Large-scale Velocity Research Articles

Dynamics of large-scale quantities in Rayleigh-Bénard convection.

In this paper we estimate the relative strengths of various terms of the Rayleigh-Bénard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity U or the Péclet number that is applicable for arbitrary Rayleigh number Ra and Prandtl number Pr. Our formula fits reasonably well with the earlier simulation and experimental results. Our analysis also shows that the wall-bounded convection has enhanced viscous force compared to free turbulence. We also demonstrate how correlations deviate the Nusselt number scaling from the theoretical prediction of Ra^{1/2} to the experimentally observed scaling of nearly Ra^{0.3}.

UGC 3672: an unusual merging triplet of gas-rich galaxies in the Lynx–Cancer void

We present HI 21cm and optical observations of UGC 3672 which is located near the centre of the nearby Lynx-Cancer void. We find that UGC 3672 consists of an approximately linearly aligned triplet of gas rich dwarfs with large scale velocity continuity along the triplet axis. The faintest component of the triplet is extremely gas-rich (MHI/LB ~ 17) and also extremely metal deficient (12+log(O/H) ~ 7.0). The metallicity of this dwarf is close to the 'floor' observed in star forming galaxies. Low resolution HI images show that the galaxy triplet is located inside a common HI envelope, with fairly regular, disk like kinematics. At high angular resolution however, the gas is found to be confined to several filamentary tidal tails and bridges. The linear alignment of the galaxies, along with the velocity continuity that we observe, is consistent with the galaxies lying along a filament. We argue that the location of this highly unusual system in an extremely low density environment is not a coincidence, but is a consequence of structure formation proceeding more slowly and also probing smaller scales than in regions with average density. Our observations also indicate that wet mergers of galaxies flowing along filaments is a possible pathway for the formation of gas rich disks. The UGC 3672 system provides an interesting opportunity to study the kind of interactions typical between high redshift extremely gas rich unevolved small systems that lie at base of the hierarchical galaxy formation model.

Earth evolution and dynamics—a tribute to Kevin Burke

Kevin Burke’s original and thought-provoking contributions have been published steadily for the past 60 years, and more than a decade ago he set out to resolve how plate tectonics and mantle plumes interact by proposing a simple conceptual model, which we will refer to as the Burkian Earth. On the Burkian Earth, mantle plumes take us from the deepest mantle to sub-lithospheric depths, where partial melting occurs, and to the surface, where hotspot lavas erupt today, and where large igneous provinces and kimberlites have erupted episodically in the past. The arrival of a plume head contributes to continental break-up and punctuates plate tectonics by creating and modifying plate boundaries. Conversely, plate tectonics makes an essential contribution to the mantle through subduction. Slabs restore mass to the lowermost mantle and are the triggering mechanism for plumes that rise from the margins of the two large-scale low shear-wave velocity structures in the lowermost mantle, which Burke christened TUZO and JASON. Situated just above the core–mantle boundary, beneath Africa and the Pacific, these are stable and antipodal thermochemical piles, which Burke reasons represent the immediate after-effect of the moon-forming event and the final magma ocean crystallization.

What controls the low ice number concentration in the upper troposphere?

Abstract. Cirrus clouds in the tropical tropopause play a key role in regulating the moisture entering the stratosphere through their dehydrating effect. Low ice number concentrations ( < 200 L−1) and high supersaturations (150–160 %) have been observed in these clouds. Different mechanisms have been proposed to explain these low ice number concentrations, including the inhibition of homogeneous freezing by the deposition of water vapour onto pre-existing ice crystals, heterogeneous ice formation on glassy organic aerosol ice nuclei (IN), and limiting the formation of ice number from high-frequency gravity waves. In this study, we examined the effect from three different representations of updraft velocities, the effect from pre-existing ice crystals, the effect from different water vapour deposition coefficients (α = 0.1 or 1), and the effect of 0.1 % of the total secondary organic aerosol (SOA) particles acting as IN. Model-simulated ice crystal numbers are compared against an aircraft observational dataset.Including the effect from water vapour deposition on pre-existing ice particles can effectively reduce simulated in-cloud ice number concentrations for all model setups. A larger water vapour deposition coefficient (α = 1) can also efficiently reduce ice number concentrations at temperatures below 205 K, but less so at higher temperatures. SOA acting as IN is most effective at reducing ice number concentrations when the effective updraft velocities are moderate ( ∼ 0.05–0.2 m s−1). However, the effects of including SOA as IN and using (α = 1) are diminished when the effect from pre-existing ice is included.When a grid-resolved large-scale updraft velocity ( < 0.1 m s−1) is used, the ice nucleation parameterization with homogeneous freezing only or with both homogeneous freezing and heterogeneous nucleation is able to generate low ice number concentrations in good agreement with observations for temperatures below 205 K as long as the pre-existing ice effect is included. For the moderate updraft velocity ( ∼ 0.05–0.2 m s−1), simulated ice number concentrations in good agreement with observations at temperatures below 205 K can be achieved if effects from pre-existing ice, a larger water vapour deposition coefficient (α = 1), and SOA IN are all included. Using the sub-grid-scale turbulent kinetic energy (TKE)-based updraft velocity ( ∼ 0–2 m s−1) always overestimates the ice number concentrations at temperatures below 205 K but compares well with observations at temperatures above 205 K when the pre-existing ice effect is included.

Inner–outer interactions in rough-wall turbulence

ABSTRACTHere we revisit the inner–outer interaction model (IOIM) of Marusic et al. (Science, vol. 329, 2010, pp. 193–196) that enables the prediction of statistics of the fluctuating streamwise velocity in the inner region of wall-bounded turbulent flows from a large-scale velocity signature measured in the outer region of the flow. The model is characterised by two empirically observed inner–outer interactions: superposition of energy from outer region large-scale motions; and amplitude modulation by these large-scale motions of a small-scale ‘universal’ signal (u*), which in smooth-wall flows is Reynolds number invariant. In the present study, the inner–outer interactions in rough-wall turbulent boundary layers are examined within the framework of the IOIM. Simultaneous two-point hot-wire anemometry measurements enable quantification, via the model parameters, of the strengths of superposition and amplitude modulation effects in a rough-wall flow, and these are compared to a smooth-wall flow. It is shown that the present rough-wall significantly reduces the effects of superposition, while increasing the amplitude modulation effect. The former is true even in flows that exhibit outer region similarity. Using the model parameters obtained from the two-point measurements, predictions of inner region streamwise velocity statistics and spectra are compared to measurements over a range of friction and roughness Reynolds numbers. These results indicate that the u* signal does depend on roughness Reynolds number (k+s), but is robust to changes in friction Reynolds number (δ+). Additionally, the superposition strength is shown to be relatively independent of both roughness and friction Reynolds number. The implications of the present results on the suitability of the IOIM as a predictive tool in rough-wall turbulence are discussed.

Dynamos at extreme magnetic Prandtl numbers: insights from shell models

ABSTRACTWe present a magnetohydrodynamic (MHD) shell model suitable for computation of various energy fluxes of MHD turbulence for very small and very large magnetic Prandtl numbers Pm; such computations are inaccessible to direct numerical simulations. For small Pm, we observe that both kinetic and magnetic energy spectra scale as k−5/3 in the inertial range, but the dissipative magnetic energy scales as k−11/3exp (− k/kη). Here the kinetic energy at large length scale feeds the large-scale magnetic field that cascades to small-scale magnetic field, which gets dissipated by Joule heating. The large-Pm dynamo has a similar behaviour except that the dissipative kinetic energy scales as k−13/3. For this case, the large-scale velocity field transfers energy to the large-scale magnetic field, which gets transferred to small-scale velocity and magnetic fields; the energy of the small-scale magnetic field also gets transferred to the small-scale velocity field, and the energy thus accumulated is dissipated by the viscous force.

Extended self-similarity in moment-generating-functions in wall-bounded turbulence at high Reynolds number

In wall-bounded turbulence, the moment generating functions (MGFs) of the streamwise velocity fluctuations $\left<\exp(qu_z^+)\right>$ develop power-law scaling as a function of the wall normal distance $z/\delta$. Here $u$ is the streamwise velocity fluctuation, $+$ indicates normalization in wall units (averaged friction velocity), $z$ is the distance from the wall, $q$ is an independent variable and $\delta$ is the boundary layer thickness. Previous work has shown that this power-law scaling exists in the log-region {\small $3Re_\tau^{0.5}\lesssim z^+$, $z\lesssim 0.15\delta$}, where $Re_\tau$ is the friction velocity-based Reynolds numbers. Here we present empirical evidence that this self-similar scaling can be extended, including bulk and viscosity-affected regions $30<z^+$, $z<\delta$, provided the data are interpreted with the Extended-Self-Similarity (ESS), i.e. self-scaling of the MGFs as a function of one reference value, $q_o$. ESS also improves the scaling properties, leading to more precise measurements of the scaling exponents. The analysis is based on hot-wire measurements from boundary layers at $Re_\tau$ ranging from $2700$ to $13000$ from the Melbourne High-Reynolds-Number-Turbulent-Boundary-Layer-Wind-Tunnel. Furthermore, we investigate the scalings of the filtered, large-scale velocity fluctuations $u^L_z$ and of the remaining small-scale component, $u^S_z=u_z-u^L_z$. The scaling of $u^L_z$ falls within the conventionally defined log region and depends on a scale that is proportional to {\small $l^+\sim Re_\tau^{1/2}$}; the scaling of $u^{S}_z$ extends over a much wider range from $z^+\approx 30$ to $z\approx 0.5\delta$. Last, we present a theoretical construction of two multiplicative processes for $u^L_z$ and $u^S_z$ that reproduce the empirical findings concerning the scalings properties as functions of $z^+$ and in the ESS sense.

Vorticity and mixing in Rayleigh–Taylor Boussinesq turbulence

The Rayleigh–Taylor instability induced turbulence is studied under the Boussinesq approximation focusing on vorticity and mixing. A direct numerical simulation has been carried out with an auto-adaptive multidomain Chebyshev–Fourier–Fourier numerical method. The spatial resolution is increased up to$(24\times 40)\times 940^{2}=848\,M$collocation points. The Taylor Reynolds number is$\mathit{Re}_{\unicode[STIX]{x1D706}_{zz}}\approx 142$and a short inertial range is observed. The nonlinear growth rate of the turbulent mixing layer is found to be close to$\unicode[STIX]{x1D6FC}_{b}=0.021$. Our conclusions may be summarized as follows.(i) The simulation data are in agreement with the scalings for the pressure ($k^{-7/3}$) and the vertical mass flux ($k^{-7/3}$).(ii) Mean quantities have a self-similar behaviour, but some inhomogeneity is still present. For higher-order quantities the self-similar regime is not fully achieved.(iii) In the self-similar regime, the mean dissipation rate and the enstrophy behave as$\langle \overline{\unicode[STIX]{x1D700}}\rangle \propto t$and$\langle \overline{\unicode[STIX]{x1D714}_{i}\,\unicode[STIX]{x1D714}_{i}}^{1/2}\rangle \propto t^{1/2}$, respectively.(iv) The large-scale velocity fluctuation probability density function (PDF) is Gaussian, while vorticity and dissipation PDFs show large departures from Gaussianity.(v) The pressure PDF exhibits strong departures from Gaussianity and is skewed. This is related to vortex coherent structures.(vi) The intermediate scales of the mixing are isotropic, while small scales remain anisotropic. This leaves open the possibility of a small-scale buoyancy. Velocity intermediate scales are also isotropic, while small scales remain anisotropic. Mixing and dynamics are therefore consistent.(vii) Properties and behaviours of vorticity and enstrophy are detailed. In particular, equations for these quantities are written down under the Boussinesq approximation.(viii) The concentration PDF is quasi-Gaussian. The vertical concentration gradient is both non-Gaussian and strongly skewed.

The tau of galaxy clusters

The recent emergence of detections of the kinetic Sunyeav-Zel'dovich (kSZ) effect through cross-correlation techniques is encouraging for the prospects of future cosmic microwave background (CMB) experiments. Extracting information on the large-scale velocity fields and constraining cosmological parameters from such kSZ measurements requires an understanding of the optical depth to CMB photons through halos. Using cosmological hydrodynamic simulations we find that there exists a low-scatter relation between the optical depth and thermal Sunyeav-Zel'dovich (tSZ) signal of halos within a physical aperture. We propose that such a relation can be used to break the degeneracy between optical depth and line-of-sight velocity in kSZ measurements. The limiting factors in our proposal are systematic uncertainties associated with the sub-grid physics models in the simulations, which we calculate to be less than 10 percent. We discuss future observational measurements that could potentially be used to mitigate the systematic uncertainties in this scaling relation.

The effects of bar–spiral coupling on stellar kinematics in the Galaxy

We investigate models of the Milky Way disc taking into account simultaneously the bar and a two-armed quasi-static spiral pattern. Away from major resonance overlaps, the mean stellar radial motions in the plane are essentially a linear superposition of the isolated effects of the bar and spirals. Thus, provided the bar is strong enough, even in the presence of spiral arms, these mean radial motions are predominantly affected by the Galactic bar for large scale velocity fluctuations. This is evident when comparing the peculiar line-of-sight velocity power spectrum of our coupled models with bar-only models. However, we show how forthcoming spectroscopic surveys could disentangle bar-only non-axisymmetric models of the Galaxy from models in which spiral arms have a significant amplitude. We also point out that overlaps of low-order resonances are sufficient to enhance stellar churning within the disc, even when the spirals amplitude is kept constant. Nevertheless, for churning to be truly non-local, stronger or (more likely) transient amplitudes would be needed: otherwise the disc is actually mostly unaffected by churning in the present models. Finally, regarding vertical breathing modes, the combined effect of the bar and spirals on vertical motions is a clear non-linear superposition of the isolated effects of both components, significantly superseding the linear superposition of modes produced by each perturber separately, thereby providing an additional effect to consider when analysing the observed breathing mode of the Galactic disc in the extended Solar neighbourhood.

MJO Moisture Budget during DYNAMO in a Cloud-Resolving Model

Abstract Contributions by different physical processes and cloud types to the sum of the large-scale vertical moisture advection and apparent moisture sink observed by the DYNAMO field campaign northern sounding array during the passage of a Madden–Julian oscillation (MJO) event are estimated using a cloud-resolving model. The sum of these two moisture budget terms is referred to as the column-confined moisture tendency MC. Assuming diabatic balance, the contribution of different physical processes and cloud types to the large-scale vertical velocity and MC can be estimated using simulated diabatic tendencies and the domain-averaged static stability and vertical moisture gradient. Low-level moistening preceding MJO passage is captured by MC and dominated by the effects of shallow clouds. Because of the large vertical moisture gradient at this level, condensational heating in these clouds generates ascent and vertical moisture advection overwhelming the removal of water vapor by condensation. Shallow convective eddy transport also contributes to low-level moistening during this period. Eddy transport by congestus and deep convective clouds contributes to subsequent mid- and upper-level moistening, respectively, as well as low-level drying. Because the upper-level vertical moisture gradient is small, ice deposition within stratiform clouds has a net drying effect. The weak eddy transport in stratiform clouds is unable to compensate for this drying. Nonprecipitating clouds mainly modulate MC through their effects on radiation. During the enhanced phase, reduced longwave cooling results in less subsidence and drying; the opposite occurs during the suppressed phase. Large-scale horizontal advection, which is not included in MC, is responsible for much of the drying during the dissipating phase.

Plasma motions and non-thermal line broadening in flaring twisted coronal loops

Observation of coronal EUV spectral lines sensitive to different temperatures offers an opportunity to evaluate the thermal structure and flows in flaring atmospheres. This can be used to estimate the partitioning between the thermal and kinetic energies. Our aim is to model large-scale (50-10000km) velocity distributions in order to interpret non-thermal broadening of different spectral EUV lines. The developed models allow us to understand the origin of the observed spectral line shifts and broadening, and link these features to particular physical effects in flaring atmospheres. We use ideal MHD to derive twisted magnetic fluxtube configurations in a stratified atmosphere. The evolution of these fluxtubes is followed using resistive MHD, with anomalous resistivity depending on the local density and temperature. The model also takes into account the thermal conduction and radiative losses. The model allows us to evaluate average velocities and velocity dispersions, which would be interpreted as `non-thermal' velocities in observations, at different temperatures for different parts of the models. Our models show qualitative and quantitative agreement with observations. The line-of-sight (LOS) velocity dispersions demonstrate substantial correlation with the temperature, increasing from about 20-30 km/s around 1 MK to about 200-400 km/s near 10-20 MK. The average LOS velocities also correlate with velocity dispersions, although they demonstrate a very strong scattering, compared to observations. We also note that near foot-points the velocity dispersions across the magnetic field are systematically lower than those along the field. We conclude, that the correlation between the flow velocities, velocity dispersions and temperatures are likely to indicate that the same heating mechanism is responsible for heating the plasma, its turbulisation and expansion/evaporation.

Explicit expressions for eddy-diffusivity fields and effective large-scale advection in turbulent transport

Large-scale transport is investigated in terms of new explicit expressions for eddy diffusivities and effective advection obtained from asymptotic perturbative methods. The carrier flow is formed by a large-scale component plus a small-scale contribution mimicking a turbulent flow. The scalar dynamics is observed in its pre-asymptotic regimes (i.e. on scales comparable to those of the large-scale velocity). The resulting eddy diffusivity is thus a tensor field which explicitly depends on the large-scale velocity. Small-scale interactions also cause the emergence of an effective large-scale (compressible) advection field which, as a result of the present study however, turns out to be of negligible importance. Two issues are addressed by means of Lagrangian simulations: quantifying the possible deterioration of the eddy-diffusivity/effective advection description by reducing to zero the spectral gap separating the large-scale velocity component from the small-scale component; comparing the accuracy of our closure against other simple, reasonable, options. Answering these questions is important in view of possible applications of our closure to tracer dispersion in environmental flows.

Full waveform inversion with an auxiliary bump functional

Least-squares inversion of seismic arrivals can provide remarkably detailed models of the Earth's subsurface. However, cycle skipping associated with these oscillatory arrivals is the main cause for local minima in the least-squares objective function. Therefore, it is often difficult for descent methods to converge to the solution without an accurate initial large-scale velocity estimate. The low frequencies in the arrivals, needed to update the large-scale components in the velocity model, are usually unreliable or absent. To overcome this difficulty, we propose a multi-objective inversion scheme that uses the conventional least-squares functional along with an auxiliary data-domain objective. As the auxiliary objective effectively replaces the seismic arrivals by bumps, we call it the bump functional. The bump functional minimization can be made far less sensitive to cycle skipping and can deal with multiple arrivals in the data. However, it can only be used as an auxiliary objective since it usually does not provide a unique model after minimization even when the regularized-least-squares functional has a unique global minimum and hence a unique solution. The role of the bump functional during the multi-objective inversion is to guide the optimization towards the global minimum by pulling the trapped solution out of the local minima associated with the least-squares functional whenever necessary. The computational complexity of the bump functional is equivalent to that of the least-squares functional. In this paper, we describe various characteristics of the bump functional using simple and illustrative numerical examples. We also demonstrate the effectiveness of the proposed multi-objective inversion scheme by considering more realistic examples. These include synthetic and field data from a cross-well experiment, surface-seismic synthetic data with reflections and synthetic data with refracted arrivals at long offsets.

Towards physics responsible for large-scale Lyman-α forest bias parameters

Using a series of carefully constructed numerical experiments based on hydrodynamic cosmological SPH simulations, we attempt to build an intuition for the relevant physics behind the large scale density (bδ) and velocity gradient (bη) biases of the Lyman-α forest. Starting with the fluctuating Gunn-Peterson approximation applied to the smoothed total density field in real-space, and progressing through redshift-space with no thermal broadening, redshift-space with thermal broadening and hydrodynamically simulated baryon fields, we investigate how approximations found in the literature fare. We find that Seljak's 2012 analytical formulae for these bias parameters work surprisingly well in the limit of no thermal broadening and linear redshift-space distortions. We also show that his bη formula is exact in the limit of no thermal broadening. Since introduction of thermal broadening significantly affects its value, we speculate that a combination of large-scale measurements of bη and the small scale flux PDF might be a sensitive probe of the thermal state of the IGM. We find that large-scale biases derived from the smoothed total matter field are within 10–20% to those based on hydrodynamical quantities, in line with other measurements in the literature.

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow.

3D-PTV is a quantitative flow measurement technique that aims to track the Lagrangian paths of a set of particles in three dimensions using stereoscopic recording of image sequences. The basic components, features, constraints and optimization tips of a 3D-PTV topology consisting of a high-speed camera with a four-view splitter are described and discussed in this article. The technique is applied to the intermediate flow field (5 <x/d <25) of a circular jet at Re ≈ 7,000. Lagrangian flow features and turbulence quantities in an Eulerian frame are estimated around ten diameters downstream of the jet origin and at various radial distances from the jet core. Lagrangian properties include trajectory, velocity and acceleration of selected particles as well as curvature of the flow path, which are obtained from the Frenet-Serret equation. Estimation of the 3D velocity and turbulence fields around the jet core axis at a cross-plane located at ten diameters downstream of the jet is compared with literature, and the power spectrum of the large-scale streamwise velocity motions is obtained at various radial distances from the jet core.

The Musca cloud: A 6 pc-long velocity-coherent, sonic filament

Filaments play a central role in the molecular clouds' evolution, but their internal dynamical properties remain poorly characterized. To further explore the physical state of these structures, we have investigated the kinematic properties of the Musca cloud. We have sampled the main axis of this filamentary cloud in $^{13}$CO and C$^{18}$O (2--1) lines using APEX observations. The different line profiles in Musca shows that this cloud presents a continuous and quiescent velocity field along its $\sim$6.5 pc of length. With an internal gas kinematics dominated by thermal motions (i.e., $\sigma_{NT}/c_s\lesssim1$) and large-scale velocity gradients, these results reveal Musca as the longest velocity-coherent, sonic-like object identified so far in the ISM. The transonic properties of Musca present a clear departure from the predicted supersonic velocity dispersions expected in the Larson's velocity dispersion-size relationship, and constitute the first observational evidence of a filament fully decoupled from the turbulent regime over multi-parsec scales.

The coupling between inner and outer scales in a zero pressure boundary layer evaluated using a Hölder exponent framework

This work considers the connectivity between large and small scales in boundary-layer turbulence by formalizing the modulation effect of the small scales by the large in terms of the pointwise Hölder condition for the small scales. We re-investigate a previously published dataset from this perspective and are able to characterize the coupling effectively using the (cross-)correlative relations between the large scale velocity and the small scale Hölder exponents. The nature of this coupling varies as a function of dimensionless distance from the wall based on inner-scaling, , as well as on the boundary-layer height, δ. In terms of the fundamental change in the sign of the coupling between large and small scales, the critical height appears to be . Below this height, small scale structures are associated with (and occur earlier than) maxima in the large scale velocity. Above this height, while the lag is similar in magnitude, the small scale structures are associated with minima in the large scale velocity. To consider these results further, we introduce a modified quadrant analysis and show that it is the coupling to the large scale low velocity state that is critical for the dynamics.

Scale interactions in a mixing layer – the role of the large-scale gradients

The interaction between the large and the small scales of turbulence is investigated in a mixing layer, at a Reynolds number based on the Taylor microscale ($Re_{{\it\lambda}}$) of $250$, via direct numerical simulations. The analysis is performed in physical space, and the local vorticity root-mean-square (r.m.s.) is taken as a measure of the small-scale activity. It is found that positive large-scale velocity fluctuations correspond to large vorticity r.m.s. on the low-speed side of the mixing layer, whereas, they correspond to low vorticity r.m.s. on the high-speed side. The relationship between large and small scales thus depends on position if the vorticity r.m.s. is correlated with the large-scale velocity fluctuations. On the contrary, the correlation coefficient is nearly constant throughout the mixing layer and close to unity if the vorticity r.m.s. is correlated with the large-scale velocity gradients. Therefore, the small-scale activity appears closely related to large-scale gradients, while the correlation between the small-scale activity and the large-scale velocity fluctuations is shown to reflect a property of the large scales. Furthermore, the vorticity from unfiltered (small scales) and from low pass filtered (large scales) velocity fields tend to be aligned when examined within vortical tubes. These results provide evidence for the so-called ‘scale invariance’ (Meneveau &amp; Katz, Annu. Rev. Fluid Mech., vol. 32, 2000, pp. 1–32), and suggest that some of the large-scale characteristics are not lost at the small scales, at least at the Reynolds number achieved in the present simulation.

Modeling the Interaction between Quasigeostrophic Vertical Motion and Convection in a Single Column

Abstract A single-column modeling approach is proposed to study the interaction between convection and large-scale dynamics using the quasigeostrophic (QG) framework. This approach extends the notion of “parameterization of large-scale dynamics,” previously applied in the tropics via the weak temperature gradient approximation and other comparable methods, to the extratropics, where balanced adiabatic dynamics plays a larger role in inducing large-scale vertical motion. The diabatic heating in an air column is resolved numerically by a single-column model or a cloud-resolving model. The large-scale vertical velocity, which controls vertical advection of temperature and moisture, is computed through the QG omega equation including the dry adiabatic terms and the diabatic heating term. The component due to diabatic heating can be thought of as geostrophic adjustment to that heating and couples the convection to the large-scale vertical motion. The approach is demonstrated using two representations of convection: a single-column model and linear response functions derived by Z. Kuang from a large set of cloud-resolving simulations. The results are qualitatively similar in both cases. The behavior of convection that is strongly coupled to large-scale dynamics is significantly different from that in the uncoupled case. The positive feedback of the diabatic heating on the large-scale vertical motion reduces the stability of the system, extends the decay time scale after initial perturbations, and increases the amplitude of convective responses to transient large-scale perturbations or imposed forcings. The diabatic feedback of convection on vertical motion is strongest for horizontal wavelengths on the order of the Rossby deformation radius.