Buoyant Parcel Research Articles

A Novel Framework to Study Trace Gas Transport in Deep Convective Clouds

AbstractDeep convective clouds reach the upper troposphere (8–15 km height). In addition to moisture and aerosol particles, they can bring aerosol precursor gases and other reactive trace gases from the planetary boundary layer to the cloud top. In this paper, we present a method to estimate trace gas transport based on the analysis of individual air parcel trajectories. Large eddy simulation of an idealized deep convective cloud was used to provide realistic environmental input to a parcel model. For a buoyant parcel, we found that the trace gas transport approximately follows one out of three scenarios, determined by a combination of the equilibrium vapor pressure (containing information about water‐solubility and pure component saturation vapor pressure) and the enthalpy of vaporization. In one extreme, the trace gas will eventually be completely removed by precipitation. In the other extreme, there is almost no vapor condensation on hydrometeors and most of the gas is transported to the top of the cloud. The scenario in between these two extremes is also characterized by strong gas condensation, but a small fraction of the trace gas may still be transported aloft. This approach confirms previously suggested patterns of inert trace gas behavior in deep convective clouds, agrees with observational data, and allows estimating transport in analytically simple and computationally efficient way compared to explicit cloud‐resolving model calculations.

Effective buoyancy at the surface and aloft

It is shown here that a wide, buoyant parcel of air at the surface accelerates far less rapidly than it does aloft. In particular, analytical formulae are derived for the effective buoyancy (i.e. the net vertical acceleration due to parcel buoyancy and environmental response) of idealized cylinders of diameterDand heightH, located in free space and at the surface. These formulae quantify the decrease of effective buoyancy with increasing aspect ratioD/H, and show that this effect is more pronounced for surface cylinders, especially whenD/H> 1. We gain intuition for these results by considering the pressure fields generated by these buoyant parcels, and we test our results with large‐eddy simulations. Our formulae can inform parametrizations of the vertical velocity equation for clouds, and also provide a quantitative map of the ‘grey zone’ in numerical modelling between hydrostatic and non‐hydrostatic regimes.

Buoyancy-driven perturbations in a rapidly rotating, electrically conducting fluid: part III – effect of the lorentz force

The velocity, pressure, perturbation magnetic field, helicity and electromotive force driven by an isolated buoyant parcel in an unbounded, rapidly rotating, electrically conducting fluid in the limit of small Elsasser number and very small Ekman number are calculated, visualized and analyzed. On the scale of the parcel, the solution is identical to that obtained in the limit of small Ekman number and zero Elsasser number. On the scale of the Taylor-column, it is elongated in the direction of the applied magnetic field and compressed in the direction perpendicular to it. The α-effect calculated by averaging the electromotive force on planes normal to rotation is strongly anisotropic: near the parcel and in the inner part of the Taylor-column it is strongest when the applied magnetic field is perpendicular to rotation and gravity; in the outer part of the Taylor-column it is strongest when the applied magnetic field is in the same plane as rotation and gravity.

Buoyancy-driven perturbations in a rapidly rotating, electrically conducting fluid: part I – flow and magnetic field

The steady velocity, perturbation pressure and perturbation magnetic field, driven by an isolated buoyant parcel of Gaussian shape in a rapidly rotating, unconfined, incompressible electrically conducting fluid in the presence of an imposed uniform magnetic field, are obtained by means of the Fourier transform in the limit of small Ekman number. Lorentz and inertial forces are neglected. The solution requires at most evaluation of a single integral and is found in closed form in some spatial regions. The solution has structure on two disparate scales: on the scale of the buoyant parcel and on the scale of the Taylor column, which is elongated in the direction of the rotation axis. The detailed structures of the flow and pressure depend linearly on the relative orientation of gravity and rotation, with the solution for arbitrary orientation being a linear combination of two limiting cases in which these vectors are colinear (polar case) and perpendicular (equatorial case). The perturbation magnetic field depends additionally on the relative orientation of the imposed magnetic field, and three limiting cases of interest are presented in which gravity and rotation are colinear (polar–toroidal case), gravity and imposed field are colinear (equatorial–radial case) and all three are mutually perpendicular (equatorial–toroidal case). Visualization and analysis of the velocity and perturbation magnetic field vectors are facilitated by dividing these vector fields into geostrophic and ageostrophic protions. In all cases, the geostrophic and ageostrophic portions have different structure on the Taylor-column scale. The buoyancy force is balanced by a pressure force in the polar case and by a flux of momentum in the equatorial case. The pressure force and momentum flux do not decay in strength with increasing axial distance. Far from the parcel, the axial mass flux varies as the inverse one-third power of distance from the parcel. The velocity has a single geostrophic vortex in the polar case and two vortices in the equatorial case. The perturbation magnetic field has two, four and one geostrophic vortices in the polar–toroidal, equatorial–radial and equatorial–toroidal cases, respectively. To facilitate comparison of the present results with numerical simulations carried out in a finite domain, a set of boundary conditions are developed, with may be applied at a finite distance from the parcel.

Episodic Mixing and Buoyancy-Sorting Representations of Shallow Convection: A Diagnostic Study

Episodic mixing and buoyancy-sorting (EMBS) models have been proposed as a physically more realistic alternative to entraining plume models of cumulus convection. Applying these models to shallow nonprecipitating clouds requires assumptions about the rate at which undilute subcloud air is eroded into the environment, an algorithm to calculate the eventual detrainment level of cloud‐environment mixtures, and the probability distribution of mixing fraction. A diagnostic approach is used to examine the sensitivity of an EMBS model to these three closure assumptions, given equilibrium convection with known large-scale forcings taken from phase III of the Barbados Oceanographic Meteorological Experiment (BOMEX). The undilute eroding rate (UER) is retrieved and found to decrease exponentially with height above cloud base, suggesting a strong modulation by the cloud size distribution. The EMBS model is also used to calculate convective transport by individual clouds of varying thickness. No single cloud from this ensemble can balance the large-scale BOMEX forcing; the observed equilibrium requires a population of clouds with a cloud size distribution that is maximum for small clouds and decreases monotonically with cloud size. The EMBS model depends sensitively on the assumptions governing the detrainment of positively buoyant mixtures. In particular, given the requirement that positively buoyant mixtures detrain at their neutral buoyancy level, there is no positive definite undilute eroding rate that is consistent with the BOMEX forcing. The model is less sensitive to the assumed distribution of cloud‐environment mixtures, given a multiple mixing treatment of positively buoyant parcels and detrainment at the unsaturated neutral buoyancy level.

On the structure of a Taylor column driven by a buoyant parcel in an unbounded rotating fluid

The velocity and pressure fields produced in a homogeneous rapidly rotating fluid driven by an isolated buoyant parcel are investigated. Gravity and rotation are allowed to have arbitrary orientations and the parcel shape is assumed Gaussian. Inertial forces and time-dependent effects are ignored. The linear problem is easily solved by three-dimensional Fourier transform, and the inversion is facilitated by assuming the Ekman number, E, to be very small. In this limit the fields form a Taylor column extended in the direction of the rotation axis. In the absence of rigid boundaries no boundary layers occur. The velocity and pressure in the vicinity of the parcel are found in closed form while elsewhere (within the Taylor column) they are expressed in terms of relatively simple scalar integrals which are easily evaluated.Within the buoyant parcel, the momentum balance is baroclinic, involving Coriolis, pressure and buoyancy forces. Outside the parcel, the balance is geostrophic at unit order. The viscous force is important at order E and determines the axial structure of the Taylor column. In contrast to the case of flow driven by a rigid body, no ‘Taylor slug’ of recirculating flow occurs. The velocity and pressure decay algebraically with distance from the parcel, with the scale of variation being a/E in the axial direction and a in the radial direction, where a is the parcel radius. In the vicinity of the parcel, the return flow occurs in a broad region surrounding the parcel. The structure of flow in the vicinity of the parcel is independent of the Ekman number. This return flow sweeps the fringes of the parcel backward, making the net rise speed significantly slower than that of a rigid sphere of identical buoyancy. The return flow also acts to deform the parcel; this deformation is quantified.

Small-scale helicity and α -effect in the Earth's core

It is a commonly held belief that the combination of rotation and buoyancy creates a net helicity and electromotive force (EMF), known as an α -effect, and hence, dynamo action. We investigate this possibility for a simple, but dynamically complete, model, consisting of a small, isolated buoyant parcel rising in an infinite extent of rotating electrically conducting Boussinesq fluid in the presence of a large-scale magnetic field. We show that the leading order in the local magnetic Reynolds number, assumed small, is that the total helicity and EMF are identically zero, due to symmetry. This is in effect an anti-dynamo theorem, to be overcome if dynamo action is to occur. The helicity and EMF densities are found to be concentrated in wakes having spatial extent much larger than the scale of the buoyant parcel. The wakes are aligned with rotation if Coriolis force dominates Lorentz (forming a foreshortened Taylor column) and with the magnetic field if Lorentz dominates Coriolis. Consequently, the integrals of helicity and EMF over a half-space on either side of the parcel are non-zero. These distributions have the potential of creating wavelike dynamo action as the buoyant parcel rises through the outer core. In the case that the Coriolis force is dominant and the viscous force is very weak, it is found that the half-space integral of helicity is inversely proportional to the square root of the Ekman number. This is a counterintuitive result, depending on the action of a very weak viscous force at very large distance from the buoyant parcel.

A model of the dynamical structure of Earth's outer core

The dynamical state of the outer core is quantified, assuming that the convective pattern consists of buoyant parcels which rise to the top, forcing a broad descending flow in the bulk of the outer core. This convective circulation is assumed sufficiently rapid that the outer core is close to a well-mixed adiabatic state. Small compositional deviations from this state, resulting from the secular evolution of composition as the solid inner core grows, make the descending portion of the outer core stably stratified. Thermal deviations result from the mismatch between effective volumetric heating and the divergence of conducted heat. Effective volumetric heating is the sum of secular cooling, compressional heating and Ohmic heating. Divergence of heat is negative and larger in magnitude than effective volumetric heating throughout the core, resulting in a stabilizing thermal gradient in the descending fluid which reinforces the compositional gradient. The compositional and thermal contributions to the stable stratification are of comparable magnitudes. The strength of stratification depends on the strength of the convective circulation, which is unquantified. This stratification, coupled with Coriolis and Lorentz forces, has the potential to inhibit turbulence in the descending portions of the outer core. The thermal and compositional perturbations arising from processes at the inner-core boundary and core–mantle boundary are quantified and the dynamic behavior of the rising parcels is discussed and quantified. Depending on the sign and magnitude of exchanges of heat and composition, convective motions may be inhibited or suppressed near the top of the outer core.

On the local nature of turbulence in Earth's outer core

Abstract Numerical simulations are described that strongly suggest that any large buoyant mass in the Earth's outer core will be rapidly broken up into plate-like structures elongated in the directions of the rotation axis and of the prevailing magnetic field, giving rise to the highly anisotropic motions foreseen by Braginsky and Meytlis (1990) which will then form the dominant characteristic of the local fluid flow. This result casts serious doubt on the hypothesis of Moffatt (1989) that core flow is driven by buoyant parcels or plumes periodically released from Earth's inner core.

The Magnetostrophic Rise of A Buoyant Parcel In the Earth's Core

Accepted 1993 September 21. Received 1993 September 21; in original form 1993 April 30 SUMMARY The dynamics of a buoyant parcel (or blob) of fluid released from the mushy zone on the inner core boundary (ICB) is considered. Estimates of the density defect and of the rise velocity are obtained from consideration of mass conservation and magnetostrophic force balance. When Lorentz and Coriolis forces are of comparable orders of magnitude, the disturbance remains localized in a neighbourhood of the blob even in the absence of viscous effects, and an inviscid analysis is possible. The instantaneous velocity and magnetic field associated with a given localized buoyancy distribution are then determined, and on the assumption that the velocity is approximately uniform throughout the blob, its trajectory from ICB to core-mantle boundary (CMB) is deduced. Both westward drift and poleward migration of erupting field loops are indicated. The effects of turbulent diffusion on the blob are considered. The prospects for constructing a dynamo theory based on this ‘blob scenario’ are discussed.

The diffusive interface at low stability: the importance of non-linearity and turbulent entrainment

The diffusion and convection at low temperature at an interface separating a cold, low salinity upper layer from a warmer, more saline lower layer are examined. The densities of the layers are assumed equal and an approximate, non-linear equation of state is used. The vertical transports are determined from the molecular, diffusive fluxes through the interface. The diffusion creates instabilities at the interface, which convect into the layers. The transition from diffusion to convection is estimated from a Rayleigh number based upon the penetration depth of the density anomaly. The convection occurs as quasi-stationary plumes, maintained by inflow of lighter/denser water, driven by horizontal pressure gradients induced by the density redistribution. The turbulent energy produced in the layers is calculated from the terminal vertical velocity of the buoyant parcels and the horizontal and vertical length scales of the convection. The turbulent energy density is found to depend on layer depth and buoyancy fluxes through the interface cannot be used directly as estimates of the turbulence production. Both turbulent entrainment and the non-linear equation of state could be of less importance for the transport though a diffusive interface in the oceans than what is inferred from corresponding laboratory experiments. DOI: 10.1034/j.1600-0870.1991.00006.x

Evidence of active ground deformation on the mid‐ocean ridge: Axial Seamount, Juan de Fuca Ridge, April‐June 1988

Since September 1987 a precision bottom pressure recorder (BPR) has been deployed within the summit caldera of Axial Seamount on the central Juan de Fuca Ridge. The instrument is capable of measuring pressure to 1 mbar resolution and recording these measurements at 64 samples per hour for up to 15 months. After removal of oscillatory signals due to tidal and oceanographic effects and linear trends caused by sensor drift, any significant change in the pressure record should indicate a change of depth associated with vertical ground movement. In subaerial volcanic systems, such ground movements commonly indicate active inflation or deflation of underlying magma bodies and are frequently coincident with rift eruptions. Axial Seamount was selected for this pilot study for three primary reasons: (1) its tectonic setting, (2) the presence of a well‐formed summit caldera, and (3) observational evidence of geologically recent volcanic activity. Results from the first 9 months of the BPR deployment revealed a significant change in pressure, which is interpreted to represent a 15‐cm subsidence of the caldera floor during two 2‐ to 3‐week periods in April–June 1988. Also during these periods, an anomalous decline in temperature at the site was recorded that is correlated with an apparent increase in current velocity at the Axial Seamount Hydrothermal Emissions Study (ASHES) vent field, suggesting vigorous advection of cold water into the caldera. Concurrent oceanographic data from Geosat and from current meter arrays do not indicate any large‐scale oceanographic phenomena capable of generating these simultaneous events. One mechanism to explain simultaneous ground subsidence and temperature decline at the caldera center and increased bottom current at the caldera margin is the generation of a buoyant parcel of heated water in response to the intrusion or the eruption of magma associated with volcanic deflation. Such a parcel must have been sufficiently buoyant and proximal to induce horizontal entrainment currents capable of producing the bottom water conditions that were observed at both sites. Similar volcanic events also may have generated large midwater plumes that have been described previously along the southern Juan de Fuca Ridge.

Calculations of the ascent of a saturated buoyant parcel with mixing

Calculations of the ascent of a saturated buoyant parcel with mixing

Calculations of the ascent of a saturated buoyant parcel with mixing

AbstractNumerical computations are made to show how the vertical velocity, temperature, humidity‐mixing ratio and liquid‐water content of a cloudy parcel will vary with height and time as it ascends from the condensation level, rises through, and mixes with, the surrounding environment whose temperature and humidity distributions are specified. The rate at which the parcel is diluted by mixing is formulated in two different ways which lead to essentially the same conclusions. This treatment does not attempt a detailed description of the mixing processes but arrives at rather critical values for a single parameter used to represent the rate of mixing. If this is sufficiently large to prevent the vertical motion undergoing large oscillations (such as are experienced by a closed parcel), the first‐formed cloud is small ‐ usually only a few hundred metres deep over land and perhaps less than 100 m deep over the oceans. This implies that large clouds must evolve by successive thermals rising through air which has been warmed and moistened by their predecessors. Computations are made to demonstrate this stage‐by‐stage growth. The formation and growth of the first visible cloud appears to depend rather critically upon the excess temperature and velocity with which the thermal reaches the condensation level. These conclusions, and also the computed vertical profiles of temperature, updraught speed and liquid‐water in these small clouds, appear to be consistent with observations.

DIFFUSION, ENTRAINMENT AND FRICTIONAL DRAG ASSOCIATED WITH NON-SATURATED, BUOYANT AIR PARCELS RISING THROUGH A TURBULENT AIR MASS

Abstract The entrainment equations of Houghton and Cramer have been extended to include the effects of diffusion of heat and momentum and the frictional pressure drag. The equations developed from these considerations show that certain combinations of parcel size, temperature difference, vertical velocity, and turbulence permit buoyant air parcels to pass from the bottom to the top of the turbulent ground layer. Other combinations lead to rapid dissipation of the parcel's temperature difference and velocity. The equations have been checked against three sets of observations within unstable, dry air masses. Observed properties of buoyant parcels existing in super-adiabatic atmospheres agree, within observational error, with combinations leading to extended survival of air bubbles as predicted by the equations. One set of data leads to the approximation of the value of the coefficient of pressure drag, 0.1, associated with an air parcel moving through the air.