Stochastic dynamics and model reduction of amplifier flows: the backward facing step flow

2013 ◽  
Vol 719 ◽  
pp. 406-430 ◽  
Author(s):  
G. Dergham ◽  
D. Sipp ◽  
J.-Ch. Robinet
Keyword(s):  
Stochastic Dynamics ◽  
Empirical Orthogonal Functions ◽  
Backward Facing Step ◽  
Orthogonal Functions ◽  
Step Flow ◽  
Flow Response ◽  
Entire Flow ◽  
Random Flow ◽  
Value Decomposition ◽  
And Diffusion

AbstractMethods for investigating and approximating the linear dynamics of amplifier flows are examined in this paper. The procedures are derived for incompressible flow over a two-dimensional backward-facing step. First, the singular value decomposition of the resolvent is performed over a frequency range in order to identify the optimal and suboptimal harmonic forcing and responses of the flow. These forcing/responses are shown to be organized into two categories: the first accounting for the Orr and Kelvin–Helmholtz instabilities in the shear layer and the second for the advection and diffusion of perturbations in the free stream. Next, we investigate the dynamics of the flow when excited by a white in space and time noise. We compute the predominant patterns of the random flow which optimally account for the sustained variance, the empirical orthogonal functions (EOFs), as well as the predominant forcing structures which optimally contribute to the sustained variance, the stochastic optimals (SOs). The leading EOFs and SOs are expressed as a linear combination of the suboptimal forcing and responses of the flow and are related to particular instability mechanisms and/or frequency intervals. Finally, we use the leading EOFs, SOs and balanced modes (obtained from balanced truncation) to build low-order models of the flow dynamics. These models are shown to accurately recover the time propagator and resolvent of the original dynamical system. In other words, such models capture the entire flow response from any forcing and may be used in the design of efficient closed-loop controllers for amplifier flows.

Eigen-glaciers: elucidating hidden features in the flow of Sermeq Kujalleq (Jakobshavn Glacier), Greenland.

2021 ◽  
Author(s):  
David Ashmore ◽  
Douglas Mair ◽  
Jonathan Higham ◽  
Stephen Brough ◽  
James Lea ◽  
...  
Keyword(s):  
Flow Field ◽  
Environmental Flows ◽  
Empirical Orthogonal Functions ◽  
Orthogonal Functions ◽  
Ice Dynamics ◽  
Relative Contribution ◽  
Glacier Terminus ◽  
Hydrological System ◽  
Ice Velocity ◽  
Value Decomposition

<p>The increasing volume and spatio-temporal resolution of satellite-derived ice velocity data has created new exploratory opportunities for the quantitative analysis of glacier dynamics. One potential technique, Proper Orthogonal Decomposition (POD), also known as Empirical Orthogonal Functions, has proven to be a powerful and flexible technique for revealing coherent structures in a wide variety of environmental flows: mapping hydraulic vortex shedding patterns, the dynamics of fluidised granular beds, and the magnetohydrodynamics of sunspots.</p><p>POD exactly describes a series of snapshots from a flow field with the product of ranked spatially orthogonal Eigenfunctions, or “modes” of spatial weighting, and one-dimensional “temporal” coefficients (Eigenvectors). In many cases the variance of the flow field is well described by just a few dominant modes. The orthogonal nature of each mode, by definition, means that the relative contribution of independent forcing mechanisms on the flow can, in theory, be separated.</p><p>In this study we investigate the applicability of POD to freely available TanDEM-X/TerraSAR-X derived ice velocity datasets of Sermeq Kujalleq (Jakobshavn Glacier), Greenland. We outline the POD procedure using the singular value decomposition of a rearranged and resampled velocity matrix and investigate the factors responsible for the dominant modes. We find dominant modes interpreted as relating to the stress-reconfiguration at the glacier terminus and the development of the glacier hydrological system, but also find that the POD is sensitive to data resampling and quality. With the proliferation of publicly available optical and radar derived velocity products (e.g. MEaSUREs/ESA CCI) we suggest POD, and potentially other modal decomposition techniques, will become increasingly useful in future studies of ice dynamics.</p>

Empirical Methods in Short-Term Climate Prediction

2006 ◽  
Author(s):  
Huug van den Dool
Keyword(s):  
Climate Prediction ◽  
Empirical Orthogonal Functions ◽  
Data Sets ◽  
Seasonal Forecasts ◽  
Short Term ◽  
Orthogonal Functions ◽  
Ocean Atmosphere Interaction ◽  
Global Coverage ◽  
Atmosphere Interaction ◽  
Global Data

This clear and accessible text describes the methods underlying short-term climate prediction at time scales of 2 weeks to a year. Although a difficult range to forecast accurately, there have been several important advances in the last ten years, most notably in understanding ocean-atmosphere interaction (El Nino for example), the release of global coverage data sets, and in prediction methods themselves. With an emphasis on the empirical approach, the text covers in detail empirical wave propagation, teleconnections, empirical orthogonal functions, and constructed analogue. It also provides a detailed description of nearly all methods used operationally in long-lead seasonal forecasts, with new examples and illustrations. The challenges of making a real time forecast are discussed, including protocol, format, and perceptions about users. Based where possible on global data sets, illustrations are not limited to the Northern Hemisphere, but include several examples from the Southern Hemisphere.

scholarly journals Spatio-Temporal Patterns of Mass Changes in Himalayan Glaciated Region from EOF Analyses of GRACE Data

2021 ◽  
Vol 13 (2) ◽  
pp. 265
Author(s):  
Harika Munagapati ◽  
Virendra M. Tiwari
Keyword(s):  
Temperature Anomaly ◽  
Mass Gain ◽  
Snow Accumulation ◽  
Empirical Orthogonal Functions ◽  
Total Water ◽  
Orthogonal Functions ◽  
Grace Data ◽  
Grace Satellite ◽  
Spatio Temporal ◽  
Gravity Recovery

The nature of hydrological seasonality over the Himalayan Glaciated Region (HGR) is complex due to varied precipitation patterns. The present study attempts to exemplify the spatio-temporal variation of hydrological mass over the HGR using time-variable gravity from the Gravity Recovery and Climate Experiment (GRACE) satellite for the period of 2002–2016 on seasonal and interannual timescales. The mass signal derived from GRACE data is decomposed using empirical orthogonal functions (EOFs), allowing us to identify the three broad divisions of HGR, i.e., western, central, and eastern, based on the seasonal mass gain or loss that corresponds to prevailing climatic changes. Further, causative relationships between climatic variables and the EOF decomposed signals are explored using the Granger causality algorithm. It appears that a causal relationship exists between total precipitation and total water storage from GRACE. EOF modes also indicate certain regional anomalies such as the Karakoram mass gain, which represents ongoing snow accumulation. Our causality result suggests that the excessive snowfall in 2005–2008 has initiated this mass gain. However, as our results indicate, despite the dampening of snowfall rates after 2008, mass has been steadily increasing in the Karakorum, which is attributed to the flattening of the temperature anomaly curve and subsequent lower melting after 2008.

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