Vertical discretizations giving optimal representation of normal modes: Sensitivity to the form of the pressure-gradient term

2006 ◽  
Vol 132 (621) ◽  
pp. 2809-2825 ◽  
Author(s):  
J. Thuburn
Keyword(s):  
Pressure Gradient ◽  
Normal Modes ◽  
Gradient Term ◽  
Optimal Representation ◽  
Pressure Gradient Term

scholarly journals Inherent dissipation of upwind-biased potential temperature advection and its feedback on model dynamics

2021 ◽  
Author(s):  
Almut Gaßmann
Keyword(s):  
Energy Conservation ◽  
Pressure Gradient ◽  
Potential Temperature ◽  
Gradient Term ◽  
Advection Scheme ◽  
Temperature Advection ◽  
Advection Schemes ◽  
Pressure Gradient Term ◽  
Diffusive Fluxes ◽  
Total Energy Conservation

<p>Higher order upwind biased advection schemes are often used for potential temperature advection in dynamical cores of atmospheric models. The inherent diffusive and anti-diffusive fluxes are interpreted here as the effect of irreversible sub-gridscale dynamics. For those, total energy conservation and positive internal entropy production must be guaranteed. As a consequence of energy conservation, the pressure gradient term should be formulated in Exner pressure form. The presence of local antidiffusive fluxes in potential temperature advection schemes foils the validity of the second law of thermodynamics. Due to this failure, a spurious wind acceleration into the wrong direction is locally induced via the pressure gradient term. When correcting the advection scheme to be more entropically consistent, the spurious acceleration is avoided, but two side effects come to the fore: (i) the overall accuracy of the advection scheme decreases and (ii) the now purely diffusive fluxes become more discontinuous compared to the original ones, which leads to more sudden body forces in the momentum equation. Therefore the amplitudes of excited gravity waves from jets and fronts increase compared to the original formulation with inherent local antidiffusive fluxes.</p><p>The means used for supporting the argumentation line are theoretical arguments concerning total energy conservation and internal entropy production, pure advection tests, one-dimensional advection-dynamics interaction tests and evaluation of runs with a global atmospheric dry dynamical core.</p>

scholarly journals Effects of Pressure Gradient on Convective Heat Transfer in a Boundary Layer Flow of a Maxwell Fluid Past a Stretching Sheet

2021 ◽  
Vol 26 (3) ◽  
pp. 104-118
Author(s):  
A.N. Kashif ◽  
F. Salah ◽  
D.S. Sankar ◽  
M.D.N. Izyan ◽  
K.K. Viswanathan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Stretching Sheet ◽  
Maxwell Fluid ◽  
Gradient Term ◽  
Pressure Gradient Term ◽  
Layer Flow

Abstract The pressure gradient term plays a vital role in convective heat transfer in the boundary layer flow of a Maxwell fluid over a stretching sheet. The importance of the effects of the term can be monitored by developing Maxwell’s equation of momentum and energy with the pressure gradient term. To achieve this goal, an approximation technique, i.e. Homotopy Perturbation Method (HPM) is employed with an application of algorithms of Adams Method (AM) and Gear Method (GM). With this approximation method we can study the effects of the pressure gradient (m), Deborah number (β), the ratio of the free stream velocity parameter to the stretching sheet parameter (ɛ) and Prandtl number (Pr) on both the momentum and thermal boundary layer thicknesses. The results have been compared in the absence and presence of the pressure gradient term m . It has an impact of thinning of the momentum and boundary layer thickness for non-zero values of the pressure gradient. The convergence of the system has been taken into account for the stretching sheet parameter ɛ. The result of the system indicates the significant thinning of the momentum and thermal boundary layer thickness in velocity and temperature profiles. On the other hand, some results show negative values of f '(η) and θ (η) which indicates the case of fluid cooling.

scholarly journals Semianalytical Solution of the Nonlinear Dual-Porosity Flow Model with the Quadratic Pressure Gradient Term

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Jiang-Tao Li ◽  
Ren-Shi Nie ◽  
Yong-Lu Jia ◽  
Dan-Ling Wang
Keyword(s):  
Pressure Gradient ◽  
Flow Model ◽  
Flow Behavior ◽  
Nonlinear Flow ◽  
Dual Porosity ◽  
Model Parameters ◽  
Gradient Term ◽  
Well Production ◽  
Pressure Gradient Term ◽  
Naturally Fractured

The nonlinear dual-porosity flow model, specifically considering the quadratic pressure gradient term, wellbore storage coefficient, well skin factor, and interporosity flow of matrix to natural fractures, was established for well production in a naturally fractured formation and then solved using a semianalytical method, including Laplace transform and a transformation of the pressure function. Analytical solution of the model in Laplace space was converted to numerical solution in real space using Stehfest numerical inversion. Nonlinear flow process for well production in a naturally fractured formation with different external boundaries was simulated and analyzed using standard pressure curves. Influence of the quadratic pressure gradient coefficient on pressure curves was studied qualitatively and quantitatively in conditions of a group of fixed model parameters. The research results show that the semianalytical modelling method is applicable in simulating the nonlinear dual-porosity flow behavior.

A Terrain-Following Coordinate with Smoothed Coordinate Surfaces

2011 ◽  
Vol 139 (7) ◽  
pp. 2163-2169 ◽  
Author(s):  
J. B. Klemp
Keyword(s):  
Pressure Gradient ◽  
Computational Cost ◽  
Alternative Form ◽  
Gradient Term ◽  
Horizontal Pressure Gradient ◽  
Pressure Gradient Term ◽  
Terrain Following ◽  
Horizontal Pressure

Abstract An alternative form for a height-based terrain-following coordinate is presented here that progressively smoothes the coordinate surfaces with height to remove smaller scale (steeper) terrain structure from the surfaces. Testing this approach in comparison with traditional and hybrid terrain-following formulations in resting-atmosphere simulations demonstrates that it can significantly reduce artificial circulations caused by inaccuracies in the horizontal pressure gradient term. The simulations also suggest that some further improvement in the accuracy of the horizontal pressure gradient terms can be achieved using a simplified version of Mahrer’s approach, which can be implemented with little increase in computational cost or complexity.

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