POF Nameplate
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

Flickr Twitter UniPHY Group iResearch App Facebook

Physics of Fluids / Volume 24 / Issue 2 / ARTICLES / Geophysical Flows

Phys. Fluids 24, 026601 (2012); http://dx.doi.org/10.1063/1.3680260 (26 pages)

Gravity currents in a two-layer stratified ambient: The theory for the steady-state (front condition) and lock-released flows, and experimental confirmations

M. R. Flynn1, M. Ungarish2, and A. W. Tan1

1Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 2G8, Canada
2Department of Computer Science, Technion, Haifa 32000, Israel

View MapView Map

(Received 2 May 2011; accepted 22 December 2011; published online 1 February 2012)

We consider the propagation of a gravity current of density ρc at the bottom of a two-layer stratified ambient in a horizontal channel of height H, in the high-Reynolds number Boussinesq domain. The study emphasizes theoretical-analytical modeling, however, experimental and Navier-Stokes simulation data are also presented and their comparison with theory is discussed. The stratification parameters are S = (ρ1 − ρ2)/(ρc − ρ2) where ρ is the fluid density, and φ = h1R/H where h1R is the (unperturbed) ambient interface height. Here, 1 and 2 denote, respectively, the lower and upper layer and c denotes the gravity current. The reduced gravity is defined as g′ = (ρc/ρ2 − 1)g. Rigorous results are obtained for the steady-state analogue of the classical problem of Benjamin [J. Fluid Mech. 31, 209 (1968)]10.1017/S0022112068000133, in which the half-infinite gravity current has thickness h and speed U. We thereby demonstrate that the Froude number F = U/(g′h)1/2 is a function of a = h/H, S, and φ. In general, two solutions (or modes) may be realized. Issues of energy dissipation, sub- vs. supercriticality with respect to long internal waves and, more generally, the influence of upstream-propagating disturbances are discussed. For a gravity current released from a lock of height h0 and length x0, we derive an approximate shallow-water model and show that the motion is in this case governed by Ξ = H/h0, S, and φ. Although the shallow-water model neglects motion in the ambient layers and ignores the impact of propagation on stratification, the gravity current front speed in the slumping stage is in excellent agreement with measured data. Our theoretical solutions are consistent with previous results (in particular, Holyer and Huppert [J. Fluid Mech. 100, 739 (1980)] and Tan et al. [Environ. Fluid Mech. 11, 203 (2011)]), but have the advantages of being (i) derived without reliance on adjustable constants and ad hoc closures; (ii) applicable to a significantly broader range of dimensionless parameters; and (iii) better assessed by comparison against measured data. The present one-layer shallow-water approximation turns out to be a simple and versatile extension of existing models for homogeneous and linearly stratified ambients, and can be straightforwardly incorporated into the available prediction tools for gravity currents.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. EXPERIMENTAL PROCEDURE
  3. NUMERICAL SIMULATIONS
  4. COMPARISON BETWEEN EXPERIMENTS AND NUMERICAL SIMULATIONS
  5. THE STEADY-STATE CURRENT AND F RESULTS
    1. Formulation
    2. Rate of dissipation and head loss
    3. Results and comparisons with laboratory data
  6. SHALLOW-WATER THEORY
    1. Equations of motion
    2. Front condition
    3. Dam break and slumping
  7. DISCUSSION AND CONCLUSIONS

RELATED DATABASES

To view database links for this article, you need to log in.

KEYWORDS and PACS

Keywords

boundary layer turbulence, channel flow, gravity waves, Navier-Stokes equations, shallow water equations, stratified flow

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3680260

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    V. K. Birman, E. Meiburg, and M. Ungarish, “On gravity currents in stratified ambients,” Phys. Fluids 19, 086602 (2007)PHFLE6000019000008086602000001.


Figures (17)

Access to article objects (figures, tables, multimedia) requires a subscription; log in to view available files.
(Access to supplementary files, where available, is free for this journal.)



Close

Google Calendar

ADVERTISEMENT

Your Recent History Recent History Help

Recently Viewed

  1. Gravity currents in a two-layer stratified ambient: The theory for the steady-state (front condition) and lock-released flows, and experimental confirmations
  2. Parametric study of cylindrical converging shock waves generated based on shock dynamics theory
  3. Wavelet decomposition of forced turbulence: Applicability of the iterative Donoho-Johnstone threshold
  4. Inertial-range anisotropy in Rayleigh-Taylor turbulence
  5. The three-dimensional transition stages over the NACA-0009 airfoil at Reynolds numbers of several ten thousand
Go to AIP Home
Copyright © American Institute of Physics
close