scholarly journals Numerical Tests of the Weak Pressure Gradient Approximation

2012 ◽  
Vol 69 (9) ◽  
pp. 2846-2856 ◽  
Author(s):  
David M. Romps
Keyword(s):  
Pressure Gradient ◽  
Vertical Velocity ◽  
Hot Spot ◽  
Accurate Method ◽  
Velocity Profiles ◽  
Moist Convection ◽  
Cloud Resolving Model ◽  
Positive Time ◽  
Weak Pressure Gradient ◽  
Negative Buoyancy

Abstract Cloud-resolving simulations of convection over a surface temperature hot spot are used to evaluate the weak pressure gradient (WPG) and weak temperature gradient (WTG) approximations. The premise of the relaxed form of WTG—that vertical velocity is equal to buoyancy times a positive time scale—is found to be violated by thick layers of negative buoyancy in steady-state ascent. The premise of WPG—that horizontal divergence and pressure anomalies are collocated—is validated by these simulations. When implemented in a cloud-resolving model, WPG replicates buoyancy transients exceptionally well, including the adiabatic lifting of air below buoyancy anomalies. WTG captures neither this effect nor the associated triggering of moist convection. For steady states, WTG produces vertical velocity profiles that are too top heavy. On the other hand, WPG generates velocity profiles that closely match fully resolved hot-spot simulations. Taken together, the evidence suggests that WPG is a relatively accurate method for parameterizing supradomain-scale (SDS) dynamics.

scholarly journals Weak Pressure Gradient Approximation and Its Analytical Solutions

2012 ◽  
Vol 69 (9) ◽  
pp. 2835-2845 ◽  
Author(s):  
David M. Romps
Keyword(s):  
Pressure Gradient ◽  
Short Circuit ◽  
Boussinesq Equations ◽  
Moist Convection ◽  
Zero Column ◽  
Mass Fluxes ◽  
Convective Inhibition ◽  
Weak Pressure Gradient ◽  
Boussinesq Fluid ◽  
Different Time Scales

Abstract A weak pressure gradient (WPG) approximation is introduced for parameterizing supradomain-scale (SDS) dynamics, and this method is compared to the relaxed form of the weak temperature gradient (WTG) approximation in the context of 3D, linearized, damped, Boussinesq equations. It is found that neither method is able to capture the two different time scales present in the full 3D equations. Nevertheless, WPG is argued to have several advantages over WTG. First, WPG correctly predicts the magnitude of the steady-state buoyancy anomalies generated by an applied heating, but WTG underestimates these buoyancy anomalies. It is conjectured that this underestimation may short-circuit the natural feedbacks between convective mass fluxes and local temperature anomalies. Second, WPG correctly predicts the adiabatic lifting of air below an initial buoyancy perturbation; WTG is unable to capture this nonlocal effect. It is hypothesized that this may be relevant to moist convection, where adiabatic lifting can reduce convective inhibition. Third, WPG agrees with the full 3D equations on the counterintuitive fact that an isolated heating applied to a column of Boussinesq fluid leads to a steady ascent with zero column-integrated buoyancy. This falsifies the premise of the relaxed form of WTG, which assumes that vertical velocity is proportional to buoyancy.

Understanding changes in tropical circulations in a future warmer climate using a cloud-resolving model and a conceptual model

2021 ◽  
Author(s):  
Sramana Neogi ◽  
Martin Singh
Keyword(s):  
Surface Temperature ◽  
Vertical Velocity ◽  
Large Scale ◽  
Entrainment Rate ◽  
Moist Convection ◽  
Tropical Circulation ◽  
Thermodynamic Structure ◽  
Reference Profile ◽  
Cloud Resolving Model ◽  
Vertical Velocity Profile

<p>The interaction between large-scale tropical circulations and moist convection has been the focus of a number of studies. However, projections of how the large-scale tropical circulation may change under global warming remain uncertain because our understanding of this interaction is still limited.</p><p>Here, we use a cloud-resolving model (CRM) coupled with a supra-domain scale (SDS) parameterisation of the large-scale circulation to investigate how tropical circulations driven by sea-surface temperature (SST) gradients change in a future warmer climate. Two popular SDS parameterisation schemes are compared; the weak temperature gradient approximation and the damped-gravity-wave approximation. In both cases, the large-scale vertical velocity is related to the deviation of the simulated density profile from a reference profile taken from the same model run to radiative-convective equilibrium.</p><p>We examine how the large-scale vertical velocity profile varies with surface temperature for fixed background profile (relative SST) as well as how it varies with the surface temperature of the reference profile (background SST). The domain mean vertical velocity appears to be very top-heavy with the maximum vertical velocity becoming stronger at warmer surface temperatures. The results are understood using a simple model for the thermodynamic structure of a convecting atmosphere based on an entraining plume. The model uses a fixed entrainment rate and the relative humidity from the cloud-resolving model to predict a temperature profile. The vertical velocities calculated from these predicted temperature profiles is similar to the vertical velocity structures and their behaviour in a warmer climate that we see in the CRM simulations. The results provide insight into large scale vertical velocity structures simulated by SDS parameterisation schemes, providing a stepping stone to understanding the factors driving changes to the large-scale tropical circulation in a future warmer climate.</p>

scholarly journals Similarity Solutions of the MHD Boundary Layer Flow Past a Constant Wedge within Porous Media

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ramesh B. Kudenatti ◽  
Shreenivas R. Kirsur ◽  
Achala L. Nargund ◽  
N. M. Bujurke
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Similarity Solutions ◽  
Positive Pressure ◽  
Boundary Layer Equations ◽  
Similarity Transformations ◽  
Wide Range

The two-dimensional magnetohydrodynamic flow of a viscous fluid over a constant wedge immersed in a porous medium is studied. The flow is induced by suction/injection and also by the mainstream flow that is assumed to vary in a power-law manner with coordinate distance along the boundary. The governing nonlinear boundary layer equations have been transformed into a third-order nonlinear Falkner-Skan equation through similarity transformations. This equation has been solved analytically for a wide range of parameters involved in the study. Various results for the dimensionless velocity profiles and skin frictions are discussed for the pressure gradient parameter, Hartmann number, permeability parameter, and suction/injection. A far-field asymptotic solution is also obtained which has revealed oscillatory velocity profiles when the flow has an adverse pressure gradient. The results show that, for the positive pressure gradient and mass transfer parameters, the thickness of the boundary layer becomes thin and the flow is directed entirely towards the wedge surface whereas for negative values the solutions have very different characters. Also it is found that MHD effects on the boundary layer are exactly the same as the porous medium in which both reduce the boundary layer thickness.

scholarly journals Weak Pressure Gradient over the Iberian Peninsula and African Dust Outbreaks: A New Dust Long-Transport Scenario

2012 ◽  
Vol 93 (8) ◽  
pp. 1125-1132 ◽  
Author(s):  
Luis Negral ◽  
Stella Moreno-Grau ◽  
Xavier Querol ◽  
José Moreno ◽  
Mar Viana ◽  
...  
Keyword(s):  
Pressure Gradient ◽  
Iberian Peninsula ◽  
African Dust ◽  
Weak Pressure Gradient

Parameterization of the Vertical Velocity Equation for Shallow Cumulus Clouds

2012 ◽  
Vol 140 (8) ◽  
pp. 2424-2436 ◽  
Author(s):  
Stephan R. de Roode ◽  
A. Pier Siebesma ◽  
Harm J. J. Jonker ◽  
Yoerik de Voogd
Keyword(s):  
Pressure Gradient ◽  
Vertical Velocity ◽  
Weather Prediction ◽  
Specific Humidity ◽  
Thermodynamic Quantities ◽  
Small Contribution ◽  
Cumulus Clouds ◽  
Shallow Cumulus ◽  
Sink Term ◽  
Velocity Equation

Abstract The application of a steady-state vertical velocity equation for parameterized moist convective updrafts in climate and weather prediction models is currently common practice. This equation usually contains an advection, a buoyancy, and a lateral entrainment term, whereas the effects of pressure gradient and subplume contributions are typically incorporated as proportionality constants a and b for the buoyancy and the entrainment terms, respectively. A summary of proposed values of these proportionality constants a and b in the literature demonstrates that there is a large uncertainty in their most appropriate values. To shed new light on this situation an analysis is presented of the full vertical budget equation for shallow cumulus clouds obtained from large eddy simulations of three different Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study (GCSS) intercomparison cases. It is found that the pressure gradient term is the dominant sink term in the vertical velocity budget, whereas the entrainment term only gives a small contribution. This result is at odds with the parameterized vertical velocity equation in the literature as it employs the entrainment term as the major sink term. As a practical solution the damping effect of the pressure term may be parameterized in terms of the lateral entrainment rates as used for thermodynamic quantities like the total specific humidity. By using a least squares method, case-dependent optimal values are obtained for the proportionality constants a and b, which are linearly related with each other. This relation can be explained from a linear relationship between the lateral entrainment rate and the buoyancy.

Velocity and Temperature Profiles in Turbulent Boundary Layer Flows Experiencing Streamwise Pressure Gradients

1997 ◽  
Vol 119 (3) ◽  
pp. 433-439 ◽  
Author(s):  
R. J. Volino ◽  
T. W. Simon
Keyword(s):  
Experimental Data ◽  
Pressure Gradient ◽  
Velocity Profiles ◽  
Temperature Profiles ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Prandtl Numbers ◽  
Energy Equations ◽  
Near Wall

The standard turbulent law of the wall, devised for zero pressure gradient flows, has been previously shown to be inadequate for accelerating and decelerating turbulent boundary layers. In this paper, formulations for mean velocity profiles from the literature are applied and formulations for the temperature profiles are developed using a mixing length model. These formulations capture the effects of pressure gradients by including the convective and pressure gradient terms in the momentum and energy equations. The profiles which include these terms deviate considerably from the standard law of the wall; the temperature profiles more so than the velocity profiles. The new profiles agree well with experimental data. By looking at the various terms separately, it is shown why the velocity law of the wall is more robust to streamwise pressure gradients than is the thermal law of the wall. The modification to the velocity profile is useful for evaluation of more accurate skin friction coefficients from experimental data by the near-wall fitting technique. The temperature profile modification improves the accuracy with which one may extract turbulent Prandtl numbers from near-wall mean temperature data when they cannot be determined directly.

scholarly journals Biorheological Model on Flow of Herschel-Bulkley Fluid through a Tapered Arterial Stenosis with Dilatation

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
S. Priyadharshini ◽  
R. Ponalagusamy
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Power Law ◽  
Flow Resistance ◽  
Velocity Profiles ◽  
Arterial Stenosis ◽  
Axial Distance ◽  
Tapered Artery ◽  
Wall Shear

An analysis of blood flow through a tapered artery with stenosis and dilatation has been carried out where the blood is treated as incompressible Herschel-Bulkley fluid. A comparison between numerical values and analytical values of pressure gradient at the midpoint of stenotic region shows that the analytical expression for pressure gradient works well for the values of yield stress till 2.4. The wall shear stress and flow resistance increase significantly with axial distance and the increase is more in the case of converging tapered artery. A comparison study of velocity profiles, wall shear stress, and flow resistance for Newtonian, power law, Bingham-plastic, and Herschel-Bulkley fluids shows that the variation is greater for Herschel-Bulkley fluid than the other fluids. The obtained velocity profiles have been compared with the experimental data and it is observed that blood behaves like a Herschel-Bulkley fluid rather than power law, Bingham, and Newtonian fluids. It is observed that, in the case of a tapered stenosed tube, the streamline pattern follows a convex pattern when we move fromr/R=0tor/R=1and it follows a concave pattern when we move fromr/R=0tor/R=-1. Further, it is of opposite behaviour in the case of a tapered dilatation tube which forms new information that is, for the first time, added to the literature.

scholarly journals An Improved Weak Pressure Gradient Scheme for Single-Column Modeling

2014 ◽  
Vol 71 (7) ◽  
pp. 2415-2429 ◽  
Author(s):  
Jacob P. Edman ◽  
David M. Romps
Keyword(s):  
Pressure Gradient ◽  
Gravity Waves ◽  
Large Scale ◽  
Atmospheric Models ◽  
Wave Resonance ◽  
Single Column ◽  
The One ◽  
New Formulation ◽  
Weak Pressure Gradient ◽  
Steady State Solutions

Abstract A new formulation of the weak pressure gradient approximation (WPG) is introduced for parameterizing large-scale dynamics in limited-domain atmospheric models. This new WPG is developed in the context of the one-dimensional, linearized, damped, shallow-water equations and then extended to Boussinesq and compressible fluids. Unlike previous supradomain-scale parameterizations, this formulation of WPG correctly reproduces both steady-state solutions and first baroclinic gravity waves. In so doing, this scheme eliminates the undesirable gravity wave resonance in previous versions of WPG. In addition, this scheme can be extended to accurately model the emission of gravity waves with arbitrary vertical wavenumber.

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