Vertical Momentum Flux Research Articles

Momentum Transport in Shallow Cumulus Clouds and Its Parameterization by Higher‐Order Closure

AbstractIt is challenging to parameterize subgrid vertical momentum fluxes in marine shallow cumulus layers that contain a jet in the profile of horizontal wind. In a large‐eddy simulation of such a layer, it is found that the momentum flux in the direction of strongest wind magnitude has a three‐layer structure. The lowest layer, from the ocean surface up to the jet maximum, has downgradient momentum flux. The middle layer, from the jet maximum up to an altitude several hundred meters above, has upgradient (i.e., countergradient) momentum flux because of transport of low‐magnitude momentum upward through the jet maximum. In the upper layer, the layer‐average momentum flux is weak. The budget of momentum flux shows that in the middle and upper layers, both the buoyancy production term and turbulent advection (i.e., third‐order flux‐of‐flux) terms are important.To parameterize the profile of momentum flux in a single‐column model, the momentum flux is prognosed in this study. The buoyancy production and flux‐of‐flux terms are parameterized by integrating them over a subgrid probability density function with an assumed normal‐mixture shape. The resulting parameterized fluxes and mean‐wind profiles are demonstrated to be comparable to those produced in large‐eddy simulations, both for two marine shallow cumulus cases with upgradient fluxes and for a continental cumulus case and two stratocumulus cases with downgradient fluxes. In the two marine shallow cumulus cases, the parameterization is able to capture the upgradient momentum flux above the jet maximum and the weak momentum fluxes aloft.

Observations of Near-Surface Vertical Wind Profiles and Vertical Momentum Fluxes from VORTEX-SE 2017: Comparisons to Monin–Obukhov Similarity Theory

AbstractObservations of near-surface vertical wind profiles and vertical momentum fluxes obtained from a Doppler lidar and instrumented towers deployed during VORTEX-SE in the spring of 2017 are analyzed. In particular, departures from the predictions of Monin–Obukhov similarity theory (MOST) are documented on thunderstorm days, both in the warm air masses ahead of storms and within the cool outflow of storms, where MOST assumptions (e.g., horizontal homogeneity and a steady state) are least credible. In these regions, it is found that the nondimensional vertical wind shear near the surface commonly exceeds predictions by MOST. The departures from MOST have implications for the specification of the lower boundary condition in numerical simulations of convective storms. Documenting departures from MOST is a necessary first-step toward improving the lower boundary condition and parameterization of near-surface turbulence (“wall models”) in storm simulations.

Langmuir turbulence and filament frontogenesis in the oceanic surface boundary layer

Submesoscale currents, small-scale turbulence and surface gravity waves co-exist in the upper ocean and interact in complex ways. To expose the couplings, the frontogenetic life cycle of an idealized cold dense submesoscale filament interacting with upper ocean Langmuir turbulence is investigated in large-eddy simulations (LESs) based on the incompressible wave-averaged equations. The simulations utilize large domains and fine meshes with $6.4\times 10^{9}$ grid points. Case studies are made with surface winds or surface cooling with waves oriented in across-filament (perpendicular) or down-filament (parallel) directions relative to the two-dimensional filament axis. The currents $u$, $v$ and $w$ are aligned with the across-filament, down-filament and vertical directions, respectively. Frontogenesis is induced by across-filament Lagrangian secondary circulations in the boundary layer, and it is shown to be strongly impacted by surface waves, in particular the propagation direction relative to the filament axis. In a horizontally heterogeneous boundary layer, surface waves induce both mean and fluctuating Stokes-drift vortex forces that modify a linear, hydrostatic turbulent thermal wind (TTW) approximation for momentum. Down-filament winds and waves are found to be especially impactful, they significantly reduce the peak level of frontogenesis by fragmenting the filament into primary and secondary down-welling sites in a broad frontal zone over a width ${\sim}500~\text{m}$. At peak frontogenesis, opposing down-filament jets $\langle v\rangle$ overlie each other resulting in a vigorous vertical shear layer $\unicode[STIX]{x2202}_{z}\langle v\rangle$ with large vertical momentum flux $\langle v^{\prime }w^{\prime }\rangle$. Filament arrest is induced by a lateral shear instability that generates horizontal momentum flux $\langle u^{\prime }v^{\prime }\rangle$ at low wavenumbers. The turbulent vertical velocity patterns, indicative of coherent Langmuir cells, change markedly across the horizontal domain with both across-filament and down-filament winds under the action of submesoscale currents.

Energy Balance Analysis and Turbulence Profile of a Darrieus-type Vertical Axis Wind Turbine

Vertical axis wind turbines (VAWTs) extract energy through reduction of the kinetic and turbulent kinetic energies, and the vertical momentum flux. Detailed turbulence profiling and energy balance analysis were attempted through direct turbulence quantification using the Eddy Covariance method. A high-frequency sonic anemometer was employed to measure flow and turbulence upwind and downwind of a Darrieus-type VAWT at different positions that cover the entire windswept area. The data was processed and analysed using a custom Matlab script. Energy balance analysis showed that there was a significant drop in kinetic energy before and after the VAWT (72% to 42%) but a small increase in turbulent kinetic energy (28% to 31%). The results also showed that the rotational direction of VAWT contributed to a higher value of longitudinal turbulence at the windward edge of the VAWT. The VAWT affected the flow field upwind by generating reverse flows. The largest vertical momentum flux transfer occurred downwind of the windward side of the VAWT. Spectral analysis shows that the VAWT produced smaller but faster momentum flux vortices due to the rotating rotors in the 1 Hz to 5 Hz range. This data and results have important applications to accurately model complex flows around VAWTs.

Observations of Turbulent Heat and Momentum Fluxes during Wildland Fires in Forested Environments

AbstractTurbulent fluxes of heat and momentum in the vicinity of wildland fires contribute to the redistribution of heat and momentum in the fire environment, which in turn can affect the heating of fuels, fire behavior, and smoke dispersion. As an extension of previous observational studies of turbulence regimes in the vicinity of wildland fires in forested environments, this study examines the effects of spreading surface fires and forest overstory vegetation on turbulent heat and momentum fluxes from near the surface to near the top of the overstory vegetation. Profiles of high-frequency (10 Hz) wind velocity and temperature measurements during two prescribed fire experiments are used to assess the relative contributions of horizontal and vertical turbulent fluxes of heat and momentum to the total heat and momentum flux fields. The frequency-dependent temporal variability of the turbulent heat and momentum fluxes before, during, and after fire-front passage is also examined using cospectral analyses. The study results highlight the effects that surface wildland fires and forest overstory vegetation collectively can have on the temporal and vertical variability of turbulent heat and momentum fluxes in the vicinity of the fires and the substantial departures of heat and momentum cospectra from typical atmospheric surface-layer cospectra that can occur before, during, and after fire-front passage.

A study of the dynamical characteristics of inertia–gravity waves in the Antarctic mesosphere combining the PANSY radar and a non-hydrostatic general circulation model

Abstract. This study aims to examine the dynamical characteristics of gravity waves with relatively low frequency in the Antarctic mesosphere via the first long-term simulation using a high-top high-resolution non-hydrostatic general circulation model (NICAM). Successive runs lasting 7 days are performed using initial conditions from the MERRA reanalysis data with an overlap of 2 days between consecutive runs in the period from April to August in 2016. The data for the analyses were compiled from the last 5 days of each run. The simulated wind fields were closely compared to the MERRA reanalysis data and to the observational data collected by a complete PANSY (Program of the Antarctic Syowa MST/IS radar) radar system installed at Syowa Station (39.6∘ E, 69.0∘ S). It is shown that the NICAM mesospheric wind fields are realistic, even though the amplitudes of the wind disturbances appear to be larger than those from the radar observations. The power spectrum of the meridional wind fluctuations at a height of 70 km has an isolated and broad peak at frequencies slightly lower than the inertial frequency, f, for latitudes from 30 to 75∘ S, while another isolated peak is observed at frequencies of approximately 2π∕8 h at latitudes from 78 to 90∘ S. The spectrum of the vertical fluxes of the zonal momentum also has an isolated peak at frequencies slightly lower than f at latitudes from 30 to 75∘ S at a height of 70 km. It is shown that these isolated peaks are primarily composed of gravity waves with horizontal wavelengths of more than 1000 km. The latitude–height structure of the momentum fluxes indicates that the isolated peaks at frequencies slightly lower than f originate from two branches of gravity wave propagation paths. It is thought that one branch originates from 75∘ S due to topographic gravity waves generated over the Antarctic Peninsula and its coast, while more than 80 % of the other branch originates from 45∘ S and includes contributions by non-orographic gravity waves. The existence of isolated peaks in the high-latitude region in the mesosphere is likely explained by the poleward propagation of quasi-inertia–gravity waves and by the accumulation of wave energies near the inertial frequency at each latitude.

Turbulent Transport in the Gray Zone: A Large Eddy Model Intercomparison Study of the CONSTRAIN Cold Air Outbreak Case

AbstractTo quantify the turbulent transport at gray zone length scales between 1 and 10 km, the Lagrangian evolution of the CONSTRAIN cold air outbreak case was simulated with seven large eddy models. The case is characterized by rather large latent and sensible heat fluxes and a rapid deepening rate of the boundary layer. In some models the entrainment velocity exceeds 4 cm/s. A significant fraction of this growth is attributed to a strong longwave radiative cooling of the inversion layer. The evolution and the timing of the breakup of the stratocumulus cloud deck differ significantly among the models. Sensitivity experiments demonstrate that a decrease in the prescribed cloud droplet number concentration and the inclusion of ice microphysics both act to speed up the thinning of the stratocumulus by enhancing the production of precipitation. In all models the formation of mesoscale fluctuations is clearly evident in the cloud fields and also in the horizontal wind velocity. Resolved vertical fluxes remain important for scales up to 10 km. The simulation results show that the resolved vertical velocity variance gradually diminishes with a coarsening of the horizontal mesh, but the total vertical fluxes of heat, moisture, and momentum are only weakly affected. This is a promising result as it demonstrates the potential use of a mesh size‐dependent turbulent length scale for convective boundary layers at gray zone model resolutions.

INTERACTIONS OF WAVES WITH IDEALIZED HIGH-RELIEF BOTTOM ROUGHNESS

Interactions between waves and high-relief bottom roughness were investigated using Large Eddy Simulations of oscillatory flow over an infinite array of regularly spaced hemispheres. Simulation results were analyzed using a spatially- and phase-averaged momentum balance to provide insight into how flow-topography interactions affect wave-driven oscillating flows. Phase-averaging was applied first, and then spatial averaging was applied over volumes with horizontal length scales greater than the size of a single solid obstacle but fine enough in the vertical direction that the vertical structure of the dynamics was resolved. Spatial averaging of the momentum equation results in terms that represent drag and inertial forces, and a dispersive stress term that represents a vertical momentum flux induced by the spatial heterogeneity of the phase-averaged flow. These new terms require parameterization in coastal ocean wave and circulation models.

Effect of the Granularity of Heterogeneous Forest Cover on the Drag Coefficient

We investigated the effect of the granularity of heterogeneous forest cover on the momentum absorption by conducting a large-eddy simulation of the flow over a surface covered by square-shaped forest/non-forest patches ranging in size from 64 to 512 m. The modification of the drag coefficient by heterogeneity is analyzed using integral identity equations, which decompose the drag coefficient into contributions from the momentum fluxes, pressure, and forest form drag. From a macroscopic viewpoint, the drag coefficient significantly differs in each case, and its tendency is not monotonic with the granularity. The identity equation shows that the effect of the vertical momentum flux becomes persistent on the non-forest area with an increase in patch size, with the spatial development altering the drag contribution, assigning increasing importance to the forest area. The drag coefficient defined from a local viewpoint shows a strong overshoot at the front edge of the forest patch, with a sudden decrease away from the front edge. A distance of almost 10 forest heights is required to arrive at a nearly homogeneous condition. However, spatial development is still obvious in the mean advection and pressure deviation terms with spanwise heterogeneity inducing an overshoot of the drag coefficient by enhancing the secondary flow. As such, the effect of the edge remains in a transitional manner, even if a locally homogeneous region is observed in the downstream and at the centre of patches.

Uncertainties in gravity wave parameters, momentum fluxes, and flux divergences estimated from multi-layer measurements of mesospheric nightglow layers

Measurements of dynamic parameters of atmospheric gravity waves, mainly the vertical wavelength, the momentum flux and the momentum flux divergence, are affected by large uncertainties crudely documented in the scientific literature. By using methods of error analysis, we have quantified these uncertainties for frequently observed temporal and spatial wave scales. The results show uncertainties of ∼10%, ∼35%, and ∼65%, at least, in the vertical wavelength, momentum flux, and flux divergence, respectively. The large uncertainties in the momentum flux and flux divergence are dominated by uncertainties in the Brunt-Väisälä frequency and in spatial separation of the nightglow layers, respectively. The measured uncertainties in fundamental wave parameters such as the wave amplitude, intrinsic period, horizontal wavelength, and wave orientation are ∼10% or less and estimated directly from our nightglow image data set. Other key environmental quantities such as the scale height and the Brunt-Väisälä frequency, frequently considered as constants in gravity wave parameter estimations schemes, are actually quite variable, presenting uncertainties of ∼4% and ∼9%, respectively, according to the several solar activity and seasonal atmosphere scenarios from the NRLMSISE-00 model simulated here.

Sediment Dynamics in Wind Wave‐Dominated Shallow‐Water Environments

AbstractSediment dynamics driven by waves and currents in shallow‐water estuarine environments impacts many physical and biological processes and is important to the estuary‐wide sediment budget. Observational restrictions have limited our ability to understand the physics governing sediment entrainment and mixing in these environments. To this end, we use direct numerical simulation to simulate sediment transport processes in shallow, combined wave‐ and current‐driven flows. Simulations are run with depth‐averaged currents ranging from 0 to 9 cm/s, while wave conditions are held constant with a bottom orbital velocity and period of 10 cm/s and 3 s, respectively. Our results indicated that for wave‐dominated conditions, waves reduce vertical momentum fluxes and the associated bottom drag, thereby accelerating mean currents. Conversely, currents do not significantly affect the wave velocity field. However, they increase the bed shear stress and change the timing and duration of sediment entrainment throughout the wave cycle. Counterintuitively, these effects lead to lower suspended sediment concentrations near the bed for a portion of the wave cycle. By analyzing sediment fluxes, waves are shown to drive near‐bed sediment dynamics while currents control vertical mixing above the buffer layer, where downward settling is predominantly balanced by the current‐generated vertical turbulent sediment flux. In the absence of currents, sediment concentrations are negligible above the wave boundary layer because mixing is weak. We show that the time‐ and phase‐averaged sediment concentration profiles for wave and current conditions resemble the theoretical Rouse profile derived for equilibrium conditions in statistically steady, unidirectional turbulent channel flow.

The Impact of Mountain Waves on an Idealized Baroclinically Unstable Large-Scale Flow

Abstract The feedback of mountain waves and low-level blocking on an idealized baroclinically unstable wave passing over an isolated ridge is examined through numerical simulation. Theoretical analysis implies that the volume-integrated perturbation momentum budget is dominated by mean-flow deceleration, the divergence of vertical fluxes of horizontal momentum, and the Coriolis force acting on the perturbation ageostrophic wind. These do indeed appear as the dominant balances in numerically computed budgets averaged over layers containing 1) wave breaking in the lower stratosphere, 2) flow blocking with wave breaking near the surface, and 3) a region of pronounced horizontally averaged mean-flow deceleration in the upper troposphere where there is no wave breaking. The local impact of wave breaking on the jet in the lower stratosphere is dramatic, with winds in the jet core reduced by almost 50% relative to the no-mountain case. Although it is the layer with the strongest average deceleration, the local patches of decelerated flow are weakest in the upper troposphere. The cross-mountain pressure drag over a 2-km-high ridge greatly exceeds the vertical momentum flux at mountain-top level because of low-level wave breaking, blocking, and lateral flow diversion. These pressure drags and the low-level momentum fluxes are significantly different from corresponding values computed for simulations with steady forcing matching the instantaneous conditions over the mountain in the evolving large-scale flow.

The Multiscale Impacts of Organized Convection in Global 2‐D Cloud‐Resolving Models

AbstractThis paper studies the mechanisms behind the multiscale organization of tropical moist convection using a trio of cloud‐resolving atmospheric simulations performed in a periodic two‐dimensional 32,000‐km domain. A simulation with interactive surface fluxes and long‐wave radiation over a constant sea surface temperature of 300.15 K produces a planetary‐scale self‐aggregated patch of convection after 80 days of simulation. Fixing the surface fluxes and radiative cooling at a constant value suppresses this planetary‐scale organization. However, increasing the stability at the tropopause by adding stratospheric heating produces a simulation, which generates a planetary‐scale wave after just 30 days. This planetary‐scale wave modulates eastward propagating synoptic‐scale waves, which in turn modulate westward propagating mesoscale convective system. Low‐pass filters are used to diagnose the feedbacks, which produce large‐scale variance of zonal velocity, buoyancy, and humidity. The planetary‐scale buoyancy variance and zonal velocity variance are related to the available potential energy (APE) and kinetic energy (KE) budgets, respectively. In the simulation with stratospheric heating, planetary‐scale KE is created by vertical fluxes of zonal momentum, converted to APE, and then dissipated by latent heating, mixing, and other buoyancy sources. Without stratospheric heating, the KE produced by these feedbacks is strongly damped in the stratosphere. The mesoscale eddy flux convergence of zonal momentum dominates the total vertical flux feedback on the planetary‐scale KE, and its vertical structure is consistent with the westward propagating mesoscale convective systems. Overall, these results demonstrate that these eddy fluxes can organize two‐dimensional deep convection on planetary scales in the absence of other diabatic feedbacks.

Turbulent transport of energy across a forest and a semiarid shrubland

Abstract. The role of secondary circulations has recently been studied in the context of well-defined surface heterogeneity in a semiarid ecosystem where it was found that energy balance closure over a desert–forest system and the structure of the boundary layer was impacted by advection and flux divergence. As a part of the CliFF (“Climate feedbacks and benefits of semi-arid forests”, a collaboration between KIT, Germany, and the Weizmann Institute, Israel) campaign, we studied the boundary layer dynamics and turbulent transport of energy corresponding to this effect in Yatir Forest situated in the Negev Desert in Israel. The forest surrounded by small shrubs presents a distinct feature of surface heterogeneity, allowing us to study the differences between their interactions with the atmosphere above by conducting measurements with two eddy covariance (EC) stations and two Doppler lidars. As expected, the turbulence intensity and vertical fluxes of momentum and sensible heat are found to be higher above the forest compared to the shrubland. Turbulent statistics indicative of nonlocal motions are also found to differ over the forest and shrubland and also display a strong diurnal cycle. The production of turbulent kinetic energy (TKE) over the forest is strongly mechanical, while buoyancy effects generate most of the TKE over the shrubland. Overall TKE production is much higher above the forest compared to the shrubland. The forest is also found to be more efficient in dissipating TKE. The TKE budget appears to be balanced on average both for the forest and shrubland, although the imbalance of the TKE budget, which includes the role of TKE transport, is found to be quite different in terms of diurnal cycles for the forest and shrubland. The difference in turbulent quantities and the relationships between the components of TKE budget are used to infer the characteristics of the turbulent transport of energy between the desert and the forest.

Large-scale coherent flow structures in rough-bed open-channel flow observed in fluctuations of three-dimensional velocity, skin friction and bed pressure

ABSTRACTThe dynamics of large-scale coherent structures (LSCS) are investigated in a rough-bed flow over the whole water column and longitudinal and transverse turbulent fluxes of momentum are compared. The relation between LSCS and fluctuations of skin friction and near-bed surface pressure is examined in order to understand the effects of LSCS on the bed. The study was carried out in an open channel with a non-moving permeable bed of screeded loose-mixed gravel (D50 = 1.5 cm) at Reynolds numbers ranging from 3.19 × 104 to 1.08 × 105. Quasi-instantaneous full-depth three-dimensional (3D) velocity profiles with high spatial and temporal resolution measured with an acoustic Doppler velocity profiler (ADVP) are combined with the signals of a hot-film sensor mounted on the top of the gravel and a piezoresistive pressure transducer placed in the top layer of the bed particles at the centre of the channel. Vertical turbulent momentum flux is clearly dominated by ejections and sweeps over most of the water column. Near the bed, contributions of sweeps are larger than those of ejections. This is reversed at the mid-depth (z/h = 0.5). No preferential quadrant orientation is seen for the transverse momentum flux. A correlation between LSCS dynamics in the water column and data from the sensors on the bed is made evident. Sweeps correlate with positive fluctuations of bottom pressure and skin friction while ejections correlate with negative ones.

Secondary Gravity Waves in the Winter Mesosphere: Results From a High‐Resolution Global Circulation Model

AbstractThis study analyzes a new high‐resolution general circulation model with regard to secondary gravity waves in the mesosphere during austral winter. The model resolves gravity waves down to horizontal and vertical wavelengths of 165 and 1.5 km, respectively. The resolved mean wave drag agrees well with that from a conventional model with parameterized gravity waves up to the midmesosphere in winter and up to the upper mesosphere in summer. About half of the zonal‐mean vertical flux of westward momentum in the southern winter stratosphere is due to orographic gravity waves. The high intermittency of the primary orographic gravity waves gives rise to secondary waves that result in a substantial eastward drag in the winter mesopause region. This induces an additional eastward maximum of the mean zonal wind at z ∼ 100 km. Radar and lidar measurements at polar latitudes and results from other high‐resolution global models are consistent with this finding. Hence, secondary gravity waves may play a significant role in the general circulation of the winter mesopause region.

On the distortions in calculated GW parameters during slanted atmospheric soundings

Abstract. The significant distortions introduced in the measured atmospheric gravity wavelengths by soundings other than those in vertical and horizontal directions, are discussed as a function of the elevation angle of the sounding path and the gravity wave aspect ratio. Under- or overestimation of real vertical wavelengths during the measurement process depends on the value of these two parameters. The consequences of these distortions on the calculation of the energy and the vertical flux of horizontal momentum are analyzed and discussed in the context of two experimental limb satellite setups: GPS-LEO radio occultations and TIMED/SABER ((Atmosphere using Broadband Emission Radiometry/Thermosphere–Ionosphere–Mesosphere–Energetics and Dynamics)) measurements. Possible discrepancies previously found between the momentum flux calculated from satellite temperature profiles, on site and from model simulations, may to a certain degree be attributed to these distortions. A recalculation of previous momentum flux climatologies based on these considerations seems to be a difficult goal.

The Effect of Internal Gravity Waves on Fluctuations in Meteorological Parameters of the Atmospheric Boundary Layer

Variations in the intensity of turbulence during wave activity in the stable atmospheric boundary layer over a homogeneous steppe surface have been analyzed. Eight wave activity episodes recorded with a Doppler sodar in August 2015 at the Tsimlyansk Scientific Station of the Obukhov Institute of Atmospheric Physics have been studied. These episodes include seven trains of Kelvin–Helmholtz waves and one train of buoyancy waves. Variations in the rms deviation of the vertical wind-velocity component, the temperature structure parameter, and vertical heat and momentum fluxes have been estimated for each episode of wave activity. It has been found that Kelvin–Helmholtz waves slightly affect the intensity of turbulence, while buoyancy waves cause the temperature structure parameter and the vertical fluxes to increase by more than an order of magnitude.

Vertical Momentum Fluxes Induced by Weakly Nonlinear Internal Waves on the Shelf

Free inertia-gravity internal waves in a two-dimensional stratified flow of an ideal fluid with a vertical velocity shear are considered in the Boussinesq approximation. The boundary-value problem for the amplitude of the vertical velocity of internal waves has complex coefficients; therefore, the wave frequency has an imaginary correction and the eigenfunction is complex. It is shown that the wave is weakly damped, the vertical wave momentum fluxes being nonzero and can be greater than the turbulent fluxes. The Stokes drift velocity component transverse to the direction of wave propagation is nonzero and less than the longitudinal component by an order of magnitude. The dispersion curves of the first two modes are cut off in the low-frequency domain due to the influence of critical layers in which the wave frequency taken with the Doppler shift is equal to the inertial frequency.

Orographic–convective flows, wave reflection, and gravity-wave momentum fluxes in a two-layer hydrostatic atmosphere

ABSTRACTDynamical aspects of flows forced by either convective heating or a mountain have been extensively studied, but those forced by both convective heating and a mountain have been less studied. Here, we theoretically examine orographic–convective flows, gravity-wave reflection, and gravity-wave momentum fluxes in a stably stratified two-layer hydrostatic atmosphere. The upper layer (stratosphere) has a larger static stability than the lower layer (troposphere), and the basic-state wind has a constant shear in the troposphere and is uniform in the stratosphere. The equations governing small-amplitude perturbations in a two-dimensional, steady-state, inviscid, non-rotating system in the presence of orographic forcing and convective forcing are analytically solved. Then, the analytic solutions are analysed to understand how orographically and convectively forced flows vary with changes in basic-state wind speed, stratospheric static stability, and the location of the convection relative to the mountain. Over the upslope of the mountain, the convectively forced deep upward motion is positively combined with the orographic uplift, thus giving rise to enhanced upward motion there. The ratio of the convectively forced vertical velocity to the orographically forced vertical velocity at the cloud base height over an upslope location of the mountain is analysed to further understand the linear interaction between orographically and convectively forced flows. The gravity-wave reflection at the tropopause plays an important role in orographic–convective flows. The gravity-wave reflection at the tropopause amplifies the symmetric (anti-symmetric) structure of orographically (convectively) forced waves. The vertical fluxes of the horizontal momentum are analytically obtained. The total momentum flux contains the component resulting from the non-linear interaction between orographically and convectively forced waves. It is found that the non-linear interaction component can be as important as each of the orographic and convective components in the total momentum flux depending on the location of the convection relative to the mountain.