scholarly journals Towards the closure of momentum budget analyses in the WRF (v3.8.1) model

2020 ◽  
Vol 13 (3) ◽  
pp. 1737-1761
Author(s):  
Ting-Chen Chen ◽  
Man-Kong Yau ◽  
Daniel J. Kirshbaum
Keyword(s):  
Wrf Model ◽  
Retrieval Method ◽  
Residual Term ◽  
Numerical Studies ◽  
Budget Analysis ◽  
Momentum Budget ◽  
Simulated System ◽  
Slantwise Convection ◽  
The One ◽  
General Guidance

Abstract. Budget analysis of a tendency equation is widely utilized in numerical studies to quantify different physical processes in a simulated system. While such analysis is often post-processed when the output is made available, it is well acknowledged that the closure of a budget is difficult to achieve without temporal and/or spatial averaging. Nevertheless, the development of errors in such calculations has not been systematically investigated. In this study, an inline budget retrieval method is first developed in the WRF v3.8.1 model and tested on a 2D idealized slantwise convection case with a focus on the momentum equations. This method extracts all the budget terms following the model solver, which gives a high accuracy, with a residual term always less than 0.1 % of the tendency term. Then, taking the inline values as truth, several offline budget analyses with different commonly used simplifications are performed to investigate how they may affect the accuracy of the estimation of individual terms and the resultant residual. These assumptions include using a lower-order advection operator than the one used in the model, neglecting grid staggering, or following a mathematically equivalent but transformed format of the governing equations. Errors in these post-processed analyses are found mostly over the area where the dynamics are the most active, thus impairing the subsequent physical interpretation. A maximum 99th percentile residual can reach >50 % of the concurrent tendency term, indicating the danger of neglecting the residual term as done in many budget studies. This work provides general guidance not only for budget diagnoses with the WRF model but also for minimizing the errors in post-processed budget calculations.

scholarly journals Towards the closure of momentum budget analyses in the WRF (v3.8.1) model

2019 ◽  
Author(s):  
Ting-Chen Chen ◽  
Man K. Yau ◽  
Daniel J. Kirshbaum
Keyword(s):  
Wrf Model ◽  
Post Processing ◽  
Retrieval Method ◽  
Residual Term ◽  
Numerical Studies ◽  
Budget Analysis ◽  
Momentum Budget ◽  
Slantwise Convection ◽  
The One ◽  
General Guidance

Abstract. Budget analysis of a tendency equation is widely utilized in numerical studies to quantify different physical processes in a simulated system. While such analysis is often post-processed when the output is made available, it is well-acknowledged that the closure of a budget is difficult to achieve without averaging. Nevertheless, the potential rise of the errors in such calculation has not been systematically investigated. In this study, an inline budget retrieval method is first developed in the WRF v3.8.1 model and tested on a 2D idealized slantwise convection case with a focus on the momentum equations. This method extracts all the budget terms following the model solver, which gives a high accuracy with a residual term always less than 0.02 % of the tendency term. Then, taking the inline values as truth, several post-processing budget analyses with different commonly-used simplifications are performed to investigate how they may affect the accuracy of the estimation of individual terms and the resultant residual. These assumptions include using a lower order advection operator than the one used in the model, neglecting the C staggering grids, or following a mathematically-equivalent but transformed format of equation. Errors in these post-processed analyses are found mostly over the area where the dynamics are the most active, impairing the subsequent physical interpretation. A maximum 99th percentile residual can reach 800 % of the concurrent tendency term, indicating the danger of neglecting the residual term as done in many budget studies. This work provides general guidance not only for applying an inline budget retrieval to the WRF model but for minimizing the errors in post-processing budget calculations.

scholarly journals On the Two-phase Fractional Stefan Problem

2020 ◽  
Vol 20 (2) ◽  
pp. 437-458 ◽  
Author(s):  
Félix del Teso ◽  
Jørgen Endal ◽  
Juan Luis Vázquez
Keyword(s):  
Free Boundary ◽  
Stefan Problem ◽  
Free Boundary Problems ◽  
Classical Problem ◽  
Nonlocal Diffusion ◽  
Two Phase ◽  
Boundary Problems ◽  
Numerical Studies ◽  
The One ◽  
Evolution Type

AbstractThe classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion. We start the paper by reviewing the main properties of the classical problem that are of interest to us. Then we introduce the fractional Stefan problem and develop the basic theory. After that we center our attention on selfsimilar solutions, their properties and consequences. We first discuss the results of the one-phase fractional Stefan problem, which have recently been studied by the authors. Finally, we address the theory of the two-phase fractional Stefan problem, which contains the main original contributions of this paper. Rigorous numerical studies support our results and claims.

A parameterization of slantwise convection in the WRF model

2021 ◽  
Author(s):  
Ting-Chen Chen ◽  
Man-Kong Yau ◽  
Daniel J. Kirshbaum
Keyword(s):  
General Circulation ◽  
Wrf Model ◽  
Real Data ◽  
General Circulation Models ◽  
Added Value ◽  
Cumulus Parameterization ◽  
Moisture Loss ◽  
Precipitation Event ◽  
Cyclonic Storm ◽  
Slantwise Convection

Abstract In this study, we introduce a parameterization scheme for slantwise convection (SC) to be considered for models that are too coarse to resolve slantwise convection explicitly (with a horizontal grid spacing coarser than 15 km or less). This SC scheme operates in a locally defined 2D cross-section perpendicular to the deep-layer-averaged thermal wind. It applies momentum tendency to adjust the environment toward slantwise neutrality with a prescribed adjustment timescale. Condensational heating and the associated moisture loss are also considered. To evaluate the added value of the SC scheme, we implement it in the Weather Research and Forecasting (WRF) model to supplement the existing cumulus parameterization schemes for upright convection and test for two different numerical setups: a 2D idealized, unforced release of conditional symmetric instability (CSI) in an initially conditionally stable environment, and a 3D real-data precipitation event containing both CSI and conditional instability along the cold front of a cyclonic storm near the UK. Both test cases show significant improvements for the coarse-gridded (40-km) simulations when parameterizing slantwise convection. Compared to the 40-km simulations with only the upright convection scheme, the counterparts with the additional SC scheme exhibit a larger extent of CSI neutralization, generate a stronger grid-resolved slantwise circulation, and produce greater amounts of precipitation, all in better agreement with the corresponding fine-gridded reference simulations. Given the importance of slantwise convection in midlatitude weather systems, our results suggest that there exist potential benefits of parameterizing slantwise convection in general circulation models.

BOSE–EINSTEIN CONDENSATION IN BULK AND CONFINED SOLID HELIUM

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5081-5092 ◽  
Author(s):  
L. REATTO ◽  
M. ROSSI ◽  
D. E. GALLI
Keyword(s):  
Wave Function ◽  
Ground State ◽  
Solid Helium ◽  
System Size ◽  
Einstein Condensation ◽  
Cylindrical Pore ◽  
Simulated System ◽  
The One ◽  
Bose Einstein ◽  
Energy Computation

We address the question if the ground state of solid 4 He has the number of lattice sites equal to the number of atoms (commensurate state) or if it is different (incommensurate state). We point out that energy computation from simulation as performed by now cannot be used to decide this question and that the presently best variational wave function, a shadow wave function, gives an incommensurate state. We have extended the calculation of the one–body density matrix ρ1 to the exact Shadow Path Integral Ground State method. Calculation of ρ1 at ρ = 0.031 Å-3 shows that Vacancy–Interstitial pair processes are present also in the exact computation but the simulated system size is too small to infer the presence of off–diagonal long range order. Variational simulations of 4 He confined in a narrow cylindrical pore are also discussed.

A New Damage Detection Method for Aging Offshore Platform Using Two Measurements

2013 ◽  
Vol 479-480 ◽  
pp. 1185-1189
Author(s):  
Fu Shun Liu ◽  
Wen Wen Chen ◽  
Dong Ping Yang ◽  
Jun Fei Qin ◽  
Zhan Gang Yue ◽  
...  
Keyword(s):  
Damage Detection ◽  
Damage Assessment ◽  
Assessment Method ◽  
Offshore Platforms ◽  
Correction Factors ◽  
Dynamic Tests ◽  
Severity Estimation ◽  
Numerical Studies ◽  
Damage Indicator ◽  
The One

A new damage assessment method is proposed for aging offshore platforms based on dynamic tests. The stiff nesses of the measured model corresponding to the two measurement moments are estimated by a series of stiffness-correction factors, respectively. Based on these stiffness-correction factors a new damage indicator is defined aiming at reducing influences of existed damages accumulated before the first measurement on damage assessment occurred between the two adjacent measurements. One theoretical improvement is that the requirement using the stiffness matrix of FEM to replace the one of the measured model can be ignored in the calculation of MSE of the measured model. The other development is influences of damages accumulated before the first measurement on damage detection occurs between the two measurements could be reduced greatly, which is very important for aging platforms because these platforms have not been tested aiming at damage detection during their previous service life, especially for most platforms in China. A jacket platform is chosen for numerical studies, and numerical results show that the proposed method could identify damages occurred between the two measurements properly, even including damage severity estimation.

scholarly journals Axisymmetric simulation of viscoelastic filament thinning with the Oldroyd-B model

2018 ◽  
Vol 851 ◽  
Author(s):  
Emre Turkoz ◽  
Jose M. Lopez-Herrera ◽  
Jens Eggers ◽  
Craig B. Arnold ◽  
Luc Deike
Keyword(s):  
Stress Component ◽  
Fluid Flows ◽  
Theoretical Description ◽  
Slender Body ◽  
Complex Materials ◽  
Two Phase ◽  
Practical Applications ◽  
Numerical Studies ◽  
Fundamental Understanding ◽  
The One

A fundamental understanding of the filament thinning of viscoelastic fluids is important in practical applications such as spraying and printing of complex materials. Here, we present direct numerical simulations of the two-phase axisymmetric momentum equations using the volume-of-fluid technique for interface tracking and the log-conformation transformation to solve the viscoelastic constitutive equation. The numerical results for the filament thinning are in excellent agreement with the theoretical description developed with a slender body approximation. We show that the off-diagonal stress component of the polymeric stress tensor is important and should not be neglected when investigating the later stages of filament thinning. This demonstrates that such numerical methods can be used to study details not captured by the one-dimensional slender body approximation, and pave the way for numerical studies of viscoelastic fluid flows.

scholarly journals Response of Near-Surface Meteorological Conditions to Advection under Impact of the Green Roof

Atmosphere ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 759
Author(s):  
Haochen Tan ◽  
Pallav Ray ◽  
Mukul Tewari ◽  
James Brownlee ◽  
Ajaya Ravindran
Keyword(s):  
Surface Temperature ◽  
Urban Areas ◽  
Green Roof ◽  
Wrf Model ◽  
Single Layer ◽  
Meteorological Conditions ◽  
Rapid Urbanization ◽  
Near Surface ◽  
Budget Analysis ◽  
The Impact

Due to rapid urbanization, the near-surface meteorological conditions over urban areas are greatly modulated. To capture such modulations, sophisticated urban parameterizations with enhanced hydrological processes have been developed. In this study, we use the single-layer urban canopy model (SLUCM) available within the Weather Research and Forecasting (WRF) model to assess the response of near-surface temperature, wind, and moisture to advection under the impact of the green roof. An ensemble of simulations with different planetary boundary layer (PBL) schemes is conducted in the presence (green roof (GR)) and absence (control (CTL)) of green roof systems. Our results indicate that the near-surface temperature is found to be driven primarily by the surface heat flux with a minor influence from the zonal advection of temperature. The momentum budget analysis shows that both zonal and meridional momentum advection during the evening and early nighttime plays an important role in modulating winds over urban areas. The near-surface humidity remains nearly unchanged in GR compared to CTL, although the physical processes that determine the changes in humidity were different, in particular during the evening when the GR tends to have less moisture advection due to the reduced temperature gradient between the urban areas and the surroundings. Implications of our results are discussed.

Experimental investigation on the secondary instability of liquid-fluidized beds and the formation of bubbles

2002 ◽  
Vol 470 ◽  
pp. 359-382 ◽  
Author(s):  
PAUL DURU ◽  
ÉLISABETH GUAZZELLI
Keyword(s):  
Fluidized Beds ◽  
Secondary Instability ◽  
Analytical Models ◽  
Physical Origin ◽  
Weakly Nonlinear ◽  
One Dimensional ◽  
Numerical Studies ◽  
Wavy Structure ◽  
Nonlinear Simulations ◽  
The One

The objective of the present work is to investigate experimentally the secondary instability of the one-dimensional voidage waves occurring in two-dimensional liquid- fluidized beds and to examine the physical origin of bubbles, i.e. regions devoid of particles, which arise in fluidization. In the case of moderate-density glass particles, we observe the formation of transient buoyant blobs clearly resulting from the destabilization of the one-dimensional wavy structure. With metallic beads of the same size but larger density, the same destabilization occurs but it leads to the formation of real bubbles. Comparison with previous analytical and numerical studies is attempted. Whereas the linear and weakly nonlinear analytical models are not appropriate, the direct nonlinear simulations provide a qualitative agreement with the observed destabilization mechanism.

NUMERICAL STUDIES ON THE VIBRATIONAL SPECTRUM OF FIBONACCI CHAIN: A MULTIFRACTAL ANALYSIS

1991 ◽  
Vol 05 (05) ◽  
pp. 825-841 ◽  
Author(s):  
WLODZIMIERZ SALEJDA
Keyword(s):  
Vibrational Spectrum ◽  
Multifractal Analysis ◽  
Scaling Laws ◽  
Model Parameters ◽  
Local Scaling ◽  
One Dimensional ◽  
Dynamic Matrix ◽  
Numerical Studies ◽  
Wide Range ◽  
The One

A harmonic Hamiltonian modelling the lattice dynamics of the one-dimensional Fibonacci-type quasicrystal is studied numerically. The multifractal analysis of vibrational spectrum is performed. It is found that the integrated normalized density of states [Formula: see text], where x denotes the square of the eigenenergy of the dynamic matrix, exhibits a finite range of scaling indices α (i.e. α min ≤α≤ α max ) describing the local scaling laws of [Formula: see text]. The α-f spectra and the Renyi dimensions [Formula: see text] are calculated in a wide range of model parameters taking into account the next-nearest-neighbour (NNN) interactions of atoms. In particular, we have observed that: (1) The α-f spectra are smooth in the interval [Formula: see text]; (2) If the so-called parameter of quasi-periodicity Q increases, then αmin and the fractal dimension of vibrational spectra [Formula: see text] decrease; (3) If the strength of NNN interactions h grows then α min decreases but D increases.

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