Convergence to Steady-state and Boundary Layer Profiles in a Linear Chromatography System

2015 ◽  
Vol 75 (2) ◽  
pp. 745-761 ◽  
Author(s):  
Joaquín Menacho ◽  
J. Solà-Morales
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Convergence To Steady State ◽  
Linear Chromatography

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

Contribution of vertical advection to supergradient wind in tropical cyclone boundary layer: A numerical study

2021 ◽  
Author(s):  
Rong Fei ◽  
Yuqing Wang ◽  
Yuanlong Li
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Wind Speed ◽  
Tropical Cyclone ◽  
Vertical Structure ◽  
Numerical Study ◽  
Substantial Reduction ◽  
Vertical Advection ◽  
Physics Model ◽  
Tropical Cyclone Boundary Layer

AbstractThe existence of supergradient wind in the interior of the boundary layer is a distinct feature of a tropical cyclone (TC). Although the vertical advection is shown to enhance supergradient wind in TC boundary layer (TCBL), how and to what extent the strength and structure of supergradient wind are modulated by vertical advection are not well understood. In this study, both a TCBL model and an axisymmetric full-physics model are used to quantify the contribution of vertical advection process to the strength and vertical structure of supergradient wind in TCBL. Results from the TCBL model show that the removal of vertical advection of radial wind reduces both the strength and height of supergradient wind by slightly more than 50%. The removal of vertical advection of agradient wind reduces the height of the supergradient wind core by ~30% but increases the strength of supergradient wind by ~10%. Results from the full-physics model show that the removal of vertical advection of radial wind or agradient wind reduces both the strength and height of supergradient wind but the removal of that of radial wind produces a more substantial reduction (52%) than the removal of that of agradient wind (35%). However, both the intensification rate and final intensity of the simulated TCs in terms of maximum 10-m wind speed show little differences in experiments with and without the vertical advection of radial or agradient wind, suggesting that supergradient wind contributes little to either the intensification rate or the steady-state intensity of the simulated TC.

Unsteady convective exchange flows in cavities

1998 ◽  
Vol 368 ◽  
pp. 127-153 ◽  
Author(s):  
J. J. STURMAN ◽  
G. N. IVEY
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Boundary Layer Thickness ◽  
Buoyancy Flux ◽  
Exchange Flow ◽  
Flushing Time ◽  
Exchange Flows ◽  
Buoyancy Forcing ◽  
Convective Exchange ◽  
Approach To Steady State

Horizontal exchange flows driven by spatial variation of buoyancy fluxes through the water surface are found in a variety of geophysical situations. In all examples of such flows the timescale characterizing the variability of the buoyancy fluxes is important and it can vary greatly in magnitude. In this laboratory study we focus on the effects of this unsteadiness of the buoyancy forcing and its influence on the resulting flushing and circulation processes in a cavity. The experiments described all start with destabilizing forcing of the flows, but the buoyancy fluxes are switched to stabilizing forcing at three different times spanning the major timescales characterizing the resulting cavity-scale flows. For destabilizing forcing, these timescales are the flushing time of the region of forcing, and the filling-box timescale, the time for the cavity-scale flow to reach steady state. When the forcing is stabilizing, the major timescale is the time for the fluid in the exchange flow to pass once through the forcing boundary layer. This too is a measure of the time to reach steady state, but it is generally distinct from the filling-box time. When a switch is made from destabilizing to stabilizing buoyancy flux, inertia is important and affects the approach to steady state of the subsequent flow. Velocities of the discharges from the end regions, whether forced in destabilizing or stabilizing ways, scaled as u∼(Bl)1/3 (where B is the forcing buoyancy flux and l is the length of the forcing region) in accordance with Phillips' (1966) results. Discharges with destabilizing and stabilizing forcing were, respectively, Q−∼(Bl)1/3H and Q+∼(Bl)1/3δ (where H is the depth below or above the forcing plate and δ is the boundary layer thickness). Thus Q−/Q+>O(1) provided H>O(δ), as was certainly the case in the experiments reported, demonstrating the overall importance of the flushing processes occurring during periods of cooling or destabilizing forcing.

scholarly journals Oxidation photochemistry in the Southern Atlantic boundary layer: unexpected deviations of photochemical steady state

2011 ◽  
Vol 11 (3) ◽  
pp. 7045-7093 ◽  
Author(s):  
Z. Hosaynali Beygi ◽  
H. Fischer ◽  
H. D. Harder ◽  
M. Martinez ◽  
R. Sander ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Atlantic Ocean ◽  
Atmospheric Chemistry ◽  
Marine Boundary Layer ◽  
Air Pollutant ◽  
Photochemical Oxidant ◽  
Important Region ◽  
Atmospheric Observations ◽  
Oxidation Efficiency

Abstract. Ozone (O3) is a photochemical oxidant, an air pollutant and a greenhouse gas. As the main precursor of the hydroxyl radical (OH) it strongly affects the oxidation power of the atmosphere. The remote marine boundary layer (MBL) is considered an important region in terms of chemical O3 loss; however surface-based atmospheric observations are sparse and the photochemical processes are not well understood. To investigate the photochemistry under the clean background conditions of the Southern Atlantic Ocean, ship measurements of NO, NO2, O3, JNO2, J(O1D), HO2, OH, ROx and a range of meteorological parameters were carried out. The concentrations of NO and NO2 measured on board the French research vessel Marion-Dufresne (28° S–57° S, 46° W–34° E) in March 2007, are among the lowest yet observed. The data is evaluated for consistency with photochemical steady state (PSS) conditions, and the calculations indicate substantial deviations from PSS (Φ>1). The deviations observed under low NOx conditions (5–25 pptv) demonstrate a remarkable upward tendency in the Leighton ratio (used to characterize PSS) with increasing NOx mixing ratio and JNO2 intensity. It is a paradigm in atmospheric chemistry that OH largely controls the oxidation efficiency of the atmosphere. However, evidence is growing that for unpolluted low-NOx (NO + NO2) conditions the atmospheric oxidant budget is poorly understood. Nevertheless, for the very cleanest conditions, typical for the remote marine boundary layer, good model agreement with measured OH and HO2 radicals has been interpreted as accurate understanding of baseline photochemistry. Here we show that such agreement can be deceptive and that a yet unidentified oxidant is needed to explain the photochemical conditions observed at 40°–60° S over the Atlantic Ocean.

Katabatic flow along a differentially cooled sloping surface

2007 ◽  
Vol 571 ◽  
pp. 149-175 ◽  
Author(s):  
ALAN SHAPIRO ◽  
EVGENI FEDOROVICH
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Vegetation Type ◽  
Lower Boundary ◽  
Terminal State ◽  
Asymptotic Solutions ◽  
Normal Velocity ◽  
Katabatic Flow ◽  
Prandtl Model ◽  
Surface Buoyancy

Buoyancy inhomogeneities on sloping surfaces arise in numerous situations, for example, from variations in snow/ice cover, cloud cover, topographic shading, soil moisture, vegetation type, and land use. In this paper, the classical Prandtl model for one-dimensional flow of a viscous stably stratified fluid along a uniformly cooled sloping planar surface is extended to include the simplest type of surface inhomogeneity – a surface buoyancy that varies linearly down the slope. The inhomogeneity gives rise to acceleration, vertical motions associated with low-level convergence, and horizontal and vertical advection of perturbation buoyancy. Such processes are not accounted for in the classical Prandtl model. A similarity hypothesis appropriate for this inhomogeneous flow removes the along-slope dependence from the problem, and, in the steady state, reduces the Boussinesq equations of motion and thermodynamic energy to a set of coupled nonlinear ordinary differential equations. Asymptotic solutions for the velocity and buoyancy variables in the steady state, valid for large values of the slope-normal coordinate, are obtained for a Prandtl number of unity for pure katabatic flow with no ambient wind or externally imposed pressure gradient. The undetermined parameters in these solutions are adjusted to conform to lower boundary conditions of no-slip, impermeability and specified buoyancy. These solutions yield formulae for the boundary-layer thickness and slope-normal velocity component at the top of the boundary layer, and provide an upper bound of the along-slope surface-buoyancy gradient beyond which steady-state solutions do not exist. Although strictly valid for flow above the boundary layer, the steady asymptotic solutions are found to be in very good agreement with the terminal state of the numerical solution of an initial-value problem (suddenly applied surface buoyancy) throughout the flow domain. The numerical results also show that solution non-existence is associated with self-excitation of growing low-frequency gravity waves.

Convergence to Steady State in a Diffusional Sampler

SIAM Review ◽  
1988 ◽  
Vol 30 (3) ◽  
pp. 482-486 ◽  
Author(s):  
R. M. Burton, Jr. ◽  
K. Ravishankar ◽  
E. D. Palmes
Keyword(s):  
Steady State ◽  
Convergence To Steady State
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