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## Abstract

Simplified versions of the steady analytical models of density current developed by Moncrieff and So are shown to represent archetypes of cold-frontal rainbands (NCFRs) by making comparisons with the limited amount of published observational data that describe the phenomena. An overturning (or in a special case, stagnation) of the upper-level, system-relative flow of ahead of the rainband and vortidty within the cold air are important effects not included in conventional density current dynamics. The bands conserve mass energy and domain-averaged total momentum flux and involve a balance between inertial and pressure gradient effects. This is distinct from a semigeostrophic mechanism that requires a base-state baroclinity and an ageostrophic adjustment towards thermal-wind balance.

The theory also represents two-diimensional squall lines in the limiting cam when the convective available potential energy is negligible so squall lines could, in principle, be maintained solely by the kinetic energy of the mean flow and the work done by the pressure field. Furthermore, it is shown that squall lines with a deep inflow from ahead of the line and an anafront type of structure should be more prevalent than those having shallow inflows.

The basic dynamics of squall lines and narrow cold-frontal rainbands are formally shown to be analogous and their archetypal behavior can be represented by simple hydrodynamical models.

## Abstract

Simplified versions of the steady analytical models of density current developed by Moncrieff and So are shown to represent archetypes of cold-frontal rainbands (NCFRs) by making comparisons with the limited amount of published observational data that describe the phenomena. An overturning (or in a special case, stagnation) of the upper-level, system-relative flow of ahead of the rainband and vortidty within the cold air are important effects not included in conventional density current dynamics. The bands conserve mass energy and domain-averaged total momentum flux and involve a balance between inertial and pressure gradient effects. This is distinct from a semigeostrophic mechanism that requires a base-state baroclinity and an ageostrophic adjustment towards thermal-wind balance.

The theory also represents two-diimensional squall lines in the limiting cam when the convective available potential energy is negligible so squall lines could, in principle, be maintained solely by the kinetic energy of the mean flow and the work done by the pressure field. Furthermore, it is shown that squall lines with a deep inflow from ahead of the line and an anafront type of structure should be more prevalent than those having shallow inflows.

The basic dynamics of squall lines and narrow cold-frontal rainbands are formally shown to be analogous and their archetypal behavior can be represented by simple hydrodynamical models.

## Abstract

The pivotal role of mesoscale organization on the large-scale coherence of tropical convection is represented by a nonlinear dynamical model. The general model consists of two interlocked systems: a mesoscale parameterization of organized convection and a two-layer model of large-scale equatorial dynamics. The lower-layer dynamics is Rossby gyreâ€“like, whereas outflow from organized convection maintains the upper-layer circulation. The transports of zonal momentum in the vertical and meridional directions are key processes.

An archetype of the general model, in spite of being brutally simplified, represents the convective organization, momentum transport, and equatorial superrotation realized by the cloud-resolving convection parameterization or superparameterization explicit approach developed by Grabowski. The mesoscale parameterization is an analytic equivalent of the cloud-system-resolving models used in this computational approach. Finally, issues in parameterizing convective organization are discussed.

## Abstract

The pivotal role of mesoscale organization on the large-scale coherence of tropical convection is represented by a nonlinear dynamical model. The general model consists of two interlocked systems: a mesoscale parameterization of organized convection and a two-layer model of large-scale equatorial dynamics. The lower-layer dynamics is Rossby gyreâ€“like, whereas outflow from organized convection maintains the upper-layer circulation. The transports of zonal momentum in the vertical and meridional directions are key processes.

An archetype of the general model, in spite of being brutally simplified, represents the convective organization, momentum transport, and equatorial superrotation realized by the cloud-resolving convection parameterization or superparameterization explicit approach developed by Grabowski. The mesoscale parameterization is an analytic equivalent of the cloud-system-resolving models used in this computational approach. Finally, issues in parameterizing convective organization are discussed.

## Abstract

This paper investigates the effects of cloud microphysics parameterizations on simulations of warm-season precipitation at convection-permitting grid spacing. The objective is to assess the sensitivity of summertime convection predictions to the bulk microphysics parameterizations (BMPs) at fine-grid spacings applicable to the next generation of operational numerical weather prediction models. Four microphysical parameterization schemes are compared: simple ice (Dudhia), four-class mixed phase (Reisner et al.), Goddard five-class mixed phase (Tao and Simpson), and five-class mixed phase with graupel (Reisner et al.). The experimentation involves a 7-day episode (3â€“9 July 2003) of U.S. midsummer convection under moderate large-scale forcing. Overall, the precipitation coherency manifested as eastward-moving organized convection in the lee of the Rockies is insensitive to the choice of the microphysics schemes, and the latent heating profiles are also largely comparable among the BMPs. The upper-level condensate and cloudiness, upper-level radiative cooling/heating, and rainfall spectrum are the most sensitive, whereas the domain-mean rainfall rate and areal coverage display moderate sensitivity. Overall, the three mixed-phase schemes outperform the simple ice scheme, but a general conclusion about the degree of sophistication in the microphysics treatment and the performance is not achievable.

## Abstract

This paper investigates the effects of cloud microphysics parameterizations on simulations of warm-season precipitation at convection-permitting grid spacing. The objective is to assess the sensitivity of summertime convection predictions to the bulk microphysics parameterizations (BMPs) at fine-grid spacings applicable to the next generation of operational numerical weather prediction models. Four microphysical parameterization schemes are compared: simple ice (Dudhia), four-class mixed phase (Reisner et al.), Goddard five-class mixed phase (Tao and Simpson), and five-class mixed phase with graupel (Reisner et al.). The experimentation involves a 7-day episode (3â€“9 July 2003) of U.S. midsummer convection under moderate large-scale forcing. Overall, the precipitation coherency manifested as eastward-moving organized convection in the lee of the Rockies is insensitive to the choice of the microphysics schemes, and the latent heating profiles are also largely comparable among the BMPs. The upper-level condensate and cloudiness, upper-level radiative cooling/heating, and rainfall spectrum are the most sensitive, whereas the domain-mean rainfall rate and areal coverage display moderate sensitivity. Overall, the three mixed-phase schemes outperform the simple ice scheme, but a general conclusion about the degree of sophistication in the microphysics treatment and the performance is not achievable.

## Abstract

Steady-state analytic models establish two key points concerning the impact of vertical shear on density currents and the implication for convection initiation. First, shear decreases the horizontal convergence, and therefore the mean ascent, associated with downshear propagating currents. Second, shear has a basic effect on the dynamical organization. If the downshear current travels at the speed of the ambient flow at a critical (steering) level, an overturning circulation provides deep lifting. Although mean ascent is increased by shear in the case of upshear propagating currents, the lifting is comparatively shallow because jumplike ascent occurs rather than deep overturning. The convection initiation mechanism involving the downshear current is therefore very different from the upshear case.

These basic principles are borne out in two-dimensional numerical simulations. Density currents generated by a stationary cold source imposed on an initially horizontally homogeneous, sheared, and neutrally stratified ambient flow are explored. Results show that (i) if the surface flow and low-level shear vectors are in the same direction, as in a low-level jet, the effects of shear and surface flow on the density current head height counteract one another; and (ii) if they oppose one another, as in a surface jet, both conspire to lower the density current head on the downwind side but raise it on the upwind side.

As regards convection initiation by sea breezes, point (i) above shows an approximately equal but weak preference for convection exists on the leeward and windward coasts. Point (ii) shows that initiation is strongly suppressed on the windward coast, but strongly enhanced on the leeward one. The hypothesis that sea breezes are more intense in offshore flow therefore holds only if shear and surface flow have opposite sign or if the flow is unsheared.

Concerning convection initiation by thunderstorm outflows, downshear propagating outflows provide the deepest lifting if they move at the speed of the ambient flow at a critical level, despite the fact that low-level convergence is decreased by shear. While shear strengthens the mean ascent in upshear propagating outflows there is no steering level to anchor the incipient convection to the organized ascent.

## Abstract

Steady-state analytic models establish two key points concerning the impact of vertical shear on density currents and the implication for convection initiation. First, shear decreases the horizontal convergence, and therefore the mean ascent, associated with downshear propagating currents. Second, shear has a basic effect on the dynamical organization. If the downshear current travels at the speed of the ambient flow at a critical (steering) level, an overturning circulation provides deep lifting. Although mean ascent is increased by shear in the case of upshear propagating currents, the lifting is comparatively shallow because jumplike ascent occurs rather than deep overturning. The convection initiation mechanism involving the downshear current is therefore very different from the upshear case.

These basic principles are borne out in two-dimensional numerical simulations. Density currents generated by a stationary cold source imposed on an initially horizontally homogeneous, sheared, and neutrally stratified ambient flow are explored. Results show that (i) if the surface flow and low-level shear vectors are in the same direction, as in a low-level jet, the effects of shear and surface flow on the density current head height counteract one another; and (ii) if they oppose one another, as in a surface jet, both conspire to lower the density current head on the downwind side but raise it on the upwind side.

As regards convection initiation by sea breezes, point (i) above shows an approximately equal but weak preference for convection exists on the leeward and windward coasts. Point (ii) shows that initiation is strongly suppressed on the windward coast, but strongly enhanced on the leeward one. The hypothesis that sea breezes are more intense in offshore flow therefore holds only if shear and surface flow have opposite sign or if the flow is unsheared.

Concerning convection initiation by thunderstorm outflows, downshear propagating outflows provide the deepest lifting if they move at the speed of the ambient flow at a critical level, despite the fact that low-level convergence is decreased by shear. While shear strengthens the mean ascent in upshear propagating outflows there is no steering level to anchor the incipient convection to the organized ascent.

## Abstract

The effects of three distinct stratifications on density current dynamics are investigated using a nonhydrostatic numerical model: (i) a stably stratified layer underneath a deep neutrally stratified flow, representing a nocturnal boundary layer over land; (ii) a neutrally stratified layer underlying a deep stably stratified flow, representing a daytime boundary layer; and (iii) a continuously stratified atmosphere.

In the first case, a weak or intermediate stratification decreases the height of density currents and increases the propagation speed. The same result holds in strongly stratified situations as long as the generated disturbances in the neighborhood of the head do not propagate away. Classical density currents occur in weak stratification, multiheaded density currents in intermediate stratification, and multiheaded density currents with solitary waveâ€“like or borelike disturbances propagating ahead of the current in strong stratification.

In the second case, the upper-layer stratification consistently reduces the density-current height and its propagation speed. The simulated system resembles laboratory density currents and is not much affected by the overlying stratification.

Finally, in continuously stratified flow, the effect of stratification is similar to the second case. The density current becomes shallower and moves more slowly as the stratification is increased. The modeled system has the basic features of density currents if the stratification is weak or moderate, but it becomes progressively less elevated as stratification increases. In strong stratification the density current assumes a wedgelike structure.

The simulation results are compared with the authorsâ€™ previously obtained analytical results, and the physical mechanisms for the effect of stratification are discussed.

## Abstract

The effects of three distinct stratifications on density current dynamics are investigated using a nonhydrostatic numerical model: (i) a stably stratified layer underneath a deep neutrally stratified flow, representing a nocturnal boundary layer over land; (ii) a neutrally stratified layer underlying a deep stably stratified flow, representing a daytime boundary layer; and (iii) a continuously stratified atmosphere.

In the first case, a weak or intermediate stratification decreases the height of density currents and increases the propagation speed. The same result holds in strongly stratified situations as long as the generated disturbances in the neighborhood of the head do not propagate away. Classical density currents occur in weak stratification, multiheaded density currents in intermediate stratification, and multiheaded density currents with solitary waveâ€“like or borelike disturbances propagating ahead of the current in strong stratification.

In the second case, the upper-layer stratification consistently reduces the density-current height and its propagation speed. The simulated system resembles laboratory density currents and is not much affected by the overlying stratification.

Finally, in continuously stratified flow, the effect of stratification is similar to the second case. The density current becomes shallower and moves more slowly as the stratification is increased. The modeled system has the basic features of density currents if the stratification is weak or moderate, but it becomes progressively less elevated as stratification increases. In strong stratification the density current assumes a wedgelike structure.

The simulation results are compared with the authorsâ€™ previously obtained analytical results, and the physical mechanisms for the effect of stratification are discussed.

## Abstract

A numerical model investigation is conducted of the effects of ambient flow and shear upon the propagation and morphology of density currents. The model is initialized with a horizontally homogeneous wind profile superimposed on a cold-air source that initiates and maintains the density currents. The base state is neutrally stratified and free-slip lower and upper boundary conditions are used.

A headwind (i.e., relative flow in the direction opposing the system movement) raises the density current head compared to calm surroundings, while a tailwind has the opposite effect. A weak or moderate shear elevates the head for the downshear-traveling system and a shallow multihead structure appears in strong shear. In contrast, the upshear-moving system is largely insensitive to the shear. In uniform flow, the propagation speed is linearly proportional to the ambient wind speed, reduced or enhanced by about three-quarters depending on the airflow direction. In uniform shear, a linear relationship approximates the relationship between the advance rate of density current and the value of the shear, particularly for the upshear-moving system.

An idealized dynamical model is developed for the moderate shear case in terms of a Froude number â„±. The model has three branches, namely, a borelike region, an overturning updraft, and a stagnant region that moves bodily with the system. The Froude number calculated from the numerical model data is â„± â‰ˆ 0.7, which lies within die range of analytic solutions obtained.

With regard to the initiation of convection over an island or peninsula in an unsheared or weakly sheared ambient flow, a sea-breeze circulation will preferentially cause convection on the leeward side and a land breeze on the windward side. The opposite occurs when the ambient flow has moderate to strong low-level shearâ€”that is, the sea breeze will cause convection on the windward side and a land breeze on the leeward side. The mean-flow momentum and mean-flow shear thus affect convection initiation in opposing ways. There is a dearth of observational data on density currents in shear flow with which to evaluate our dynamical modelâ€”in particular, the role of the overturning updraft, which is a new concept as regards density current dynamics.

## Abstract

A numerical model investigation is conducted of the effects of ambient flow and shear upon the propagation and morphology of density currents. The model is initialized with a horizontally homogeneous wind profile superimposed on a cold-air source that initiates and maintains the density currents. The base state is neutrally stratified and free-slip lower and upper boundary conditions are used.

A headwind (i.e., relative flow in the direction opposing the system movement) raises the density current head compared to calm surroundings, while a tailwind has the opposite effect. A weak or moderate shear elevates the head for the downshear-traveling system and a shallow multihead structure appears in strong shear. In contrast, the upshear-moving system is largely insensitive to the shear. In uniform flow, the propagation speed is linearly proportional to the ambient wind speed, reduced or enhanced by about three-quarters depending on the airflow direction. In uniform shear, a linear relationship approximates the relationship between the advance rate of density current and the value of the shear, particularly for the upshear-moving system.

An idealized dynamical model is developed for the moderate shear case in terms of a Froude number â„±. The model has three branches, namely, a borelike region, an overturning updraft, and a stagnant region that moves bodily with the system. The Froude number calculated from the numerical model data is â„± â‰ˆ 0.7, which lies within die range of analytic solutions obtained.

With regard to the initiation of convection over an island or peninsula in an unsheared or weakly sheared ambient flow, a sea-breeze circulation will preferentially cause convection on the leeward side and a land breeze on the windward side. The opposite occurs when the ambient flow has moderate to strong low-level shearâ€”that is, the sea breeze will cause convection on the windward side and a land breeze on the leeward side. The mean-flow momentum and mean-flow shear thus affect convection initiation in opposing ways. There is a dearth of observational data on density currents in shear flow with which to evaluate our dynamical modelâ€”in particular, the role of the overturning updraft, which is a new concept as regards density current dynamics.

## Abstract

The dynamical theory of mass and momentum transport by organized convection, produced by Moncrieff, is extended using a hydrodynamical model, a two-dimensional buoyant model, and a quasi-three-dimensional buoyant model. Each is characterized by three relative flow branches that idealize the structure of squall-line cloud systems.

Despite the physical and structural diversity, a clear similarity in mass and momentum transports holds for the entire hierarchy, such as the negative-dominant momentum flux by systems propagating in the positive x-direction. Shear and buoyancy are shown to alter the details but not the overall nature of the dynamical transports. In particular. both mass and momentum fluxes are insensitive to the Froude numbers in the hydrodynamical model. The two-dimensional buoyant model enhances the momentum flux amplitude but has a much less noticeable impact on mass fluxes. In contrast, the three-dimensional buoyant model has a larger mass flux and raises the heights of the mass and momentum flux extrema. The low-level inflow shear has a similar effect in these models by increasing both mass and momentum fluxes. Buoyancy affects transports largely through modifying the flow field while the inflow shear influences transports by strengthening the low-level convergence.

## Abstract

The dynamical theory of mass and momentum transport by organized convection, produced by Moncrieff, is extended using a hydrodynamical model, a two-dimensional buoyant model, and a quasi-three-dimensional buoyant model. Each is characterized by three relative flow branches that idealize the structure of squall-line cloud systems.

Despite the physical and structural diversity, a clear similarity in mass and momentum transports holds for the entire hierarchy, such as the negative-dominant momentum flux by systems propagating in the positive x-direction. Shear and buoyancy are shown to alter the details but not the overall nature of the dynamical transports. In particular. both mass and momentum fluxes are insensitive to the Froude numbers in the hydrodynamical model. The two-dimensional buoyant model enhances the momentum flux amplitude but has a much less noticeable impact on mass fluxes. In contrast, the three-dimensional buoyant model has a larger mass flux and raises the heights of the mass and momentum flux extrema. The low-level inflow shear has a similar effect in these models by increasing both mass and momentum fluxes. Buoyancy affects transports largely through modifying the flow field while the inflow shear influences transports by strengthening the low-level convergence.

## Abstract

The effects of quasi-two-dimensional convective bands on the environmental flow are investigated by comparing the observed mass and momentum fluxes and horizontal pressure changes to those predicted by the Moncrieff archetypal model (M92). The model idealizes the organized convection as two-dimensional and steady state, with three flow branchesâ€”a front-to-rear jump updraft, a front overturning updraft, and a rear overturning current, which can be an updraft or a downdraft. Flow through the branches satisfies mass continuity and Bernoulli's equation. The vertical divergence of line-normal momentum flux averaged over the volume is constrained to be zero. Coriolis and buoyancy effects are neglected. The model predicts the vertical mass flux, the vertical divergence of the vertical flux of line-normal momentum, and the pressure change across the line (independent of height). A simple equation for the vertical transport of line-parallel momentum follows from the model assumptions.

Case studies show a systematic linkage of fluxes and structure and a relationship of some of these changes to differences in the environmental sounding. The M92 successfully replicates the general shapes of the vertical mass flux and line-normal momentum flux profiles, and to some degree how they change with environment. The M92 correctly predicts both the magnitude and shape of the curves in cases occurring in near-neutral environments (low buoyancy or high shear) and with system width-to-depth ratios close to the dynamically based value of 4:1. The model is less successful for systems in more unstable environments or those with large horizontal extent, probably due to the neglect of the generation of horizontal momentum by the buoyancy distribution. The observed sign of the average pressure changes across the line is consistent with that predicted by the model in the upper half of the system, where some case studies suggest that buoyancy effects should be minimized. Letting the model (4:1 aspect ratio) represent the dynamically active part of a mesoscale system, the rearward advective broadening of the inert anvil region is simply related to the (rearward) outflow speed of the jump updraft, *U*
_{1}. Since *U*
_{1} increases as tropospheric shear decreases, the model correctly associates broad mesoscale systems with small tropospheric shear. Success in predicting the vertical flux of line-parallel momentum was fair.

## Abstract

The effects of quasi-two-dimensional convective bands on the environmental flow are investigated by comparing the observed mass and momentum fluxes and horizontal pressure changes to those predicted by the Moncrieff archetypal model (M92). The model idealizes the organized convection as two-dimensional and steady state, with three flow branchesâ€”a front-to-rear jump updraft, a front overturning updraft, and a rear overturning current, which can be an updraft or a downdraft. Flow through the branches satisfies mass continuity and Bernoulli's equation. The vertical divergence of line-normal momentum flux averaged over the volume is constrained to be zero. Coriolis and buoyancy effects are neglected. The model predicts the vertical mass flux, the vertical divergence of the vertical flux of line-normal momentum, and the pressure change across the line (independent of height). A simple equation for the vertical transport of line-parallel momentum follows from the model assumptions.

Case studies show a systematic linkage of fluxes and structure and a relationship of some of these changes to differences in the environmental sounding. The M92 successfully replicates the general shapes of the vertical mass flux and line-normal momentum flux profiles, and to some degree how they change with environment. The M92 correctly predicts both the magnitude and shape of the curves in cases occurring in near-neutral environments (low buoyancy or high shear) and with system width-to-depth ratios close to the dynamically based value of 4:1. The model is less successful for systems in more unstable environments or those with large horizontal extent, probably due to the neglect of the generation of horizontal momentum by the buoyancy distribution. The observed sign of the average pressure changes across the line is consistent with that predicted by the model in the upper half of the system, where some case studies suggest that buoyancy effects should be minimized. Letting the model (4:1 aspect ratio) represent the dynamically active part of a mesoscale system, the rearward advective broadening of the inert anvil region is simply related to the (rearward) outflow speed of the jump updraft, *U*
_{1}. Since *U*
_{1} increases as tropospheric shear decreases, the model correctly associates broad mesoscale systems with small tropospheric shear. Success in predicting the vertical flux of line-parallel momentum was fair.

## Abstract

The collective effects of organized convection the environment were estimated using a two-dimensional, two-way nested cloud-resolving numerical model with a large outer domain (4500 km). As initial conditions, the authors used an idealized environment of the onset stage of the December 1992 westerly wind burst that occurred during the Tropical Oceans Global Atmosphere Coupled Ocean-Atmosphere Response Experiment.

Two key aspects relating to convective parameterization were examined. First, the transports, sources, and sinks of heat, moisture, and momentum were derived using the model-produced dataset. In particular, the total momentum flux compares well with Moncrieff's dynamical theory. Second, the bulk energetics of the cloud system were examined using the model-produced dataset. The authors found that the shear generation of kinetic energy is comparable to the buoyancy generation and dominates the sum of the buoyancy and water-loading generation. This means that, in addition to the thermodynamic generation of kinetic energy, shear generation should be included in the closure condition for the parameterization of organized convection in large-scale models.

A simple mass-flux-based parameterization scheme is outlined for organized convection that consistently treats dynamical and thermodynamical fluxes.

## Abstract

The collective effects of organized convection the environment were estimated using a two-dimensional, two-way nested cloud-resolving numerical model with a large outer domain (4500 km). As initial conditions, the authors used an idealized environment of the onset stage of the December 1992 westerly wind burst that occurred during the Tropical Oceans Global Atmosphere Coupled Ocean-Atmosphere Response Experiment.

Two key aspects relating to convective parameterization were examined. First, the transports, sources, and sinks of heat, moisture, and momentum were derived using the model-produced dataset. In particular, the total momentum flux compares well with Moncrieff's dynamical theory. Second, the bulk energetics of the cloud system were examined using the model-produced dataset. The authors found that the shear generation of kinetic energy is comparable to the buoyancy generation and dominates the sum of the buoyancy and water-loading generation. This means that, in addition to the thermodynamic generation of kinetic energy, shear generation should be included in the closure condition for the parameterization of organized convection in large-scale models.

A simple mass-flux-based parameterization scheme is outlined for organized convection that consistently treats dynamical and thermodynamical fluxes.

## Abstract

A nonlinear analytic model is used to study the bulk characteristics of energy conserving density currents in stratified and sheared environments. The idealized representation of latent heating in a stratified flow is a unique feature that interactively couples the dynamic and thermodynamic fields.

A stable stratification decreases the height of density currents but increases the corresponding propagation speed. In contrast, the density current is deeper and moves more slowly once latent heating is included. As for the effect of shear, the depth and the translation speed of density currents increase as the ambient shear varies from negative to positive (in the direction of propagation), with the exception of a strongly stable environment. A key addition to density current dynamics is the upper-level overturning circulation ahead of the system. This feature is very different from the blocked or choked upper-level structure found in the companion paper of Liu and Moncrieff. The distinction is attributed to the effect of different shear profiles on density current dynamics.

These analytic results quantifying the role of shear and latent heating in density-current-like phenomena in the atmosphere should now be evaluated against high-resolution numerical simulations and observations.

## Abstract

A nonlinear analytic model is used to study the bulk characteristics of energy conserving density currents in stratified and sheared environments. The idealized representation of latent heating in a stratified flow is a unique feature that interactively couples the dynamic and thermodynamic fields.

A stable stratification decreases the height of density currents but increases the corresponding propagation speed. In contrast, the density current is deeper and moves more slowly once latent heating is included. As for the effect of shear, the depth and the translation speed of density currents increase as the ambient shear varies from negative to positive (in the direction of propagation), with the exception of a strongly stable environment. A key addition to density current dynamics is the upper-level overturning circulation ahead of the system. This feature is very different from the blocked or choked upper-level structure found in the companion paper of Liu and Moncrieff. The distinction is attributed to the effect of different shear profiles on density current dynamics.

These analytic results quantifying the role of shear and latent heating in density-current-like phenomena in the atmosphere should now be evaluated against high-resolution numerical simulations and observations.