stability analysis is conducted for the onset of natural convection driven by a concentration gradient in a horizontal layer of a near-critical binary fluid mixture. The problem is regarded as a limiting case of double-diffusive convection. The governing equations for small perturbations after normal-mode expansion are solved numerically with finite difference discretization to obtain the critical concentration Rayleigh number. It is found that, when the height of the fluid layer is small, the initial density stratification is negligible and the theoretical criterion developed under Boussinesq approximation with the modified Rayleigh number is accurate even extremely close to the critical point. However, for a large height, the initial density stratification makes the fluid layer become more unstable, and deviations from theoretical predictions are observed. We further propose a method to estimate these deviations, which can be used to check the applicability of the theoretical criterion. As the second part of the study, we apply the criterion to interpret the onset of convection for a transient problem: a near-critical binary fluid mixture confined in a two-dimensional cavity submitted to concentration increases at the bottom wall. The numerical results demonstrate four typical behaviours of the concentration boundary layer: onset of convection, collapse of the concentration boundary layer, return to stability, and remaining stable. Comparisons between numerical results and the stability criterion are made, where consistencies are found except for the behaviour of return to stability. We attribute the inconsistency to the existence of lateral walls, whose stabilizing effect is strong when the return to stability happens.

Non-parallel flow corrections for the stability of shear flows

1973 ◽  
Vol 59 (3) ◽  
pp. 571-591 ◽  
Author(s):  
Chi-Hai Ling ◽  
W. C. Reynolds
Keyword(s):  
Boundary Layer ◽  
Shear Flow ◽  
Parallel Flow ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Blasius Boundary Layer ◽  
Stability Of Shear Flows ◽  
Parallel Shear Flow ◽  
The Stability ◽  
Small Disturbances

The proper corrections for non-parallel flow to the eigenvalues for small disturbances on a nearly parallel shear flow have been determined through a perturbation about the parallel flow solutions. The resulting shifts in the neutral stability curves have been calculated for the Blasius boundary layer, for the two-dimensional jet, and for the two-dimensional flat-plate wake.

scholarly journals Interaction between the Blasius boundary layer and a free surface

2018 ◽  
Vol 839 ◽  
Author(s):  
Jonathan Michael Foonlan Tsang ◽  
Stuart B. Dalziel ◽  
N. M. Vriend
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Fluid Layer ◽  
Outer Flow ◽  
Blasius Boundary Layer ◽  
Upstream Part ◽  
Deep Fluid ◽  
High Reynolds ◽  
Averaged Models ◽  
Models Of Gravity

We consider the steady supercritical flow of a fluid layer. The layer is bounded above by a free surface and below by a rigid no-slip base. The base is in two parts: the downstream part of the base is stationary, while the upstream part translates in the streamwise direction with a uniform speed; there is an abrupt transition. At high Reynolds number, a boundary layer forms in the fluid above the base downstream of the transition point. The displacement due to this boundary layer creates a perturbation to the outer flow and therefore to the free surface. We show that the Blasius boundary layer solution, which applies in an infinitely deep fluid, also applies at high Froude numbers. The Blasius solution no longer applies for flows that are just supercritical, as the outer flow is strongly affected by the presence of the boundary layer. We outline possible applications of this work to depth-averaged models of gravity currents.

New Closed-Form Thermal Boundary Layer Solutions in Shear Flow With Power-Law Velocity

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Chang Yi Wang ◽  
Chien-Cheng Chang
Keyword(s):  
Boundary Layer ◽  
Shear Flow ◽  
Power Law ◽  
Thermal Boundary Layer ◽  
Mass Diffusion ◽  
Gamma Functions ◽  
Thermal Boundary Conditions ◽  
Flux Change ◽  
Convection Problem ◽  
Parallel Shear Flow

The forced convection problem for a developing thermal boundary layer in a parallel shear flow is studied. If the shear flow has a power-law velocity profile, exact similarity thermal boundary layer solutions in terms of Gamma functions can be found. Specifically, three types of thermal boundary conditions are considered: a step temperature change, a step flux change, and a concentrated heat source. The latter is also analogous to mass diffusion form an isolated source. The mixing index for mass diffusion is found exactly.

Feedback control of instabilities in the two-dimensional Blasius boundary layer: The role of sensors and actuators

2013 ◽  
Vol 25 (5) ◽  
pp. 054106 ◽  
Author(s):  
Brandt A. Belson ◽  
Onofrio Semeraro ◽  
Clarence W. Rowley ◽  
Dan S. Henningson
Keyword(s):  
Boundary Layer ◽  
Feedback Control ◽  
Two Dimensional ◽  
Sensors And Actuators ◽  
Blasius Boundary Layer

A Statistical Study of Process Variables to Optimize a High Speed Curtain Coater: Part I

TAPPI Journal ◽  
2009 ◽  
Vol 8 (1) ◽  
pp. 20-26 ◽  
Author(s):  
PEEYUSH TRIPATHI ◽  
MARGARET JOYCE ◽  
PAUL D. FLEMING ◽  
MASAHIRO SUGIHARA
Keyword(s):  
Boundary Layer ◽  
Experimental Design ◽  
High Speed ◽  
Statistical Study ◽  
Process Variables ◽  
High Speeds ◽  
The Stability ◽  
Air Removal ◽  
Removal System

Using an experimental design approach, researchers altered process parameters and material prop-erties to stabilize the curtain of a pilot curtain coater at high speeds. Part I of this paper identifies the four significant variables that influence curtain stability. The boundary layer air removal system was critical to the stability of the curtain and base sheet roughness was found to be very important. A shear thinning coating rheology and higher curtain heights improved the curtain stability at high speeds. The sizing of the base sheet affected coverage and cur-tain stability because of its effect on base sheet wettability. The role of surfactant was inconclusive. Part II of this paper will report on further optimization of curtain stability with these four variables using a D-optimal partial-facto-rial design.

Endangered Butterflies and their Non-Native Host Plants: Examining Shifting Values of Belonging in Restoration

2019 ◽  
Vol 3 (1) ◽  
pp. 1-9
Author(s):  
Robert M. Anderson ◽  
Amy M. Lambert
Keyword(s):  
Ecological Restoration ◽  
Native Species ◽  
Puget Sound ◽  
A Value ◽  
The Social ◽  
Remote Island ◽  
Scientific Truth ◽  
Native Host

The island marble butterfly (Euchloe ausonides insulanus), thought to be extinct throughout the 20th century until re-discovered on a single remote island in Puget Sound in 1998, has become the focus of a concerted protection effort to prevent its extinction. However, efforts to “restore” island marble habitat conflict with efforts to “restore” the prairie ecosystem where it lives, because of the butterfly’s use of a non-native “weedy” host plant. Through a case study of the island marble project, we examine the practice of ecological restoration as the enactment of particular norms that define which species are understood to belong in the place being restored. We contextualize this case study within ongoing debates over the value of “native” species, indicative of deep-seated uncertainties and anxieties about the role of human intervention to alter or manage landscapes and ecosystems, in the time commonly described as the “Anthropocene.” We interpret the question of “what plants and animals belong in a particular place?” as not a question of scientific truth, but a value-laden construct of environmental management in practice, and we argue for deeper reflexivity on the part of environmental scientists and managers about the social values that inform ecological restoration.

Perempuan dan Liminalitas dalam Tradisi Perkawinan Adat di Timor Tengah Selatan

2020 ◽  
Vol 6 (1) ◽  
pp. 114
Author(s):  
Marsel Eliaser Liunokas
Keyword(s):  
Qualitative Research ◽  
Research Method ◽  
Literature Study ◽  
Qualitative Research Method ◽  
South Central ◽  
A Value ◽  
Traditional Marriage ◽  
The Village ◽  
As If

Timorese culture is patriarchal in that men are more dominant than women. As if women were not considered in traditional rituals so that an understanding was built that valued women lower than men. However, in contrast to the article to be studied, this would like to see the priority of women’s roles in traditional marriages in Belle village, South Central Timor. The role of women wiil be seen from giving awards to their parents called puah mnasi manu mnasi. This paper aims to look at the meaning of the rituals of puah mnasi maun mnasi and the role and strengths that women have in traditional marriage rituals in the village of Belle, South Central Timor. The method used for this research is a qualitative research method using interview techniques with a number of people in the Belle Villa community and literature study to strengthen this writing. Based on the data obtained this paper shows that the adat rituals of puah mnasi manu mnasi provide a value that can be learned, namely respect for women, togetherness between the two families, and brotherhood that is intertwined due to customary marital affrairs.

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