scholarly journals Development of gravity currents on rapidly changing slopes

2017 ◽  
Vol 833 ◽  
pp. 70-97 ◽  
Author(s):  
M. E. Negretti ◽  
J.-B. Flòr ◽  
E. J. Hopfinger
Keyword(s):  
Similarity Theory ◽  
Boundary Layer Separation ◽  
Gravity Currents ◽  
Bottom Friction ◽  
Reynolds Stresses ◽  
Velocity Increase ◽  
Acceleration Parameter ◽  
Boundary Slope ◽  
Layer Velocity ◽  
High Reynolds

Gravity currents often occur on complex topographies and are therefore subject to spatial development. We present experimental results on continuously supplied gravity currents moving from a horizontal to a sloping boundary, which is either concave or straight. The change in boundary slope and the consequent acceleration give rise to a transition from a stable subcritical current with a large Richardson number to a Kelvin–Helmholtz (KH) unstable current. It is shown here that depending on the overall acceleration parameter$\overline{T_{a}}$, expressing the rate of velocity increase, the currents can adjust gradually to the slope conditions (small$\overline{T_{a}}$) or go through acceleration–deceleration cycles (large$\overline{T_{a}}$). In the latter case, the KH billows at the interface have a strong effect on the flow dynamics, and are observed to cause boundary layer separation. Comparison of currents on concave and straight slopes reveals that the downhill deceleration on concave slopes has no qualitative influence, i.e. the dynamics is entirely dominated by the initial acceleration and ensuing KH billows. Following the similarity theory of Turner 1973 (Buoyancy Effects in Fluids. Cambridge University Press), we derive a general equation for the depth-integrated velocity that exhibits all driving and retarding forces. Comparison of this equation with the experimental velocity data shows that when$\overline{T_{a}}$is large, bottom friction and entrainment are large in the region of appearance of KH billows. The large bottom friction is confirmed by the measured high Reynolds stresses in these regions. The head velocity does not exhibit the same behaviour as the layer velocity. It gradually approaches an equilibrium state even when the acceleration parameter of the layer is large.

The propagation of gravity currents in a V-shaped triangular cross-section channel: experiments and theory

2014 ◽  
Vol 754 ◽  
pp. 232-249 ◽  
Author(s):  
Marius Ungarish ◽  
Catherine A. Mériaux ◽  
Cathy B. Kurz-Besson
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Viscosity Coefficient ◽  
Gravity Currents ◽  
Quantitative Agreement ◽  
Flat Bottom ◽  
Special Configuration ◽  
Theoretical Predictions ◽  
Speed Of Propagation ◽  
High Reynolds

AbstractWe investigate the motion of high-Reynolds-number gravity currents (GCs) in a horizontal channel of V-shaped cross-section combining lock-exchange experiments and a theoretical model. While all previously published experiments in V-shaped channels were performed with the special configuration of the full-depth lock, we present the first part-depth experiment results. A fixed volume of saline, that was initially of length $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}x_0$ and height $h_0$ in a lock and embedded in water of height $H_0$ in a long tank, was released from rest and the propagation was recorded over a distance of typically $ 30 x_0$. In all of the tested cases the current displays a slumping stage of constant speed $u_N$ over a significant distance $x_S$, followed by a self-similar stage up to the distance $x_V$, where transition to the viscous regime occurs. The new data and insights of this study elucidate the influence of the height ratio $H = H_0/h_0$ and of the initial Reynolds number ${\mathit{Re}}_0 = (g^{\prime }h_0)^{{{1/2}}} h_0/ \nu $, on the motion of the triangular GC; $g^{\prime }$ and $\nu $ are the reduced gravity and kinematic viscosity coefficient, respectively. We demonstrate that the speed of propagation $u_N$ scaled with $(g^{\prime } h_0)^{{{1/2}}}$ increases with $H$, while $x_S$ decreases with $H$, and $x_V \sim [{\mathit{Re}}_0(h_0/x_0)]^{{4/9}}$. The initial propagation in the triangle is 50 % more rapid than in a standard flat-bottom channel under similar conditions. Comparisons with theoretical predictions show good qualitative agreements and fair quantitative agreement; the major discrepancy is an overpredicted $u_N$, similar to that observed in the standard flat bottom case.

Experiments on the Flow Around a Sphere at High Reynolds Numbers

1969 ◽  
Vol 36 (3) ◽  
pp. 598-607 ◽  
Author(s):  
T. Maxworthy
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Distribution ◽  
Reynolds Numbers ◽  
Boundary Layer Separation ◽  
Recirculation Region ◽  
Layer Separation ◽  
High Reynolds Numbers ◽  
High Reynolds

Flow around a sphere for Reynolds numbers between 2 × 105 and 6 × 104 has been observed by measuring the pressure distribution around a circle of longitude under a variety of conditions. These include the effects of laminar and turbulent boundary layer separation, tunnel blockage, various boundary layer trip arrangements and inserting an object to disrupt the unsteady, recirculation region behind the sphere.

Axisymmetric, constantly supplied gravity currents at high Reynolds number

2011 ◽  
Vol 675 ◽  
pp. 540-551 ◽  
Author(s):  
ANJA C. SLIM ◽  
HERBERT E. HUPPERT
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Threshold Value ◽  
Gravity Currents ◽  
Water Model ◽  
Closure Condition ◽  
Area Source ◽  
Radial Extent ◽  
Long Time ◽  
High Reynolds

We consider theoretically the long-time evolution of axisymmetric, high Reynolds number, Boussinesq gravity currents supplied by a constant, small-area source of mass and radial momentum in a deep, quiescent ambient. We describe the gravity currents using a shallow-water model with a Froude number closure condition to incorporate ambient form drag at the front and present numerical and asymptotic solutions. The predicted profile consists of an expanding, radially decaying, steady interior that connects via a shock to a deeper, self-similar frontal boundary layer. Controlled by the balance of interior momentum flux and frontal buoyancy across the shock, the front advances as (g′sQ/r1/4s)4/154/5, where g′s is the reduced gravity of the source fluid, Q is the total volume flux, rs is the source radius and is time. A radial momentum source has no effect on this solution below a non-zero threshold value. Above this value, the (virtual) radius over which the flow becomes critical can be used to collapse the solution onto the subthreshold one. We also use a simple parameterization to incorporate the effect of interfacial entrainment, and show that the profile can be substantially modified, although the buoyancy profile and radial extent are less significantly impacted. Our predicted profiles and extents are in reasonable agreement with existing experiments.

Mixing in continuous gravity currents

2017 ◽  
Vol 818 ◽  
Author(s):  
Diana Sher ◽  
Andrew W. Woods
Keyword(s):  
Light Attenuation ◽  
Vertical Gradient ◽  
Gravity Currents ◽  
Mixing Zone ◽  
Ambient Fluid ◽  
Unit Width ◽  
A Value ◽  
Dense Fluid ◽  
Catch Up ◽  
High Reynolds

We present measurements of the entrainment of ambient fluid into high-Reynolds-number gravity currents produced by a steady flux of buoyancy. The currents propagate along a horizontal channel and the mixing is measured using a light attenuation technique to obtain the cross-channel average of the density throughout the current. The total volume of the current increases linearly with time, at a rate in the range $(1.8{-}2.1)Q_{o}$ for source Froude numbers, $Fr_{o}$, in the range $0.1{-}3.7$, where $Q_{o}$ is the source volume flux per unit width. Most mixing occurs either immediately downstream of the inflow or near the head of the flow, with an increasing proportion of the entrainment occurring in a mixing zone near the inflow as $Fr_{o}$ increases. A vertical gradient in the density and horizontal velocity develops in this mixing zone. This enables relatively dense fluid at the base of the current to catch up with the head, where it rises and mixes with the ambient fluid which is displaced over the head. The mixed fluid continues forward more slowly than the head, forming the relatively dilute fluid in the upper part of the current. Our data show that the depth and the depth-averaged buoyancy are primarily dependent on the position relative to the front, with the speed of the front being $\unicode[STIX]{x1D706}(Fr_{o})B_{o}^{1/3}$, where $B_{o}$ is the source buoyancy flux per unit width. Here, $\unicode[STIX]{x1D706}(Fr_{o})$ increases from 0.9 to 1.1 as $Fr_{o}$ increases from 0.1 to 3.7, while the Froude number at the head of the flow has a value of $1.1\pm 0.05$.

Compressible large eddy simulation of the unsteady evolution process in a LPT Cascade with incoming wakes

2020 ◽  
pp. 095441002096753
Author(s):  
Yunfei Wang ◽  
Huanlong Chen ◽  
Huaping Liu ◽  
Yanping Song ◽  
Fu Chen
Keyword(s):  
Boundary Layer ◽  
Large Eddy Simulation ◽  
Boundary Layer Separation ◽  
Main Flow ◽  
Reynolds Stresses ◽  
Flow Area ◽  
Eddy Simulation ◽  
Reduced Frequency ◽  
Large Eddy ◽  
The Impact

An in-house large eddy simulation (LES) code based on three-dimensional compressible N-S equations is used to research the impact of incoming wakes on unsteady evolution characteristic in a low-pressure turbine (LPT) cascade. The Mach number is 0.4 and Reynolds number is 0.6 × 105 (based on the axial chord and outlet velocity). The reduced frequency of incoming wakes is Fred = 0 (without wakes), 0.37 and 0.74. A detailed analysis of Reynolds stresses and turbulent kinetic energy inside the boundary layer has been carried out. Particular consideration is devoted to the transport process of incoming wakes and the intermittent property of the unsteady boundary layer. With the increase of reduced frequency, the inhibiting effect of wakes on boundary layer separation gradually enhances. The separation at the rear part of the suction side is weakened and the separation point moves downstream. However, incoming wakes lead to an increase in dissipation and aerodynamic losses in the main flow area. Excessive reduced frequency ( Fred = 0.74) causes the main flow area to become one of the main source areas of loss. An optimal reduced frequency exists to minimize the aerodynamic loss of the linear cascade.

Breaking of shoaling internal solitary waves

2010 ◽  
Vol 659 ◽  
pp. 289-317 ◽  
Author(s):  
PAYAM AGHSAEE ◽  
LEON BOEGMAN ◽  
KEVIN G. LAMB
Keyword(s):  
Boundary Layer ◽  
Solitary Waves ◽  
Wave Length ◽  
Boundary Layer Separation ◽  
Developmental Time ◽  
Internal Solitary Waves ◽  
Global Instability ◽  
Layer Separation ◽  
Wide Range ◽  
High Reynolds

The breaking of fully nonlinear internal solitary waves of depression shoaling upon a uniformly sloping boundary in a smoothed two-layer density field was investigated using high-resolution two-dimensional simulations. Our simulations were limited to narrow-crested waves, which are more common than broad-crested waves in geophysical flows. The simulations were performed for a wide range of boundary slopes S ∈ [0.01, 0.3] and wave slopes extending the parameter range to weaker slopes than considered in previous laboratory and numerical studies. Over steep slopes (S ≥ 0.1), three distinct breaking processes were observed: surging, plunging and collapsing breakers which are associated with reflection, convective instability and boundary-layer separation, respectively. Over mild slopes (S ≤ 0.05), nonlinearity varies gradually and the wave fissions into a train of waves of elevation as it passes through the turning point where solitary waves reverse polarity. The dynamics of each breaker type were investigated and the predominance of a particular mechanism was associated with a relative developmental time scale. The breaking location was modelled as a function of wave amplitude (a), characteristic wave length and the isopycnal length along the slope. The breaker type was characterized in wave slope (Sw = a/Lw, where Lw is a measure of half of the wavelength) versus S space, and the reflection coefficient (R), modelled as a function of the internal Iribarren number, was in agreement with other studies. The effects of grid resolution and wave Reynolds number (Rew) on R, boundary-layer separation and the evolution of global instability were studied. High Reynolds numbers (Rew ~ 104) were found to trigger a global instability, which modifies the breaking process relative to the lower Rew case, but not necessarily the breaking location, and results in a ~ 10 % increase in R, relative to the Rew ~ 103 case.

Some properties of sink-flow turbulent boundary layers

1972 ◽  
Vol 56 (2) ◽  
pp. 337-351 ◽  
Author(s):  
W. P. Jones ◽  
B. E. Launder
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
High Reynolds Number ◽  
Viscous Sublayer ◽  
Turbulent Boundary Layers ◽  
Inertial Subrange ◽  
Mean Velocity ◽  
Acceleration Parameter ◽  
Power Spectral ◽  
High Reynolds

An experimental study of asymptotic sink-flow turbulent boundary layers is reported. Three levels of acceleration corresponding to values of the acceleration parameter K of 1·5 × 10−6, 2·5 × 10×6 and 3·0 × 10×6 have been examined. In addition to mean velocity profiles, measurements have been obtained of the profiles of longitudinal turbulence intensity, and, for the lowest value of K, of the lateral and transverse components as well. Measurements at selected positions in the boundary layer of the power spectral density indicate that none of the boundary layers exhibit an inertial subrange; for the steepest acceleration, in particular, throughout the boundary layer the spectrum shapes are similar in form to those reported within the viscous sublayer of a high Reynolds number turbulent flow.

scholarly journals Unsteady separation in vortex-induced boundary layers

2014 ◽  
Vol 372 (2020) ◽  
pp. 20130348 ◽  
Author(s):  
K. W. Cassel ◽  
A. T. Conlisk
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Asymptotic Methods ◽  
Boundary Layer Separation ◽  
Unsteady Boundary Layer ◽  
Layer Separation ◽  
Unsteady Separation ◽  
High Reynolds ◽  
Reynolds Number Flows

This paper provides a brief review of the analytical and numerical developments related to unsteady boundary-layer separation, in particular as it relates to vortex-induced flows, leading up to our present understanding of this important feature in high-Reynolds-number, surface-bounded flows in the presence of an adverse pressure gradient. In large part, vortex-induced separation has been the catalyst for pulling together the theory, numerics and applications of unsteady separation. Particular attention is given to the role that Prof. Frank T. Smith, FRS, has played in these developments over the course of the past 35 years. The following points will be emphasized: (i) unsteady separation plays a pivotal role in a wide variety of high-Reynolds-number flows, (ii) asymptotic methods have been instrumental in elucidating the physics of both steady and unsteady separation, (iii) Frank T. Smith has served as a catalyst in the application of asymptotic methods to high-Reynolds-number flows, and (iv) there is still much work to do in articulating a complete theoretical understanding of unsteady boundary-layer separation.

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