scholarly journals The relaxation time for viscous and porous gravity currents following a change in flux

2017 ◽  
Vol 821 ◽  
pp. 330-342 ◽  
Author(s):  
Thomasina V. Ball ◽  
Herbert E. Huppert ◽  
John R. Lister ◽  
Jerome A. Neufeld
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Gravity Current ◽  
Singular Limit ◽  
Physical Parameters ◽  
Equilibration Time ◽  
Self Similarity ◽  
One Dimensional ◽  
High Reynolds ◽  
Time Origin

The equilibration time $\unicode[STIX]{x1D70F}$ in response to a change in flux from $Q$ to $\unicode[STIX]{x1D6EC}Q$ after an injection period $T$ applied to either a low-Reynolds-number gravity current or one propagating through a porous medium, in both axisymmetric and one-dimensional geometries, is shown to be of the form $\unicode[STIX]{x1D70F}=Tf(\unicode[STIX]{x1D6EC})$, independent of all the remaining physical parameters. Numerical solutions are used to investigate $f(\unicode[STIX]{x1D6EC})$ for each of these situations and compare very well with experimental results in the case of an axisymmetric current propagating over a rigid horizontal boundary. Analysis of the relaxation towards self-similarity provides an illuminating connection between the excess (deficit) volume from early times and an asymptotically equivalent shift in time origin, and hence a good quantitative estimate of $\unicode[STIX]{x1D70F}$. The case $\unicode[STIX]{x1D6EC}=0$ of equilibration after ceasing injection at time $T$ is a singular limit. Extensions to high-Reynolds-number currents and to the case of a constant-volume release followed by constant-flux injection are discussed briefly.

Models of the scalar spectrum for turbulent advection

1978 ◽  
Vol 88 (3) ◽  
pp. 541-562 ◽  
Author(s):  
R. J. Hill
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Schmidt Number ◽  
Temperature Fluctuations ◽  
Limited Extent ◽  
Temperature Spectrum ◽  
One Dimensional ◽  
Moderate Reynolds Number ◽  
Temperature Spectra ◽  
High Reynolds

Several models are developed for the high-wavenumber portion of the spectral transfer function of scalar quantities advected by high-Reynolds-number, locally isotropic turbulent flow. These models are applicable for arbitrary Prandtl or Schmidt number, v/D, and the resultant scalar spectra are compared with several experiments having different v/D. The ‘bump’ in the temperature spectrum of air observed over land is shown to be due to a tendency toward a viscous-convective range and the presence of this bump is consistent with experiments for large v/D. The wavenumbers defining the transition between the inertial-convective range and viscous-convective range for asymptotically large v/D (denoted k* and k1* for the three- and one-dimensional spectra) are determined by comparison of the models with experiments. A measurement of the transitional wavenumber k1* [denoted (k1*)s] is found to depend on v/D and on any filter cut-off. On the basis of the k* values it is shown that measurements of β1 from temperature spectra in moderate Reynolds number turbulence in air (v/D = 0·72) maybe over-estimates and that the inertial-diffusive range of temperature fluctuations in mercury (v/D ≃ 0·02) is of very limited extent.

scholarly journals On the use of a cell-centered finite-volume scheme on prismatic meshes in boundary layers

2021 ◽  
pp. 1-44
Author(s):  
Pavel Alexeevisch Bakhvalov
Keyword(s):  
Reynolds Number ◽  
Finite Volume ◽  
High Reynolds Number ◽  
Finite Volume Scheme ◽  
Wall Surface ◽  
One Dimensional ◽  
Volume Scheme ◽  
Dimensional Reconstruction ◽  
A Cell ◽  
High Reynolds

We consider the cell-centered finite-volume scheme with the quasi-one-dimensional reconstruction and generalize it to anisotropic prismatic meshes suitable for high-Reynolds-number problems. We offer a new algorithm of flux computation based on the reconstruction along the wall surface, whereas in the original schemes it was along the tangent to the wall surface. We also study how does the curvature of mesh elements influence the accuracy if taken into account.

On the continuum theory for the large Reynolds number spherical expansion into a near vacuum

1975 ◽  
Vol 68 (4) ◽  
pp. 625-638 ◽  
Author(s):  
N. C. Freeman ◽  
R. S. Johnson ◽  
S. Kumar ◽  
W. B. Bush
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Continuum Theory ◽  
Large Reynolds Number ◽  
Heat Conducting ◽  
Sonic Point ◽  
Spherical Expansion ◽  
High Reynolds ◽  
Background Gas ◽  
Very High

The steady, spherically symmetric flow of a compressible gas is considered. The gas is both viscous and heat-conducting. In the limit of very high Reynolds number (= α−1, α → 0) and correspondingly low pressure at infinity, the structure of the whole flow field is discussed. The five regions that arise by virtue of the limit α → 0 are briefly considered. Special care is given to the matching across the overlap domains and the first region (close to, but outside, the sonic point) and the fifth (where the pressure adjusts to its ambient value) are carefully examined. It is argued that the application of appropriate matching principles, together with judicious use of numerical solutions, allows an arbitrary pressure and temperature to be assigned to the background gas.

The Local Analytic Numerical Method for the Double Vortex Combustor Flow

1985 ◽  
Author(s):  
J. He ◽  
B. Q. Zhang
Keyword(s):  
Reynolds Number ◽  
Analytic Solutions ◽  
Navier Stokes ◽  
Hyperbolic Function ◽  
Navier Stokes Equation ◽  
One Dimensional ◽  
New Type ◽  
High Reynolds ◽  
The One ◽  
Coarse Grids

A new hyperbolic function discretization equation for two dimensional Navier-Stokes equation in the stream function vorticity from is derived. The basic idea of this method is to integrat the total flux of the general variable ϕ in the differential equations, then incorporate the local analytic solutions in hyperbolic function for the one-dimensional linearized transport equation. The hyperbolic discretization (HD) scheme can more accurately represent the conservation and transport properties of the governing equation. The method is tested in a range of Reynolds number (Re=100~2000) using the viscous incompressible flow in a square cavity. It is proved that the HD scheme is stable for moderately high Reynolds number and accurate even for coarse grids. After some proper extension, the method is applied to predict the flow field in a new type combustor with air blast double-vortex and obtained some useful results.

scholarly journals Lubricated viscous gravity currents

2015 ◽  
Vol 766 ◽  
pp. 626-655 ◽  
Author(s):  
Katarzyna N. Kowal ◽  
M. Grae Worster
Keyword(s):  
Gravity Current ◽  
Gravity Currents ◽  
Singular Limit ◽  
Vertical Shear ◽  
Surface Films ◽  
Viscous Coupling ◽  
Self Similarity ◽  
Transient Behaviour ◽  
Fingering Instability ◽  
Self Similar

AbstractWe present a theoretical and experimental study of viscous gravity currents lubricated by another viscous fluid from below. We use lubrication theory to model both layers as Newtonian fluids spreading under their own weight in two-dimensional and axisymmetric settings over a smooth rigid horizontal surface and consider the limit in which vertical shear provides the dominant resistance to the flow in both layers. There are contributions from Poiseuille-like flow driven by buoyancy and Couette-like flow driven by viscous coupling between the layers. The flow is self-similar if both fluids are released simultaneously, and exhibits initial transient behaviour when there is a delay between the initiation of flow in the two layers. We solve for both situations and show that the latter converges towards self-similarity at late times. The flow depends on three key dimensionless parameters relating the relative dynamic viscosities, input fluxes and density differences between the two layers. Provided the density difference between the two layers is bounded away from zero, we find an asymptotic solution in which the front of the lubricant is driven by its own gravitational spreading. There is a singular limit of equal densities in which the lubricant no longer spreads under its own weight in the vicinity of its nose and ends abruptly with a non-zero thickness there. We explore various regimes, from thin lubricating layers underneath a more viscous current to thin surface films coating an underlying more viscous current and find that although a thin film does not greatly influence the more viscous current if it forms a surface coating, it begins to cause interesting dynamics if it lubricates the more viscous current from below. We find experimentally that a lubricated gravity current is prone to a fingering instability.

Gravity currents propagating into shear

2015 ◽  
Vol 778 ◽  
pp. 552-585 ◽  
Author(s):  
M. M. Nasr-Azadani ◽  
E. Meiburg
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Steady State ◽  
High Reynolds Number ◽  
Gravity Current ◽  
Gravity Currents ◽  
Maximum Energy ◽  
Channel Height ◽  
High Reynolds ◽  
The Given

An analytical vorticity-based model is introduced for steady-state inviscid Boussinesq gravity currents in sheared ambients. The model enforces the conservation of mass and horizontal and vertical momentum, and it does not require any empirical closure assumptions. As a function of the given gravity current height, upstream ambient shear and upstream ambient layer thicknesses, the model predicts the current velocity as well as the downstream ambient layer thicknesses and velocities. In particular, it predicts the existence of gravity currents with a thickness greater than half the channel height, which is confirmed by direct numerical simulation (DNS) results and by an analysis of the energy loss in the flow. For high-Reynolds-number gravity currents exhibiting Kelvin–Helmholtz instabilities along the current/ambient interface, the DNS simulations suggest that for a given shear magnitude, the current height adjusts itself such as to allow for maximum energy dissipation.

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