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共查询到20条相似文献,搜索用时 31 毫秒
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An experimental study was conducted to investigate the penetration of a convective mixed layer into an overlying stably (solutally) stratified layer contained in a narrow, tall vessel when the fluid is subjected to a destabilizing heat flux from below. The interest was the evolution of the bottom mixed-layer height (\(h\)) with time (\(t\)) in the presence of side-wall effects, but without the formation of conventional double-diffusive layers. The side-wall effects are expected at small mixed-layer aspect ratios, \(\varGamma_{h} = (W/h)\), where \(W\) is the container width. This case has not been studied hitherto, although there are important environmental and industrial applications. The mixed-layer growth laws for low aspect ratio convection were formulated by assuming a balance between the vertical kinetic energy flux at the interface and the rate of change of potential energy of the fluid system due to turbulent entrainment. The effects of sidewalls were considered using similarity arguments, by taking characteristic rms velocities to be a function of \(\varGamma_{h}\), in addition to buoyancy flux (\(q_{0}\)) and \(h\). In all stages of evolution, the similarity variables \(\xi = h/W\) and \(t^{\prime } = Nt/A\), where \(A = N^{3} W^{2} /4q_{0}\) and \(N\) is the buoyancy frequency, scaled the mixed-layer evolution data remarkably well. Significant wall effects were noted when \(\varGamma_{h} < 1\), and for this case the interfacial vertical turbulent velocity and length scales were identified via scaling arguments and experimental data. 相似文献
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In this study, the flow dynamics of intrusive gravity currents past a bottom-mounted obstacle were investigated using highly resolved numerical simulations. The propagation dynamics of a classic intrusive gravity current was first simulated in order to validate the numerical model with previous laboratory experiments. A bottom-mounted obstacle with a varying non-dimensional height of \(\tilde{D}=D/H\), where D is the obstacle height and H is the total flow depth, was then added to the problem in order to study the downstream flow pattern of the intrusive gravity current. For short obstacles, the intrusion re-established itself downstream without much distortion. However, for tall obstacles, the downstream flow was found to be a joint effect of horizontal advection, overshoot-springback phenomenon, and associated Kelvin-Helmholtz instabilities. Analysis of the numerical results show that the relationship between the downstream propagation speed and the obstacle height can be subdivided into three regimes: (1) a retarding regime (\(\tilde{D}\) \(\approx \) 0–0.3) where a 30 % increase in obstacle height leads to a 20 % reduction in propagation speed, simply due to the obstacle’s retarding effect; (2) an impounding regime (\(\tilde{D}\) \(\approx \) 0.3–0.6) where the additional 30 % increase in obstacle height only leads to a further (negligible) 5 % reduction in propagation speed, due to the accelerating effect of upstream impoundment and downstream enhanced mixing; and (3) a choking regime (\(\tilde{D}\) \(\approx \) 0.6–1.0) where the propagation speed is dramatically reduced due to the dominance of the obstacle’s blocking effect. The obstacle thickness was found to be irrelevant in determining the downstream propagation speed at least for the parameter range explored in this study. The present work highlights the significance of topographic effects in stratified flows with horizontal pressure forcing. 相似文献
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We consider the propagation of a high-Reynolds-number gravity current in a horizontal channel with general cross-section whose width is \(f(z), 0 \le z\le H\), and the gravity acceleration g acts in \(-z\) direction. (The classical rectangular cross-section is covered by the particular case \(f(z) =\) const.) We assume a two-layer system of homogeneous fluids of constant densities \(\rho _{c}\) (current, of height \(h < H \)) and smaller \(\rho _{a}\) (ambient, filling the remaining part of the channel). We focus attention on the calculation and assessment of the nose Froude-number condition \(Fr = U/(g' h)^{1/2}\); here U is the speed of propagation of the current and \(g' = (\rho _{c}/\rho _{a}-1) g\) is the reduced gravity. We first revisit the steady-state current, and derive compact insightful expressions of Fr and energy dissipation as a function of \(\varphi \) (\(=\) area fraction occupied by the current in the cross-section). We show that the head loss \(\delta _0\) on the stagnation line is formally a degree of freedom in the determination of \(Fr(\varphi )\), and we clarify the strong connections with the head loss \(\delta \) in the ambient fluid, and with the overall rate of dissipation \(\dot{{\mathcal{D}}}\). We demonstrate that the closure \(\delta _0 = 0\) [suggested by Benjamin (J Fluid Mech 31, 209–248, 1968) for the rectangular cross-section] produces in general the smallest Fr for a given \(\varphi \); the results are valid for a significant range \([0, \varphi _{\max }]\), in which the current is dissipative, except for the point \(\varphi _{\max }\) where \(\delta = \dot{{\mathcal{D}}} = 0\). We show that imposing the closure \(\delta = \dot{{\mathcal{D}}} = 0\), which corresponds to an energy-conserving or non-dissipative current, produces in general unacceptable restrictions of the range of validity, and large values of Fr; in particular, deep currents (\(\varphi < 0.3\) say) must be excluded because they are inherently dissipative. On the other hand, the compromise closure \(\delta (\varphi ) =\delta _0(\varphi )\) produces the simple \(Fr(\varphi ) = \sqrt{2}(1 - \varphi )\) formula whose values and dissipation properties are very close, and the range of validity is identical, to these obtained with Benjamin’s closure (moreover, we show that this corresponds to circulation-conservation solutions). The results are illustrated for practical cross-section geometries (rectangle, \(\Delta \) and \(\nabla \) triangle, circle, and the general power-law \(f(z) = b z ^\alpha \) (\(b>0, \alpha \ge 0, 0< z \le H\)). Next, we investigate the connection of the steady-state results with the time-dependent current, and show that in a lock-released current the rate of dissipation of the system is equal to, or larger than, that obtained for Fr corresponding to the conditions at the nose of the current. The results and insights of this study cover a wide range of cross-section geometry and apply to both Boussinesq and non-Boussinesq systems; they reveal a remarkable robustness of Fr as a function of \(\varphi \). 相似文献
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Identifying demand parameters in the presence of unobservables: A combined revealed and stated preference approach 总被引:1,自引:0,他引:1
Roger H. von Haefen Daniel J. Phaneuf 《Journal of Environmental Economics and Management》2008,56(1):19-32
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Gravity currents propagating on \(12^\circ \), \(9^\circ \), \(6^\circ \), \(3^\circ \) unbounded uniform slopes and on an unbounded horizontal boundary are reported. Results show that there are two stages of the deceleration phase. In the early stage of the deceleration phase, the front location history follows \({(x_f+x_0)}^2 = {(K_I B)}^{1/2} (t+t_{I})\), where \((x_f+x_0)\) is the front location measured from the virtual origin, \(K_I\) an experimental constant, B the total buoyancy, t time and \(t_I\) the t-intercept. In the late stage of the deceleration phase for the gravity currents on \(12^\circ \), \(9^\circ \), \(6^\circ \) unbounded uniform slopes, the front location history follows \({(x_f+x_0)}^{8/3} = K_{VS} {{B}^{2/3} V^{2/9}_0 }{\nu }^{-1/3} ({t+t_{VS}})\), where \(K_{VS}\) is an experimental constant, \(V_0\) the initial volume of heavy fluid, \(\nu \) the kinematic viscosity and \(t_{VS}\) the t-intercept. In the late stage of the deceleration phase for the gravity currents on a \(3^\circ \) unbounded uniform slope and on an unbounded horizontal boundary, the front location history follows \({(x_f+x_0)}^{4} = K_{VM} {{B}^{2/3} V^{2/3}_0 }{\nu }^{-1/3} ({t+t_{VM}})\), where \(K_{VM}\) is an experimental constant and \(t_{VM}\) the t-intercept. Two qualitatively different flow morphologies are identified in the late stage of the deceleration phase. For the gravity currents on \(12^\circ \), \(9^\circ \), \(6^\circ \) unbounded uniform slopes, an ‘active’ head separates from the body of the current. For the gravity currents on a \(3^\circ \) unbounded uniform slope and on an unbounded horizontal boundary, the gravity currents maintain an integrated shape throughout the motion. Results indicate two possible routes to the final stage of the gravity currents on unbounded uniform slopes.
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