Submaximal exchange between a convectively forced basin and a large reservoir

1999 ◽  
Vol 378 ◽  
pp. 357-378 ◽  
Author(s):  
T. D. FINNIGAN ◽  
G. N. IVEY
Keyword(s):  
Steady State ◽  
Theoretical Development ◽  
Analytical Models ◽  
Geometrical Parameters ◽  
Exchange Flow ◽  
Mean Velocity ◽  
Large Reservoir ◽  
Strongly Coupled ◽  
Reservoir Conditions ◽  
Surface Buoyancy

If a sill-enclosed basin, connected to a large reservoir, is suddenly subjected to a de-stabilizing surface buoyancy flux, it will first mix vertically by turbulent convection before the resulting lateral buoyancy gradient generates a horizontal exchange flow across the sill. We present a study which examines the unsteady adjustment of such a basin under continued steady forcing. It is shown, through theoretical development and laboratory experimentation, that two consecutive unsteady regimes characterized by different dynamic balances are traversed as the flow approaches a steady state.Once established the exchange flow is controlled at the sill crest where it is hydraulically critical. In the absence of a lateral contraction, the single control at the sill crest allows a range of submaximal exchange states with the flow at the sill being dependent not only on the forcing and geometrical parameters but also on mixing conditions within the basin which are, in turn, dependent on the sill exchange. The sill–basin system is therefore strongly coupled although it remains isolated from the external reservoir conditions by a region of internally supercritical flow. Results from the laboratory experiments are used to demonstrate the link between the forcing and the exchange flow at the sill. Steady-state measurements of the interior mean velocity and buoyancy fields are also compared with previous analytical models.

scholarly journals Collision times in plasmas

1990 ◽  
Vol 8 (4) ◽  
pp. 763-770 ◽  
Author(s):  
U. Reimann ◽  
C. Toepffer
Keyword(s):  
Plasma Oscillation ◽  
Diffusion Constant ◽  
Analytical Models ◽  
Plasma Parameters ◽  
Mean Velocity ◽  
Strongly Coupled ◽  
Diffusive Regime ◽  
Angle Scattering ◽  
Transition Times ◽  
Coupled Plasmas

Collision times in plasmas are usually defined in connection with the time evolution of the ensemble-averaged scattering angle . Extrapolating the short-time behaviour ϑshort(t), one obtains the collision time tc by setting ϑshort(tc) = π/2. We have shown with the help of computer simulations that this procedure is ambiguous, as we can clearly distinguish three regimes for ϑ(t). There is always an initial ballistic regime with ϑ(t) ∝ t with dominant pairwise interactions. This lasts up to times α/υth where α is the mean distance between the particles and υth their mean velocity. This is followed by a diffusive regime with ϑ(t) ∝ t½, which is characterized by many small-angle scattering events. Eventually, this diffusion will lead to a uniform distribution of the directions of the velocity. So ϑ(t) will saturate towards π/2 in a third asymptotic regime. For large plasma parameters Γ ≫ 1, this asymptotic behaviour will be modulated by a damped oscillation of ϑ(t) with the plasma frequency. For such strongly coupled plasmas the diffusive regime is suppressed and one observes a direct transition from the initial ballistic to the asymptotic collective regime characterized by the plasma oscillation. Parameters such as the diffusion constant and the transition times are estimated with the help of analytical models.

scholarly journals Bubble wall velocity at strong coupling

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Francesco Bigazzi ◽  
Alessio Caddeo ◽  
Tommaso Canneti ◽  
Aldo L. Cotrone
Keyword(s):  
Phase Transitions ◽  
Steady State ◽  
Friction Force ◽  
Bubble Velocity ◽  
Strongly Coupled ◽  
First Order ◽  
Black Hole Background ◽  
Different Dimensions ◽  
Holographic Description ◽  
First Order Phase

Abstract Using the holographic correspondence as a tool, we determine the steady-state velocity of expanding vacuum bubbles nucleated within chiral finite temperature first-order phase transitions occurring in strongly coupled large N QCD-like models. We provide general formulae for the friction force exerted by the plasma on the bubbles and for the steady-state velocity. In the top-down holographic description, the phase transitions are related to changes in the embedding of $$ Dq\hbox{-} \overline{D}q $$ Dq ‐ D ¯ q flavor branes probing the black hole background sourced by a stack of N Dp-branes. We first consider the Witten-Sakai-Sugimoto $$ D4\hbox{-} D8\hbox{-} \overline{D}8 $$ D 4 ‐ D 8 ‐ D ¯ 8 setup, compute the friction force and deduce the equilibrium velocity. Then we extend our analysis to more general setups and to different dimensions. Finally, we briefly compare our results, obtained within a fully non-perturbative framework, to other estimates of the bubble velocity in the literature.

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.

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.

Analysis of a Transient Asymmetrically Heated/Cooled Open Thermosyphon

1993 ◽  
Vol 115 (3) ◽  
pp. 621-630 ◽  
Author(s):  
G. F. Jones ◽  
J. Cai
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Vertical Plate ◽  
Numerical Study ◽  
Vertical Wall ◽  
Constant Heat Flux ◽  
Closed Form Expression ◽  
Transient Temperature ◽  
Large Reservoir ◽  
One Dimensional

We present a numerical study of transient natural convection in a rectangular open thermosyphon having asymmetric thermal boundary conditions. One vertical wall of the thermosyphon is either heated by constant heat flux (“warmup”) or cooled by convection to the surroundings (“cooldown”). The top of the thermosyphon is open to a large reservoir of fluid at constant temperature. The vorticity, energy, and stream-function equations are solved by finite differences on graded mesh. The ADI method and iteration with overrelaxation are used. We find that the thermosyphon performs quite differently during cooldown compared with warmup. In cooldown, flows are mainly confined to the thermosyphon with little momentum and heat exchange with the reservoir. For warmup, the circulation resembles that for a symmetrically heated thermosyphon where there is a large exchange with the reservoir. The difference is explained by the temperature distributions. For cooldown, the fluid becomes stratified and the resulting stability reduces motion. In contrast, the transient temperature for warmup does not become stratified but generally exhibits the behavior of a uniformly heated vertical plate. For cooldown and Ra > 104, time-dependent heat transfer is predicted by a closed-form expression for one-dimensional conduction, which shows that Nu → Bi1/2/A in the steady-state limit. For warmup, transient heat transfer behaves as one-dimensional conduction for early times and at steady state and for Ra* ≥ 105, can be approximated as that for a uniformly heated vertical plate.

Stability of the steady state in a strongly coupled semiconductor superlattice described using a semiclassical approach

2013 ◽  
Vol 77 (12) ◽  
pp. 1444-1447 ◽  
Author(s):  
K. N. Alekseev ◽  
A. G. Balanov ◽  
A. A. Koronovskii ◽  
V. A. Maksimenko ◽  
O. I. Moskalenko ◽  
...  
Keyword(s):  
Steady State ◽  
Semiclassical Approach ◽  
Strongly Coupled ◽  
Semiconductor Superlattice ◽  
Coupled Semiconductor

Closed-form expressions for the steady-state response of damped transmission line conductors considering their bending stiffness

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1319-1329
Author(s):  
Marcelo A Ceballos ◽  
José E Stuardi
Keyword(s):  
Steady State ◽  
Transmission Line ◽  
Numerical Models ◽  
Mechanical Impedance ◽  
Steady State Solution ◽  
Bending Stiffness ◽  
Analytical Models ◽  
Dispersive Media ◽  
Overhead Transmission Line ◽  
Damper Design

This paper begins with a brief compilation of analytical models typically used to calculate the dynamic response of a conductor span belonging to an overhead transmission line, with a Stockbridge-type damper located near one of its ends. In most of analyses found in the literature, the calculation of the response is done through the superposition of waves that propagate in both longitudinal directions impinging and reflecting at the span ends and at the damper attachment points. The approach proposed in this paper allows obtaining the response as the steady-state solution of the governing differential equations providing suitable analytical expressions for conductors with bending stiffness, which are dispersive media for propagating waves. Using these analytical solutions, the influence of bending stiffness on the efficiency and on the optimal mechanical impedance of the damper, which are of great importance in damper design, can be described explicitly. At the same time, the proposed methodology avoids the need of numerical models or approximate formulas to calculate the bending strains in critical points of the conductor with a single damper.

A Comparative Analysis of Thermal Blood Perfusion Measurement Techniques

1987 ◽  
Vol 109 (3) ◽  
pp. 218-225 ◽  
Author(s):  
R. Kress ◽  
R. Roemer
Keyword(s):  
Blood Flow ◽  
Steady State ◽  
Time Window ◽  
Measurement Techniques ◽  
Temperature Response ◽  
Blood Perfusion ◽  
Analytical Models ◽  
Transient Temperature ◽  
Two Dimensional ◽  
Transient Heating

The object of this study was to devise a unified method for comparing different thermal techniques for the estimation of blood perfusion rates and to perform a comparison for several common techniques. The approach used was to develop analytical models for the temperature response for all combinations of five power deposition geometries (spherical, one- and two-dimensional cylindrical, and one- and two-dimensional Gaussian) and three transient heating techniques (temperature pulse-decay, temperature step function, and constant-power heat-up) plus one steady-state heating technique. The transient models were used to determine the range of times (the time window) when a significant portion of the transient temperature response was due to blood perfusion. This time window was defined to begin when the difference between the conduction-only and the conduction-plus-blood flow transient temperature (or power) responses exceeded a specified value, and to end when the conduction-plus-blood flow transient temperature (or power) reached a specified fraction of its steady-state value. The results are summarized in dimensionless plots showing the size of the time windows for each of the transient perfusion estimation techniques. Several conclusions were drawn, in particular: (a) low perfusions are difficult to estimate because of the dominance of conduction, (b) large heated regions are better suited for estimation of low perfusions, (c) noninvasive heating techniques are superior because they have the potential to minimize conduction effects, and (d) none of the transient techniques appears to be clearly superior to the others.

scholarly journals Technical Note: Simple formulations and solutions of the dual-phase diffusive transport for biogeochemical modeling

2014 ◽  
Vol 11 (14) ◽  
pp. 3721-3728 ◽  
Author(s):  
J. Y. Tang ◽  
W. J. Riley
Keyword(s):  
Steady State ◽  
Tracer Diffusion ◽  
Technical Note ◽  
Analytical Models ◽  
Dual Phase ◽  
Near Surface ◽  
Solution Algorithms ◽  
Biogeochemical Models ◽  
Volume Approximation ◽  
Multi Phase

Abstract. Representation of gaseous diffusion in variably saturated near-surface soils is becoming more common in land biogeochemical models, yet the formulations and numerical solution algorithms applied vary widely. We present three different but equivalent formulations of the dual-phase (gaseous and aqueous) tracer diffusion transport problem that is relevant to a wide class of volatile tracers in land biogeochemical models. Of these three formulations (i.e., the gas-primary, aqueous-primary, and bulk-tracer-based formulations), we contend that the gas-primary formulation is the most convenient for modeling tracer dynamics in biogeochemical models. We then provide finite volume approximation to the gas-primary equation and evaluate its accuracy against three analytical models: one for steady-state soil CO2 dynamics, one for steady-state soil CH4 dynamics, and one for transient tracer diffusion from a constant point source into two different sequentially aligned medias. All evaluations demonstrated good accuracy of the numerical approximation. We expect our result will standardize an efficient mechanistic numerical method for solving relatively simple, multi-phase, one-dimensional diffusion problems in land models.

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