3 results
On the propagation of internal bores
- JOSEPH B. KLEMP, RICHARD ROTUNNO, WILLIAM C. SKAMAROCK
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- Journal:
- Journal of Fluid Mechanics / Volume 331 / 25 January 1997
- Published online by Cambridge University Press:
- 21 May 2009, pp. 81-106
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According to classical hydraulic theory, the energy losses within an external bore must occur within the expanding layer. However, the application of this theory to describe the propagation of internal bores leads to contradiction with accepted gravity-current behaviour in the limit as the depth of the expanding layer ahead of the bore becomes small. In seeking an improved expression for the propagation of internal bores, we have rederived the steady front condition for a bore in a two-layer Boussinesq fluid in a channel under the assumption that the energy loss occurs within the contracting layer. The resulting front condition is in good agreement with available laboratory data and numerical simulations, and has the appropriate behaviour in both the linear long-wave and gravity-current limits. Analysis of an idealized internal bore assuming localized turbulent stresses suggests that the energy within the expanding layer should, in fact, increase. Numerical simulations with a two-dimensional non-hydrostatic model also reveal a slight increase of energy within the expanding layer and suggest that the structure of internal bores is fundamentally different from classical external bores, having the opposite circulation and little turbulence in the vicinity of the leading edge. However, if there is strong shear near the interface between layers, the structure and propagation of internal jumps may become similar to their counterparts in classical hydraulic theory. The modified jump conditions for internal bores produce some significant alterations in the traditional Froude-number dependence of Boussinesq shallow-water flow over an obstacle owing to the altered behaviour of the upstream-propagating internal bore.
On the dynamics of gravity currents in a channel
- Joseph B. Klemp, Richard Rotunno, William C. Skamarock
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- Journal:
- Journal of Fluid Mechanics / Volume 269 / 25 June 1994
- Published online by Cambridge University Press:
- 26 April 2006, pp. 169-198
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We attempt to clarify the factors that regulate the propagation and structure of gravity currents through evaluation of idealized theoretical models along with two-dimensional numerical model simulations. In particular, we seek to reconcile research based on hydraulic theory for gravity currents evolving from a known initial state with analyses of gravity currents that are assumed to be at steady state, and to compare these approaches with both numerical simulations and laboratory experiments. The time-dependent shallow-water solution for a gravity current propagating in a channel of finite depth reveals that the flow must remain subcritical behind the leading edge of the current (in a framework relative to the head). This constraint requires that hf/d ≤ 0.347, where hf is the height of the front and d is the channel depth. Thus, in the lock-exchange problem, inviscid solutions corresponding to hf/d = 0.5 are unphysical, and the actual currents have depth ratios of less than one half near their leading edge and require dissipation or are not steady. We evaluate the relevance of Benjamin's (1968) well-known formula for the propagation of steady gravity currents and clarify discrepancies with other theoretical and observed results. From two-dimensional simulations with a frictionless lower surface, we find that Benjamin's idealized flow-force balance provides a good description of the gravity-current propagation. Including surface friction reduces the propagation speed because it produces dissipation within the cold pool. Although shallow-water theory over-estimates the propagation speed of the leading edge of cold fluid in the ‘dam-break’ problem, this discrepancy appears to arise from the lack of mixing across the current interface rather than from deficiencies in Benjamin's front condition. If an opposing flow restricts the propagation of a gravity current away from its source, we show that the propagation of the current relative to the free stream may be faster than predicted by Benjamin's formula. However, in these situations the front propagation remains dependent upon the specific source conditions and cannot be generalized.
6 - Model numerics for convective-storm simulation
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- By Joseph B. Klemp, William C. Skamarock, National Center for Atmospheric Research, Boulder, Colorado
- Edited by Evgeni Fedorovich, University of Oklahoma, Richard Rotunno, National Center for Atmospheric Research, Boulder, Colorado, Bjorn Stevens, University of California, Los Angeles
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- Book:
- Atmospheric Turbulence and Mesoscale Meteorology
- Published online:
- 04 August 2010
- Print publication:
- 21 October 2004, pp 117-138
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Summary
Introduction
Over the past forty years, the numerical simulation of atmospheric convection has evolved from its infancy in two-dimensional dry thermals to highly sophisticated three-dimensional models used for numerical weather prediction (NWP) at convective scales. This advancement has been feasible because of the enormous growth in computing power, increasing from thousands to billions of calculations per second during this period (Wilhelmson and Wicker, 2001). However, significant advancements in model numerics, physical parameterizations, and data analysis have also been required to capture the complexity of atmospheric convection and convective storms in numerical simulation models. Throughout these decades, Doug Lilly has been a major force in advancing this technology, both in his own research and in motivating the achievements of others.
Lilly (1962) conducted pioneering research on the numerical simulation of buoyant thermals that laid the groundwork for the 3D convective storm models that evolved in subsequent decades. Thiswork included a newapproach for grid staggering (Lilly, 1961) and improved techniques for the treatment of subgrid turbulence in an inertial subrange using a nonlinear eddy viscosity proportional to the local shear and modified by buoyancy effects through a Richardson-number dependency. Lilly solved the full 2D compressible equations in flux form, placing strong emphasis on both numerical stability and accurate conservation (analyzed systematically for alternative numerical schemes in Lilly, 1965). Lilly fostered the development of one of the early 3D cloud models, the Klempeacute;Wilhelmson model, and in founding and directing the Center for Analysis and Prediction of Storms (CAPS), he promoted development of the Atmospheric Research and Prediction System (ARPS).