scholarly journals Estimation of friction parameters in gravity currents by data assimilation in a model hierarchy

2011 ◽  
Vol 8 (1) ◽  
pp. 159-187 ◽  
Author(s):  
A. Wirth
Keyword(s):  
Data Assimilation ◽  
Gravity Current ◽  
Gravity Currents ◽  
Water Model ◽  
Friction Laws ◽  
Quadratic Drag ◽  
Small Reynolds Numbers ◽  
Model Hierarchy ◽  
Using Data ◽  
Friction Parameters

Abstract. This paper is the last in a series of three investigating the friction laws and their parametrisation in idealised gravity currents in a rotating frame. Results on the dynamics of a gravity current (Wirth, 2009) and on the estimation of friction laws by data assimilation (Wirth and Verron, 2008) are combined to estimate the friction parameters and discriminate between friction laws in non-hydrostatic numerical simulations of gravity current dynamics, using data assimilation and a reduced gravity shallow water model. I demonstrate, that friction parameters and laws in gravity currents can be estimated using data assimilation. The results clearly show that friction follows a linear Rayleigh law for small Reynolds numbers and the estimated value agrees well with the analytical value obtained for non-accelerating Ekman layers. A significant and sudden departure towards a quadratic drag law at an Ekman layer based Reynolds number of around 800 is shown, in agreement with classical laboratory experiments. The drag coefficient obtained compare well to friction values over smooth surfaces. I show that data assimilation can be used to determine friction parameters and discriminate between friction laws and that it is a powerful tool in systematically connection models within a model hierarchy.

scholarly journals Estimation of friction parameters in gravity currents by data assimilation in a model hierarchy

Ocean Science ◽  
2011 ◽  
Vol 7 (2) ◽  
pp. 245-255 ◽  
Author(s):  
A. Wirth
Keyword(s):  
Data Assimilation ◽  
Gravity Current ◽  
Gravity Currents ◽  
Water Model ◽  
Friction Laws ◽  
Quadratic Drag ◽  
Small Reynolds Numbers ◽  
Model Hierarchy ◽  
Using Data ◽  
Friction Parameters

Abstract. This paper is the last in a series of three investigating the friction laws and their parametrisation in idealised gravity currents in a rotating frame. Results on the dynamics of a gravity current (Wirth, 2009) and on the estimation of friction laws by data assimilation (Wirth and Verron, 2008) are combined to estimate the friction parameters and discriminate between friction laws in non-hydrostatic numerical simulations of gravity current dynamics, using data assimilation and a reduced gravity shallow water model. I demonstrate, that friction parameters and laws in gravity currents can be estimated using data assimilation. The results clearly show that friction follows a linear Rayleigh law for small Reynolds numbers and the estimated value agrees well with the analytical value obtained for non-accelerating Ekman layers. A significant and sudden departure towards a quadratic drag law at an Ekman layer based Reynolds number of around 800 is shown, in agreement with classical laboratory experiments. The drag coefficient obtained compares well to friction values over smooth surfaces. I show that data assimilation can be used to determine friction parameters and discriminate between friction laws and that it is a powerful tool in systematically connecting models within a model hierarchy.

Entraining gravity currents

2013 ◽  
Vol 731 ◽  
pp. 477-508 ◽  
Author(s):  
Christopher G. Johnson ◽  
Andrew J. Hogg
Keyword(s):  
Richardson Number ◽  
Solution Structure ◽  
Large Scale ◽  
Gravity Current ◽  
Gravity Currents ◽  
Similarity Solutions ◽  
Water Model ◽  
Experimental Measurements ◽  
Entrainment Rate ◽  
Long Time

AbstractEntrainment of ambient fluid into a gravity current, while often negligible in laboratory-scale flows, may become increasingly significant in large-scale natural flows. We present a theoretical study of the effect of this entrainment by augmenting a shallow water model for gravity currents under a deep ambient with a simple empirical model for entrainment, based on experimental measurements of the fluid entrainment rate as a function of the bulk Richardson number. By analysing long-time similarity solutions of the model, we find that the decrease in entrainment coefficient at large Richardson number, due to the suppression of turbulent mixing by stable stratification, qualitatively affects the structure and growth rate of the solutions, compared to currents in which the entrainment is taken to be constant or negligible. In particular, mixing is most significant close to the front of the currents, leading to flows that are more dilute, deeper and slower than their non-entraining counterparts. The long-time solution of an inviscid entraining gravity current generated by a lock-release of dense fluid is a similarity solution of the second kind, in which the current grows as a power of time that is dependent on the form of the entrainment law. With an entrainment law that fits the experimental measurements well, the length of currents in this entraining inviscid regime grows with time approximately as ${t}^{0. 447} $. For currents instigated by a constant buoyancy flux, a different solution structure exists in which the current length grows as ${t}^{4/ 5} $. In both cases, entrainment is most significant close to the current front.

scholarly journals Enhancing CFD-LES air pollution prediction accuracy using data assimilation

2019 ◽  
Vol 165 ◽  
pp. 106383 ◽  
Author(s):  
Elsa Aristodemou ◽  
Rossella Arcucci ◽  
Laetitia Mottet ◽  
Alan Robins ◽  
Christopher Pain ◽  
...  
Keyword(s):  
Air Pollution ◽  
Data Assimilation ◽  
Prediction Accuracy ◽  
Using Data ◽  
Air Pollution Prediction ◽  
Pollution Prediction

scholarly journals Gravity currents and internal waves in a stratified fluid

2008 ◽  
Vol 616 ◽  
pp. 327-356 ◽  
Author(s):  
BRIAN L. WHITE ◽  
KARL R. HELFRICH
Keyword(s):  
Internal Waves ◽  
Wave Speed ◽  
Numerical Solutions ◽  
Gravity Current ◽  
Gravity Currents ◽  
Stratified Fluid ◽  
Front Speed ◽  
Long Wave ◽  
Conjugate State ◽  
Energy Conserving

A steady theory is presented for gravity currents propagating with constant speed into a stratified fluid with a general density profile. Solution curves for front speed versus height have an energy-conserving upper bound (the conjugate state) and a lower bound marked by the onset of upstream influence. The conjugate state is the largest-amplitude nonlinear internal wave supported by the ambient stratification, and in the limit of weak stratification approaches Benjamin's energy-conserving gravity current solution. When the front speed becomes critical with respect to linear long waves generated above the current, steady solutions cannot be calculated, implying upstream influence. For non-uniform stratification, the critical long-wave speed exceeds the ambient long-wave speed, and the critical-Froude-number condition appropriate for uniform stratification must be generalized. The theoretical results demonstrate a clear connection between internal waves and gravity currents. The steady theory is also compared with non-hydrostatic numerical solutions of the full lock release initial-value problem. Some solutions resemble classic gravity currents with no upstream disturbance, but others show long internal waves propagating ahead of the gravity current. Wave generation generally occurs when the stratification and current speed are such that the steady gravity current theory fails. Thus the steady theory is consistent with the occurrence of either wave-generating or steady gravity solutions to the dam-break problem. When the available potential energy of the dam is large enough, the numerical simulations approach the energy-conserving conjugate state. Existing laboratory experiments for intrusions and gravity currents produced by full-depth lock exchange flows over a range of stratification profiles show excellent agreement with the conjugate state solutions.

Balanced Ocean-Data Assimilation near the Equator

2002 ◽  
Vol 32 (9) ◽  
pp. 2509-2519 ◽  
Author(s):  
Gerrit Burgers ◽  
Magdalena A. Balmaseda ◽  
Femke C. Vossepoel ◽  
Geert Jan van Oldenborgh ◽  
Peter Jan van Leeuwen
Keyword(s):  
Data Assimilation ◽  
Shallow Water ◽  
General Circulation ◽  
General Circulation Models ◽  
Density Field ◽  
Water Model ◽  
Optimal Interpolation ◽  
Shallow Water Model ◽  
Ocean Data Assimilation ◽  
Zonal Velocity

Abstract The question is addressed whether using unbalanced updates in ocean-data assimilation schemes for seasonal forecasting systems can result in a relatively poor simulation of zonal currents. An assimilation scheme, where temperature observations are used for updating only the density field, is compared to a scheme where updates of density field and zonal velocities are related by geostrophic balance. This is done for an equatorial linear shallow-water model. It is found that equatorial zonal velocities can be detoriated if velocity is not updated in the assimilation procedure. Adding balanced updates to the zonal velocity is shown to be a simple remedy for the shallow-water model. Next, optimal interpolation (OI) schemes with balanced updates of the zonal velocity are implemented in two ocean general circulation models. First tests indicate a beneficial impact on equatorial upper-ocean zonal currents.

Study on the transport of COD in the sea area around Maidao off Qingdao coast using data assimilation

2007 ◽  
Vol 6 (4) ◽  
pp. 339-344 ◽  
Author(s):  
Qiang Zhao ◽  
Xiaomin Hu ◽  
Xianqing Lü ◽  
Xuejun Xiong ◽  
Bo Yang
Keyword(s):  
Data Assimilation ◽  
Qingdao Coast ◽  
Using Data ◽  
Sea Area

Aerosol Data Assimilation Using Data from Fengyun-3A and MODIS: Application to a Dust Storm over East Asia in 2011

2018 ◽  
Vol 36 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Xiaoli Xia ◽  
Jinzhong Min ◽  
Feifei Shen ◽  
Yuanbing Wang ◽  
Chun Yang
Keyword(s):  
Data Assimilation ◽  
East Asia ◽  
Dust Storm ◽  
Using Data

scholarly journals Data assimilation for volcanic ash plumes using a satellite observational operator: a case study on the 2010 Eyjafjallajökull volcanic eruption

2017 ◽  
Vol 17 (2) ◽  
pp. 1187-1205 ◽  
Author(s):  
Guangliang Fu ◽  
Fred Prata ◽  
Hai Xiang Lin ◽  
Arnold Heemink ◽  
Arjo Segers ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Volcanic Ash ◽  
Three Dimensional ◽  
Forecast Accuracy ◽  
Improve Model ◽  
Powerful Approach ◽  
Using Data ◽  
D Model

Abstract. Using data assimilation (DA) to improve model forecast accuracy is a powerful approach that requires available observations. Infrared satellite measurements of volcanic ash mass loadings are often used as input observations for the assimilation scheme. However, because these primary satellite-retrieved data are often two-dimensional (2-D) and the ash plume is usually vertically located in a narrow band, directly assimilating the 2-D ash mass loadings in a three-dimensional (3-D) volcanic ash model (with an integral observational operator) can usually introduce large artificial/spurious vertical correlations.In this study, we look at an approach to avoid the artificial vertical correlations by not involving the integral operator. By integrating available data of ash mass loadings and cloud top heights, as well as data-based assumptions on thickness, we propose a satellite observational operator (SOO) that translates satellite-retrieved 2-D volcanic ash mass loadings to 3-D concentrations. The 3-D SOO makes the analysis step of assimilation comparable in the 3-D model space.Ensemble-based DA is used to assimilate the extracted measurements of ash concentrations. The results show that satellite DA with SOO can improve the estimate of volcanic ash state and the forecast. Comparison with both satellite-retrieved data and aircraft in situ measurements shows that the effective duration of the improved volcanic ash forecasts for the distal part of the Eyjafjallajökull volcano is about 6 h.

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