A Second Order Lagrangian Model for Irregular Ocean Waves

2005 ◽  
Vol 128 (3) ◽  
pp. 177-183 ◽  
Author(s):  
Sébastien Fouques ◽  
Harald E. Krogstad ◽  
Dag Myrhaug
Keyword(s):  
Specular Reflection ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Wave Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Lagrangian Model ◽  
Lagrangian Description ◽  
Linear Wave ◽  
Irregular Solution

Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.

An Approach to Parallel Computing in an Eulerian-Lagrangian Two-Phase Flow Model

2002 ◽  
Author(s):  
Marion W. Vance ◽  
Kyle D. Squires
Keyword(s):  
Collision Detection ◽  
Stokes Equations ◽  
Lagrangian Model ◽  
Rigid Sphere ◽  
Dispersed Phase ◽  
Particle Collisions ◽  
Two Phase ◽  
Current Effort ◽  
Index Method ◽  
Parallel Solution

An approach to parallel solution of an Eulerian-Lagrangian model of dilute gas-solid flows is presented. Using Lagrangian treatments for the dispersed phase, one of the principal computational challenges arises in models in which inter-particle interactions are taken into account. Deterministic treatment of particle-particle collisions in the present work pose the most computationally intensive aspect of the simulation. Simple searches lead to algorithms whose cost is O(N2p) where Np is the particle population. The approach developed in the current effort is based on localizing collision detection neighborhoods using a cell-index method and spatially distributing those neighborhoods for parallel solution. The method is evaluated using simulations of the gas-solid turbulent flow in a vertical channel. The instantaneous position and the velocity of any particle is obtained by solving the equation of motion for a small rigid sphere assuming that the resulting force induced by the fluid reduces to the drag contribution. Binary particle collisions without energy dissipation or inter-particle friction are considered. The carrier flow is computed using Large Eddy Simulation of the incompressible Navier-Stokes equations. The entire dispersed-phase population is partitioned via static spatial decomposition of the domain to maximize parallel efficiency. Simulations on small numbers of distributed memory processors show linear speedup in processing of the collision detection step and nearly optimal reductions in simulation time for the entire solution.

Case Study of Nanjing Inner Ring on Air Pollution Dispersion from Roadway Tunnel Portals

2012 ◽  
Vol 610-613 ◽  
pp. 1895-1900 ◽  
Author(s):  
Shu Jiang Miao ◽  
Da Fang Fu
Keyword(s):  
Air Pollution ◽  
Pollutant Dispersion ◽  
Air Pollutant ◽  
Urban Traffic ◽  
Lagrangian Model ◽  
Pollution Dispersion ◽  
Piecewise Function ◽  
Air Pollutant Dispersion ◽  
Air Pollution Dispersion

The tunnel module of a rather simple Lagrangian model GRAL (Grazer Langrange model) has been chosen to study air pollutant dispersion around tunnel portals in Nanjing inner ring. Two points have been made to popularize GRAL3.5TM (the tunnel module of a Lagrangian model GRAL; the update was in May 2003) and assure it more suitable for the actual situations in Nanjing. One is to derive a piecewise function of the intermediate parameter ‘stiffness’. Another is to take Romberg NOx-NO2 scheme into account. After these 2 works on GRAL3.5TM, NO2 dispersion from portals of all the 6 tunnels in Nanjing inner ring has been simulated. The importance of limiting urban traffic volume to control air quality around tunnel portals and roadways has been emphasized.

Evaluation of the performance of different short-range atmospheric dispersion models for the monitoring of CH4 emissions from industrial facilities

2021 ◽  
Author(s):  
Bonaventure Fontanier ◽  
Pramod Kumar ◽  
Grégoire Broquet ◽  
Christopher Caldow ◽  
Olivier Laurent ◽  
...  
Keyword(s):  
High Frequency ◽  
Meteorological Data ◽  
Atmospheric Dispersion ◽  
Local Scale ◽  
Lagrangian Model ◽  
Dispersion Models ◽  
Industrial Facilities ◽  
Gaussian Plume ◽  
Gaussian Puff ◽  
Gaussian Puff Model

<p>Methane (CH<sub>4</sub>) is a powerful greenhouse gas which plays a major role in climate change. The accurate monitoring of emissions from industrial facilities is needed to ensure efficient emission mitigation strategies. Local-scale atmospheric inversions are increasingly being used to provide estimates of the rates and/or locations of CH<sub>4</sub> sources from industrial sites. They rely on local-scale atmospheric dispersion models, CH<sub>4</sub> measurements and inversion approaches. Gaussian plume models have often been used for local-scale atmospheric dispersion modelling and inversions of emissions, because of their simplicity and good performance when used in a flat terrain and relatively constant mean wind conditions. However, even in such conditions, failure to account for wind and mole fraction variability can limit the ability to exploit the full potential of these measurements at high frequency.</p><p>We study whether the accuracy of inversions can be increased by the use of more complex dispersion models. Our assessments are based on the analysis of 25 to 75-min CH<sub>4 </sub>controlled releases during a one-week campaign in October 2019 at the TOTAL’s TADI operative platform in Lacq, France (in a flat area). During this campaign, for each controlled release, we conducted near-surface in situ measurements of CH<sub>4</sub> mole fraction from both a mobile vehicle and a circle of fixed points around the emission area. Our inversions based on a Gaussian model and either the mobile or fixed-point measurements both provided estimates of the release rates with 20-30% precision.  </p><p>Here we focus on comparisons between modeling and inversion results when using this Gaussian plume model, a Lagrangian model “GRAL” and a Gaussian puff model. The parameters for the three models are based on high-frequency meteorological values from a single stationary 3D sonic anemometer. GRAL should have relatively good skills under low-wind speed conditions. The Gaussian puff is a light implementation of time-dependent modeling and can be driven by high-frequency meteorological data. The performance of these dispersion models is evaluated with various metrics from the observation field that are relevant for the inversion. These analyses lead to the exploration of new types of definitions of the observational constraint for the inversions with the Gaussian puff model, when using the timeseries from fixed measurement points. The definitions explore a range of metrics in the time domain as well as in the frequency domain.</p><p>Eventually, the Lagrangian model does not outperform the Gaussian plume model in these experiments, its application being notably limited by the short scales of the transport characteristics. On the other hand, the Gaussian puff model provides promising results for the inversion, in particular, in terms of comparison between the simulated and observed timeseries for fixed stations. Its performance when driven by a spatially uniform wind field is an incentive to explore the use of meteorological data from several sonic stations to parameterize its configuration. The fixed-point measurements are shown to allow for more robust inversions of the source location than the mobile measurements, with an average source localization error of the order of 10 m.</p>

scholarly journals A global analysis of the atmospheric pollutant modeling

2007 ◽  
Vol 22 (1) ◽  
pp. 1-9
Author(s):  
Umberto Rizza ◽  
Jonas C. Carvalho ◽  
Davidson M. Moreira ◽  
Marcelo R. Moraes ◽  
Antônio G. Goulart
Keyword(s):  
Global Analysis ◽  
Turbulent Transport ◽  
Three Dimensional ◽  
Ground Level ◽  
Lagrangian Model ◽  
Linear Superposition ◽  
Atmospheric Pollutant ◽  
Advection Diffusion Equation ◽  
Laplace Transform Technique ◽  
The Laplace Transform

In this article is carried out a comparison between Lagrangian and Eulerian modelling of the turbulent transport of pollutants within the Planetary Boundary Layer (PBL). The Lagrangian model is based on a three-dimensional form of the Langevin equation for the random velocity. The Eulerian analytical model is based on a discretization of the PBL in N sub-layers; in each of the sub-layers the advection-diffusion equation is solved by the Laplace transform technique. In the Eulerian numerical model the advective terms are solved using the cubic spline method while a Crank-Nicholson scheme is used for the diffusive terms. The models use a turbulence parameterization that considers a spectrum model, which is given by a linear superposition of the buoyancy and mechanical effects. Observed ground-level concentrations measured in a dispersion field experiment are used to evaluate the simulations.

scholarly journals Simulation of denitrification and ozone loss for the Arctic winter 2002/2003

2005 ◽  
Vol 5 (6) ◽  
pp. 1437-1448 ◽  
Author(s):  
J.-U. Grooß ◽  
G. Günther ◽  
R. Müller ◽  
P. Konopka ◽  
S. Bausch ◽  
...  
Keyword(s):  
Inorganic Nitrogen ◽  
Potential Temperature ◽  
Three Dimensional ◽  
Lagrangian Model ◽  
The Arctic ◽  
Particle Nucleation ◽  
Ozone Loss ◽  
Dimensional Version ◽  
Total Inorganic Nitrogen ◽  
Catalytic Cycles

Abstract. We present simulations with the Chemical Lagrangian Model of the Stratosphere (CLaMS) for the Arctic winter 2002/2003. We integrated a Lagrangian denitrification scheme into the three-dimensional version of CLaMS that calculates the growth and sedimentation of nitric acid trihydrate (NAT) particles along individual particle trajectories. From those, we derive the HNO3 downward flux resulting from different particle nucleation assumptions. The simulation results show a clear vertical redistribution of total inorganic nitrogen ( ), with a maximum vortex average permanent removal of over 5ppb in late December between 500 and 550K and a corresponding increase of of over 2ppb below about 450K. The simulated vertical redistribution of is compared with balloon observations by MkIV and in-situ observations from the high altitude aircraft Geophysica. Assuming a globally uniform NAT particle nucleation rate of 7.8x10-6cm-3h-1 in the model, the observed denitrification is well reproduced. In the investigated winter 2002/2003, the denitrification has only moderate impact (≤14%) on the simulated vortex average ozone loss of about 1.1ppm near the 460K level. At higher altitudes, above 600K potential temperature, the simulations show significant ozone depletion through -catalytic cycles due to the unusual early exposure of vortex air to sunlight.

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