An Introduction to Gravity Currents and Intrusions

TLDR: In this article, the Navier-Stokes equations for high-Re flows were applied to a two-layer model of the Boussinesq system in dimensionless form.

Abstract: Introduction Classification The Navier-Stokes equations Non-stratified ambient currents Shallow-water (SW) formulation for high-Re flows Motion of the interface and the continuity equation One-layer model A useful transformation The full behavior by numerical solution Dam-break stage Similarity solution The validity of the inviscid approximation The steady-state current and nose jump conditions Benjamin's analysis Jump condition Box models for 2D geometry Fixed volume current with inertial-buoyancy balance Inflow volume change Two-layer SW model Introduction The governing equations Boussinesq system in dimensionless form Jumps of interface for H < 2 Energy and work in a two-layer model Axisymmetric currents, SW formulation Governing equations A useful transformation The full behavior by numerical solution Dam-break stage Similarity solution The validity of the inviscid approximation Some comparisons Box models for axisymmetric geometry Fixed volume current with inertial-buoyancy balance Inflow volume change Effects of rotation Axisymmetric case Rotating channel Buoyancy decays: particle-driven, porous boundary, and entrainment Particle-driven currents Axisymmetric particle-driven current Extensions of particle-driven solutions Current over a porous bottom Axisymmetric current over a porous bottom Entrainment Non-Boussinesq systems Introduction Formulation Dam-break and initial slumping motion The transition and self-similar stages Summary Lubrication theory formulation for viscous currents 2D geometry Axisymmetric current Current in a porous medium II Stratified ambient currents and intrusions Continuous density transition Introduction The SW formulation SW results and comparisons with experiments and simulations Dam break Critical speed and nose-wave interaction Similarity solution The validity of the inviscid approximation Axisymmetric and rotating cases SW formulation SW and NS finite-difference results The validity of the inviscid approximation The steady-state current Steady-state flow pattern Results Comparisons and conclusions Intrusions in 2D geometry Introduction Two-layer stratification Linear transition layer Rectangular lock configurations Cylindrical lock in a fully linearly-stratified tank Similarity solution Non-symmetric intrusions Intrusions in axisymmetric geometry Introduction Two-layer stratification Fully linearly-stratified tank, part-depth locks Box models for 2D geometry Fixed volume and inertial-buoyancy balance S = 1, inflow volume change Box models for axisymmetric geometry Fixed volume and inertial-buoyancy balance S = 1, inflow volume change Lubrication theory for viscous currents with S = 1 2D geometry Axisymmetric geometry Energy Introduction 2D geometry Axisymmetric geometry SW equations: characteristics and finite-difference schemes Characteristics Numerical solution of the SW equations Navier-Stokes numerical simulations Formulation A finite-difference code Other codes Some useful formulas Leibniz's Theorem Vectors and coordinate systems