On the Anelastic Approximation for Deep Convection

Lipps, Frank B.

doi:10.1175/1520-0469(1990)047<1794:otaafd>2.0.co;2

Cited by 54 publications

(39 citation statements)

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“…Generalizations that incorporate variations in density include the Boussinesq approximation (Boussinesq 1903), which allows heating-induced buoyancy in a constant-density background, and the anelastic atmospheric (Batchelor 1953;Ogura & Phillips 1962;Dutton & Fichtl 1969;Gough 1969;Lipps & Hemler 1982, 1985Lipps 1990;Wilhelmson & Ogura 1972) and stellar ( Latour et al 1976;Gilman & Glatzmaier 1981;Glatzmaier 1984) approximations that include the effect of large-scale background stratification in the fluid density and pressure but assume small thermodynamic perturbations from the background. Low Mach number models for chemical combustion (Rehm & Baum 1978;Majda & Sethian 1985;Day & Bell 2000) and nuclear burning (Bell et al 2004) incorporate large compressibility effects due to chemical nuclear reactions and thermal processes with a spatially constant background pressure.…”

Section: Introductionmentioning

confidence: 99%

Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics

Almgren

Bell

Rendleman

et al. 2006

ApJ

125

135

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We introduce a low Mach number equation set for the large-scale numerical simulation of carbon-oxygen white dwarfs experiencing a thermonuclear deflagration. Since most of the interesting physics in a Type Ia supernova transpires at Mach numbers from 0.01 to 0.1, such an approach enables both a considerable increase in accuracy and a savings in computer time compared with frequently used compressible codes. Our equation set is derived from the fully compressible equations using low Mach number asymptotics, but without any restriction on the size of perturbations in density or temperature. Comparisons with simulations that use the fully compressible equations validate the low Mach number model in regimes where both are applicable. Comparisons to simulations based on the more traditional anelastic approximation also demonstrate the agreement of these models in the regime for which the anelastic approximation is valid. For low Mach number flows with potentially finite amplitude variations in density and temperature, the low Mach number model overcomes the limitations of each of the more traditional models and can serve as the basis for an accurate and efficient simulation tool.

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Section: Introductionmentioning

confidence: 99%

Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics

Almgren

Bell

Rendleman

et al. 2006

ApJ

125

135

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“…Anelastic mass continuity is known to be an adequate assumption in deep moist convection (e.g., Ogura and Phillips, 1962;Lipps, 1990). The general form of the mass continuity constraint is given by…”

Section: Anelastic Mass Continuity Constraint: J Cmentioning

confidence: 99%

Vertical air motion retrievals in deep convective clouds using the ARM scanning radar network in Oklahoma during MC3E

et al. 2017

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Abstract. The US Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program's Southern Great Plains (SGP) site includes a heterogeneous distributed scanning Doppler radar network suitable for collecting coordinated Doppler velocity measurements in deep convective clouds. The surrounding National Weather Service (NWS) Next Generation Weather Surveillance Radar 1988 Doppler (NEXRAD WSR-88D) further supplements this network. Radar velocity measurements are assimilated in a three-dimensional variational (3DVAR) algorithm that retrieves horizontal and vertical air motions over a large analysis domain (100 km × 100 km) at storm-scale resolutions (250 m). For the first time, direct evaluation of retrieved vertical air velocities with those from collocated 915 MHz radar wind profilers is performed. Mean absolute and root-meansquare differences between the two sources are of the order of 1 and 2 m s −1 , respectively, and time-height correlations are of the order of 0.5. An empirical sensitivity analysis is done to determine a range of 3DVAR constraint weights that adequately satisfy the velocity observations and anelastic mass continuity. It is shown that the vertical velocity spread over this range is of the order of 1 m s −1 . The 3DVAR retrievals are also compared to those obtained from an iterative upwards integration technique. The results suggest that the 3DVAR technique provides a robust, stable solution for cases in which integration techniques have difficulty satisfying velocity observations and mass continuity simultaneously.

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“…The numerical solutions presented in the paper are obtained by integrating either the anelastic Lipps-Hemler PDEs [22,23] or their incompressible Boussinesq limit [47], in absence of viscosity, friction, diabatic effects and planetary rotation. In both cases, the governing conservation laws of mass, momentum and thermodynamic properties can be compactly written as…”

Section: Governing Equationsmentioning

confidence: 99%

An unstructured-mesh atmospheric model for nonhydrostatic dynamics: Towards optimal mesh resolution

Szmelter

Zhang

Smolarkiewicz

2015

Journal of Computational Physics

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The paper advances the limited-area anelastic model [Smolarkiewicz et al., J. Comput. Phys., 254 (2013) 184] for investigation of nonhydrostatic dynamics in mesoscale atmospheric flows. New developments include the extension to a tetrahedral-based median-dual option for unstructured meshes and a static mesh adaptivity technique using an error indicator based on inherent properties of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). The model employs semi-implicit nonoscillatory forward-in-time integrators for soundproof PDEs, built on MPDATA and a robust non-symmetric Krylov-subspace elliptic solver. Finitevolume spatial discretisation adopts an edge-based data structure. Simulations of stratified orographic flows and the associated gravity-wave phenomena in media with uniform and variable dispersive properties, verify the advancement and demonstrate the potential of heterogeneous anisotropic discretisation with large variation in spatial resolution for study of complex stratified flows that can be computationally unattainable with regular grids.

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On the Anelastic Approximation for Deep Convection

Cited by 54 publications

References 0 publications

Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics

Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics

Vertical air motion retrievals in deep convective clouds using the ARM scanning radar network in Oklahoma during MC3E

An unstructured-mesh atmospheric model for nonhydrostatic dynamics: Towards optimal mesh resolution

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