Convective Momentum Research Articles

Publisher's Note: “Momentum transport in the vicinity of q min in reverse shear tokamaks due to ion temperature gradient turbulence” [Phys. Plasmas 21, 012302 (2014)

Publisher's Note: “Momentum transport in the vicinity of <i>q</i> <i>min</i> in reverse shear tokamaks due to ion temperature gradient turbulence” [Phys. Plasmas 21, 012302 (2014)

Rayleigh Damping in the Free Troposphere

Abstract This paper explores whether cumulus drag (i.e., the damping of winds by convective momentum transport) can be described by an effective Rayleigh drag (i.e., the damping of winds on a constant time scale). Analytical expressions are derived for the damping time scale and descent speed of wind profiles as caused by unorganized convection. Unlike Rayleigh drag, which has a constant damping time scale and zero descent speed, the theory predicts a damping time scale and a descent speed that both depend on the vertical wavelength of the wind profile. These results predict that short wavelengths damp faster and descend faster than long wavelengths, and these predictions are confirmed using large-eddy simulations. Both theory and simulations predict that the convective damping of large-scale circulations occurs on a time scale of O(1–10) days for vertical wavelengths in the range of 2–10 km.

Toward an Understanding of Vertical Momentum Transports in Cloud-System-Resolving Model Simulations of Multiscale Tropical Convection

Abstract This study examines the characteristics of convective momentum transport (CMT) and gravity wave momentum transport (GWMT) in two-dimensional cloud-system-resolving model simulations, including the relationships between the two transports. A linear group velocity criterion is shown to objectively separate CMT and GWMT. The GWMT contribution is mostly consistent with upward-propagating gravity waves and is present in the troposphere and the stratosphere. The CMT contribution forms a large part of the residual (nonupward-propagating contribution) and dominates the fluxes in the troposphere. Additional analysis of the vertical sensible heat flux supports the physical interpretation of the two contributions, further isolating the effects of unstable convection from vertically propagating gravity waves. The role of transient and nonconservative (friction and diabatic heating) processes in generating momentum flux and their dependence on changes in convective organization was assessed using a pseudomomentum budget analysis. Nonconservative effects were found to dominate the transports; the GWMT contribution involved a diabatic source region in the troposphere and a dissipative sink region in the stratosphere. The CMT contribution was consistent with transport between the boundary layer and free troposphere via tilted convection. Transient buoyancy–vorticity correlations highlighted wave sources in the region of convective outflow and the boundary layer. These sources were akin to the previously described “mechanical oscillator” mechanism. Fluxes associated with this upper-level source were most sensitive to convective organization, highlighting the mechanism by which changes in organization are communicated to GWMT. The results elucidate important interactions between CMT and GWMT, adding further weight to suggestions that the two transports should be linked in parameterizations.

Buoyancy-Induced Convection in a Square Enclosure Discretely Heated at One Side and Cooled either at the Top or at the Bottom Using both Gases and Liquids as Working Fluids

Laminar natural convection heat and momentum transfer in fluid-filled, square enclosures partially heated at one side and cooled either at the top or at the bottom, is studied numerically. A computational code based on the SIMPLE-C algorithm is used to solve the system of the mass, momentum and energy transfer governing equations. Simulations are performed using the Rayleigh number based on the cavity width, the thermally-active fraction of the partially heated sidewall, and the Prandtl number of the working fluid, as independent variables. It is found that the top cooling is definitely more efficient than the bottom cooling. In both cooling configurations the average Nusselt number of the cavity increases as each controlling parameter is increased. On the basis of the results obtained, a set of dimensionless correlations is developed.

Modeling and simulation of drying operations in PVC powder production line: Experimental and theoretical study of drying kinetics on particle scale

An experimental method to determine drying kinetic at a particle scale and a pneumatic dryer model are presented. The particle scale kinetics were obtained by immersion of a fixed mass of wet PVC particles (cake) in a batch dense fluidized bed containing inert hot particles (glass bead). It appears clearly that the PVC drying is controlled by a competition between internal and external transfers. The drying kinetic was described by a shrinking core type model and integrated in a one-dimensional steady-state model simulating a pneumatic dryer. A two-phase continuum model was used to describe the steady-state flow of a diluted dispersed phase (wet PVC powder) and a continuous phase (humid air) through dryer. The model takes into account the convective heat, mass and momentum transfers. The numerical results are compared with industrial experimental data. The results show that the inlet temperature is the most important parameter in the operation.

Influence of Convective Momentum Transport on Mixed Rossby–Gravity Waves: A Contribution to Tropical 2-Day Waves

Abstract Influences of convective momentum transport (CMT) on tropical waves are analytically studied with an idealized model, which captures the first-order baroclinic structure in the vertical. The CMT has significant influence on the mixed Rossby–gravity (MRG) waves, especially over the Indo-Pacific warm pool. The westward-propagating MRG wave with a small wavenumber becomes unstable because of the CMT. The convergence and geopotential are no longer in a quadrature phase relation, which is different from the classical MRG wave. As a result, there is a net source of mechanical energy within one wave period and there is an upscale momentum transfer that can have impacts on slow variabilities in the tropics, such as the Madden–Julian oscillation. The unstable MRG wave mimics the temporal and spatial features of the observed 2-day waves in tropics. Within this framework, the asymmetric structure of the MRG waves and the 2-day waves with respect to the equator are well captured by both the idealized model and observations. In addition, the CMT is found to be critical for determining the meridional scale of tropical waves. The meridional scale in the two-layer model is wider than the Rossby radius of deformation RL over the Indo-Pacific warm pool, but narrower than RL from the central to the eastern Pacific Ocean and over the Atlantic Ocean. Such variation is consistent with observations.

The Mean Climate of the Community Atmosphere Model (CAM4) in Forced SST and Fully Coupled Experiments

Abstract The Community Atmosphere Model, version 4 (CAM4), was released as part of the Community Climate System Model, version 4 (CCSM4). The finite volume (FV) dynamical core is now the default because of its superior transport and conservation properties. Deep convection parameterization changes include a dilute plume calculation of convective available potential energy (CAPE) and the introduction of convective momentum transport (CMT). An additional cloud fraction calculation is now performed following macrophysical state updates to provide improved thermodynamic consistency. A freeze-drying modification is further made to the cloud fraction calculation in very dry environments (e.g., the Arctic), where cloud fraction and cloud water values were often inconsistent in CAM3. In CAM4 the FV dynamical core further degrades the excessive trade-wind simulation, but reduces zonal stress errors at higher latitudes. Plume dilution alleviates much of the midtropospheric tropical dry biases and reduces the persistent monsoon precipitation biases over the Arabian Peninsula and the southern Indian Ocean. CMT reduces much of the excessive trade-wind biases in eastern ocean basins. CAM4 shows a global reduction in cloud fraction compared to CAM3, primarily as a result of the freeze-drying and improved cloud fraction equilibrium modifications. Regional climate feature improvements include the propagation of stationary waves from the Pacific into midlatitudes and the seasonal frequency of Northern Hemisphere blocking events. A 1° versus 2° horizontal resolution of the FV dynamical core exhibits superior improvements in regional climate features of precipitation and surface stress. Improvements in the fully coupled mean climate between CAM3 and CAM4 are also more substantial than in forced sea surface temperature (SST) simulations.

Comparison of Moist Static Energy and Budget between the GCM-Simulated Madden–Julian Oscillation and Observations over the Indian Ocean and Western Pacific

Abstract The moist static energy (MSE) anomalies and MSE budget associated with the Madden–Julian oscillation (MJO) simulated in the Iowa State University General Circulation Model (ISUGCM) over the Indian and Pacific Oceans are compared with observations. Different phase relationships between MJO 850-hPa zonal wind, precipitation, and surface latent heat flux are simulated over the Indian Ocean and western Pacific, which are greatly influenced by the convection closure, trigger conditions, and convective momentum transport (CMT). The moist static energy builds up from the lower troposphere 15–20 days before the peak of MJO precipitation, and reaches the maximum in the middle troposphere (500–600 hPa) near the peak of MJO precipitation. The gradual lower-tropospheric heating and moistening and the upward transport of moist static energy are important aspects of MJO events, which are documented in observational studies but poorly simulated in most GCMs. The trigger conditions for deep convection, obtained from the year-long cloud-resolving model (CRM) simulations, contribute to the striking difference between ISUGCM simulations with the original and modified convection schemes and play the major role in the improved MJO simulation in ISUGCM. Additionally, the budget analysis with the ISUGCM simulations shows the increase in MJO MSE is in phase with the horizontal advection of MSE over the western Pacific, while out of phase with the horizontal advection of MSE over the Indian Ocean. However, the NCEP analysis shows that the tendency of MJO MSE is in phase with the horizontal advection of MSE over both oceans.

A monotonicity preserving conservative sharp interface flow solver for high density ratio two-phase flows

This paper presents a novel approach for solving the conservative form of the incompressible two-phase Navier–Stokes equations. In order to overcome the numerical instability induced by the potentially large density ratio encountered across the interface, the proposed method includes a Volume-of-Fluid type integration of the convective momentum transport, a monotonicity preserving momentum rescaling, and a consistent and conservative Ghost Fluid projection that includes surface tension effects. The numerical dissipation inherent in the Volume-of-Fluid treatment of the convective transport is localized in the interface vicinity, enabling the use of a kinetic energy conserving discretization away from the singularity. Two- and three-dimensional tests are presented, and the solutions shown to remain accurate at arbitrary density ratios. The proposed method is then successfully used to perform the detailed simulation of a round water jet emerging in quiescent air, therefore suggesting the applicability of the proposed algorithm to the computation of realistic turbulent atomization.

Zonal Momentum Balance in the Tropical Atmospheric Circulation during the Global Monsoon Mature Months

AbstractIn this paper, zonal momentum balances of the tropical atmospheric circulation during the global monsoon mature months (January and July) are analyzed in three dimensions based on the ECMWF Interim Re-Analysis (ERA-Interim). It is found that the dominant terms in the balance of the atmospheric boundary layer (ABL) in both months are the pressure gradient force, the Coriolis force, and friction. The nonlinear advection term plays a significant role only in the Asian summer monsoon regions within the ABL. In the upper troposphere, the pressure gradient force, the Coriolis force, and the nonlinear advection are the dominant terms. The transient eddy force and the residual force (which can be explained as convective momentum transfer over open oceans) are secondary, yet cannot be neglected near the equator. Zonal-mean equatorial upper-troposphere easterlies are maintained by the absolute angular momentum advection associated with the cross-equatorial Hadley circulation. Equatorial upper-troposphere easterlies over the Asian monsoon regions are also controlled by the absolute angular momentum advection but are mainly maintained by the pressure gradient force in January. The equivalent linear Rayleigh friction, which is widely applied in simple tropical models, is calculated and the corresponding spatial distribution of the local coefficient and damping time scale are estimated from the linear regression. It is found that the linear momentum model is in general capable of crudely describing the tropical atmospheric circulation dynamics, yet the caveat should be kept in mind that the friction coefficient is not uniformly distributed and is even negative in some regions.

Analysis of Shallow Water Flow in Curved Channel Using Dispersion Stresses Method

기존 대부분의 천수흐름 해석모형에서는 연직방향으로 균일한 유속을 가정하였기 때문에 하천 만곡부에서 이차류의 영향을 고려하지 못하고 부정확한 흐름해석 결과를 도출하였다. 본 연구에서는 종횡방향 유속의 연직분포를 평균값과 이로부터의 변동량으로 분할하여 이 값들을 운동량 방정식에 대입하여 생성되는 추가적인 항인 분산응력을 포함하는 수치모형을 개발하였다. 제안된 모형을 <TEX>$30^{\circ}$</TEX>, <TEX>$90^{\circ}$</TEX>, <TEX>$270^{\circ}$</TEX>의 곡률을 가지는 수로에 적용하여 분산응력을 이용한 곡선수로에서의 천수흐름을 수치모의 하였다. 모의 결과, 운동량방정식에 포함된 분산응력항은 생성/소멸과 같은 역할을 하여, 만곡의 내측에서 외측으로 횡방향 운동량을 이동시키게 되므로 분산응력을 포함하지 않는 경우 보다 정확한 수치모의 결과를 제시하는 것으로 밝혀졌다. Most of the previous models for analysis of shallow water flow assumed the uniform velocity distributions over the flow depth so that they produced incorrect velocity prediction at meandering part due to the ignorance of secondary current. In this study, the vertical velocity profiles in longitudinal and transverse direction were decomposed as the mean and variation components, which resulted in additional dispersion stresses terms in momentum equations. The proposed model were applied at the channels with <TEX>$30^{\circ}$</TEX>, <TEX>$90^{\circ}$</TEX>, <TEX>$270^{\circ}$</TEX> bends, and shallow water flow in curved channel was analyzed using dispersion stresses. The dispersion stresses acted as a sink or source in the momentum equations, which caused the transverse convection of momentum to shift from the inner bank to the outer bank.

On the Equivalence of Two Schemes for Convective Momentum Transport

Abstract The Gregory–Kershaw–Inness (GKI) parameterization of convective momentum transport, which has a tunable parameter C, is shown to be identical to a parameterization with no pressure gradient force and a mass flux smaller by a factor of 1 − C. Using cloud-resolving simulations, the transilient matrix for momentum is diagnosed for deep convection in radiative–convective equilibrium. Using this transilient matrix, it is shown that the GKI scheme underestimates the compensating subsidence of momentum by a factor of 1 − C, as predicted. This result is confirmed using a large-eddy simulation.

Proper orthogonal decomposition investigation of turbulent Rayleigh-Bénard convection in a rectangular cavity

We consider the large-eddy simulation (LES) of turbulent Rayleigh-Bénard convection for air in a parallepipedic cavity of ratio (1:5:1) over the range Ra = 6 × 108 up to Ra = 1010 previously studied in Sergent and Le Quéré (Proceedings of the 13th European Turbulence Conference, 2011). Using proper orthogonal decomposition (POD) analysis, we confirm the existence of a large-scale circulation (LSC) consisting of quasi-stationary cross-stream rolls (y-rolls) which are aligned with the small direction of the box. Strong changes in the LSC are observed to take place over a few hundred convective time units, defined as \documentclass[12pt]{minimal}\begin{document}$\kappa /(L_{x}^{2} Ra^{1/2})$\end{document}κ/(Lx2Ra1/2), where κ is the fluid diffusivity, Lx is the height of the box and Ra is the Rayleigh number. We also show the existence of a secondary flow, which consists of horizontal rolls (z-rolls) surrounding the core of the cavity and orthogonal to the cross-stream rolls. The amplitude of these longitudinal rolls oscillates on a time scale of 50 convective units. The longitudinal rolls are associated with strong variations in the vertical momentum transfer, while cross-stream rolls are primarily responsible for more than half of the convective heat transfer and make little contribution to the convective momentum transfer. Integration of a simplified dynamical model with stationary y-rolls leads to an oscillation in the z-rolls with a characteristic period of 70 units, which supports the idea that the oscillation of the secondary rolls is determined by the primary flow structure. Using 2D linear stability analysis based on the contributions from POD modes, we show that the presence of longitudinal shear leads to the stabilization of the high wavenumber range, and we predict a roll size which is reasonably close to that observed in the LES. We conjecture that changes in the large-scale circulation of the flow are related to the fluctuating shear created by the secondary rolls and higher-order modes outside the boundary layer.

Weakly Forced Mock Walker Cells

Abstract Mock Walker cells driven by weak sea surface temperature (SST) forcing are studied using planetary-scale cloud system–resolving simulations and a simplified framework that represents convection with its linear response functions and parameterizes the large-scale flow based on the gravity wave equation. For sinusoidal SST forcings of the same amplitude, as the horizontal domain size increases, the mock Walker cells strengthen substantially and shorter vertical scales in the vertical velocity profile diminish. This is explained by the fact that temperature anomalies required to sustain a vertical velocity profile of given amplitude are stronger in cases of larger horizontal and smaller vertical scales. Such temperature anomalies become significant at planetary scales so that properly accounting for the horizontal momentum balance, including convective momentum transport (CMT), becomes necessary, while a weak temperature gradient approach that neglects horizontal momentum balance is no longer adequate. The downward advection component of the CMT in particular is important for capturing a number of features of the mock Walker cells. The extent of convective organization also affects the mock Walker cell through its effects on the sensitivities of convective heating and moistening to temperature and moisture anomalies. For strongly organized convection with deep inflows, these sensitivities are consistent with a layer mode of convective overturning, instead of the parcel mode as in unorganized convection, resulting in a weaker second baroclinic component in the mock Walker cells.

New perspectives in turbulent Rayleigh-Bénard convection

Recent experimental, numerical and theoretical advances in turbulent Rayleigh-Bénard convection are presented. Particular emphasis is given to the physics and structure of the thermal and velocity boundary layers which play a key role for the better understanding of the turbulent transport of heat and momentum in convection at high and very high Rayleigh numbers. We also discuss important extensions of Rayleigh-Bénard convection such as non-Oberbeck-Boussinesq effects and convection with phase changes.

Convectively coupled wave–environment interactions

In the tropical atmosphere, waves can couple with water vapor and convection to form large-scale coherent structures called convectively coupled waves (CCWs). The effects of water vapor and convection lead to CCW–mean flow interactions that are different from traditional wave–mean flow interactions in many ways. CCW–mean flow interactions are studied here in two types of models: a multiscale model that represents CCW structures in two spatial dimensions directly above the Earth’s equator, and an amplitude model in the form of ordinary differential equations for the CCW and mean flow amplitudes. The amplitude equations are shown to capture the qualitative behavior of the spatially resolved model, including nonlinear oscillations and a Hopf bifurcation as the climatological background wind is varied. Furthermore, an even simpler set of amplitude equations can also capture some of the essential oscillatory behavior, and it is shown to be equivalent to the Duffing oscillator. The basic interaction mechanisms are that the mean flow’s vertical shear determines the preferred propagation direction of the CCW, and the CCWs can drive changes in the mean shear through convective momentum transport, with energy transfer that is sometimes upscale and sometimes downscale. In addition to CCW–mean flow interactions, also discussed are CCW–water vapor interactions, which form the basis of the Madden–Julian Oscillation (MJO) skeleton model of the first two authors. The key parameter of the MJO skeleton model is estimated theoretically and is in agreement with previously conjectured values.

Convective Momentum Transport by Rainbands within a Madden–Julian Oscillation in a Global Nonhydrostatic Model with Explicit Deep Convective Processes. Part I: Methodology and General Results

Abstract The convective momentum transport (CMT) properties of 13 215 rainbands within a Madden–Julian oscillation (MJO) event simulated by a global nonhydrostatic model are examined. CMT vectors, which represent horizontal accelerations to the mean winds due to momentum flux convergences of deviation winds, are derived for each rainband. The CMT vectors are composited according to their locations relative to the MJO center. While a similar number of rainbands are detected in the eastern and western halves of the MJO convective envelope, CMT vectors with large zonal components are most plentiful between 0° and 20° to the west of the MJO center. The zonal components of the CMT vectors exhibit a coherent directionality and have a well-organized three-layer structure: positive near the surface, negative in the low to midtroposphere, and positive in the upper troposphere. In the low to midtroposphere, where the longitudinal difference in the mean zonal wind across the MJO is 10 m s−1 on average, the net acceleration due to CMT contributes about −16 m s−1. Possible roles of the CMT are proposed. First, the CMT delays the eastward progress of the low- to midtroposphere westerly wind, hence delaying the eastward migration of the convectively favorable region and reducing the propagation speed of the entire MJO. Second, the CMT tilts the MJO flow structure westward with height. Furthermore, the CMT counteracts the momentum transport due to large-scale flows that result from the tilted structure.

Multiscale Waves in an MJO Background and Convective Momentum Transport Feedback

Abstract The authors use linear analysis for a simple model to study the evolution of convectively coupled waves (CCWs) in a background shear and background moisture mimicking the observed structure of the Madden–Julian oscillation (MJO). This is motivated by the observation, in an idealized setting, of intraseasonal two-way interactions between CCWs and a background wind. It is found here that profiles with a bottom-heavy moisture content are more favorable to the development of mesoscale/squall line–like waves whereas synoptic-scale CCWs are typically more sensitive to the shear strength. The MJO envelope is thus divided into three regions, in terms of the types of CCWs that are favored: an onset region in front that is favorable to Kelvin waves, a mature or active region in the middle in which squall lines are prominent, and the stratiform and decay phase region in the back that is favorable to westward inertia–gravity (WIG) waves. A plausible convective momentum transport (CMT) feedback is then provided according to the results of the idealized two-way interaction model. The active region, in particular, coincides with the westerly wind burst where both Kelvin waves and squall lines are believed to play a significant role in both the deceleration of low-/high-level easterly/westerly winds and the acceleration of low-/high-level westerly/easterly winds. The WIG waves in the wake could be a precursor for a subsequent MJO event through the acceleration of low-/high-level easterly/westerly winds, which in turn favor Kelvin waves, and the cycle repeats. These results open interesting directions for future studies using observations and/or detailed numerical simulations using the full primitive equation.

Improved Madden–Julian Oscillations with Improved Physics: The Impact of Modified Convection Parameterizations

Abstract Two modifications are made to the deep convection parameterization in the NCAR Community Climate System Model, version 3 (CCSM3): a dilute plume approximation and an implementation of the convective momentum transport (CMT). These changes lead to significant improvement in the simulated Madden–Julian oscillations (MJOs). With the dilute plume approximation, temperature and convective heating perturbations become more positively correlated. Consequently, more available potential energy is generated and the intraseasonal variability (ISV) becomes stronger. The organization of ISV is also improved, which is manifest in coherent structures between different MJO phases and an improved simulation of the eastward propagation of MJOs with a reasonable eastward speed. The improved propagation can be attributed to a better simulation of the low-level zonal winds due to the inclusion of CMT. The authors posit that the large-scale zonal winds are akin to a selective conveyor belt that facilitates the organization of ISVs into highly coherent structures, which are important features of observed MJOs. The conclusions are supported by two supplementary experiments, which include the dilute plume approximation and CMT separately.

Core and edge toroidal rotation study in JT-60U

The relation between toroidal rotation velocities (Vt) in the core and edge regions is investigated in H-mode plasmas with a small external torque input from the viewpoint of momentum transport. The toroidal rotation velocity in the core region (core-Vt) gradually varies on a timescale of ∼20 ms after a rapid change in the toroidal rotation velocity in the edge region (edge-Vt) at the L–H transition. This timescale of ∼20 ms is consistent with a transport timescale using the momentum diffusivity (χϕ) and convection velocity (Vconv). In steady state, a linear correlation between the core- and edge-Vt is observed in H-mode plasmas when the ion pressure gradient (∇Pi) is small. This relation between core- and edge-Vt is also explained by momentum transport. The Vt profiles with a large ∇Pi are reproduced in the core region of r/a ∼ 0.2–0.7 by adopting a residual stress term ‘Πres = αkχϕ∇Pi’ proposed in this paper. Here r/a is the normalized plasma radius and αk1 is a radial constant. Using this formula, Vt profiles are reproduced over a wide range of plasma conditions. Parameter dependences of the edge-Vt are investigated at a constant ripple loss power, ripple amplitude and plasma current. A reduction in the CTR-rotation is observed with decreasing ion temperature gradient (∇Ti). Here CTR refers to the counter-IP direction.