Model reduction by the low-frequency approximation balancing method for unstable systems

1996 ◽  
Vol 41 (7) ◽  
pp. 995-997 ◽  
Author(s):  
Tai-Yih Chiu
Keyword(s):  
Model Reduction ◽  
Low Frequency ◽  
Unstable Systems ◽  
Frequency Approximation

Ocean Response to Wind Variations, Warm Water Volume, and Simple Models of ENSO in the Low-Frequency Approximation

2010 ◽  
Vol 23 (14) ◽  
pp. 3855-3873 ◽  
Author(s):  
Alexey V. Fedorov
Keyword(s):  
Low Frequency ◽  
Equatorial Pacific ◽  
Warm Water ◽  
Water Volume ◽  
Thermocline Depth ◽  
Phase Lag ◽  
Eastern Equatorial Pacific ◽  
The Pacific ◽  
Warm Water Volume ◽  
Frequency Approximation

Abstract Physical processes that control ENSO are relatively fast. For instance, it takes only several months for a Kelvin wave to cross the Pacific basin (Tk ≈ 2 months), while Rossby waves travel the same distance in about half a year. Compared to such short time scales, the typical periodicity of El Niño is much longer (T ≈ 2–7 yr). Thus, ENSO is fundamentally a low-frequency phenomenon in the context of these faster processes. Here, the author takes advantage of this fact and uses the smallness of the ratio ɛk = Tk/T to expand solutions of the ocean shallow-water equations into power series (the actual parameter of expansion also includes the oceanic damping rate). Using such an expansion, referred to here as the low-frequency approximation, the author relates thermocline depth anomalies to temperature variations in the eastern equatorial Pacific via an explicit integral operator. This allows a simplified formulation of ENSO dynamics based on an integro-differential equation. Within this formulation, the author shows how the interplay between wind stress curl and oceanic damping rates affects 1) the amplitude and periodicity of El Niño and 2) the phase lag between variations in the equatorial warm water volume and SST in the eastern Pacific. A simple analytical expression is derived for the phase lag. Further, applying the low-frequency approximation to the observed variations in SST, the author computes thermocline depth anomalies in the western and eastern equatorial Pacific to show a good agreement with the observed variations in warm water volume. Ultimately, this approach provides a rigorous framework for deriving other simple models of ENSO (the delayed and recharge oscillators), highlights the limitations of such models, and can be easily used for decadal climate variability in the Pacific.

Accurate Low-Frequency Approximation for Wires Within a Conducting Half-Space

2020 ◽  
Vol 62 (1) ◽  
pp. 272-275
Author(s):  
Blagoja Markovski ◽  
Leonid Grcev ◽  
Vesna Arnautovski-Toseva
Keyword(s):  
Half Space ◽  
Low Frequency ◽  
Frequency Approximation

scholarly journals A low-cost acoustic permeameter

2017 ◽  
Vol 6 (1) ◽  
pp. 199-207 ◽  
Author(s):  
Stephen A. Drake ◽  
John S. Selker ◽  
Chad W. Higgins
Keyword(s):  
Standard Deviation ◽  
Relative Error ◽  
Low Cost ◽  
Low Frequency ◽  
Environmental Noise ◽  
Intrinsic Permeability ◽  
Sampling Errors ◽  
Resonance Frequencies ◽  
The Mean ◽  
Frequency Approximation

Abstract. Intrinsic permeability is an important parameter that regulates air exchange through porous media such as snow. Standard methods of measuring snow permeability are inconvenient to perform outdoors, are fraught with sampling errors, and require specialized equipment, while bringing intact samples back to the laboratory is also challenging. To address these issues, we designed, built, and tested a low-cost acoustic permeameter that allows computation of volume-averaged intrinsic permeability for a homogenous medium. In this paper, we validate acoustically derived permeability of homogenous, reticulated foam samples by comparison with results derived using a standard flow-through permeameter. Acoustic permeameter elements were designed for use in snow, but the measurement methods are not snow-specific. The electronic components – consisting of a signal generator, amplifier, speaker, microphone, and oscilloscope – are inexpensive and easily obtainable. The system is suitable for outdoor use when it is not precipitating, but the electrical components require protection from the elements in inclement weather. The permeameter can be operated with a microphone either internally mounted or buried a known depth in the medium. The calibration method depends on choice of microphone positioning. For an externally located microphone, calibration was based on a low-frequency approximation applied at 500 Hz that provided an estimate of both intrinsic permeability and tortuosity. The low-frequency approximation that we used is valid up to 2 kHz, but we chose 500 Hz because data reproducibility was maximized at this frequency. For an internally mounted microphone, calibration was based on attenuation at 50 Hz and returned only intrinsic permeability. We found that 50 Hz corresponded to a wavelength that minimized resonance frequencies in the acoustic tube and was also within the response limitations of the microphone. We used reticulated foam of known permeability (ranging from 2 × 10−7 to 3 × 10−9 m2) and estimated tortuosity of 1.05 to validate both methods. For the externally mounted microphone the mean normalized standard deviation was 6 % for permeability and 2 % for tortuosity. The mean relative error from known measurements was 17 % for permeability and 2 % for tortuosity. For the internally mounted microphone the mean normalized standard deviation for permeability was 10 % and the relative error was also 10 %. Permeability determination for an externally mounted microphone is less sensitive to environmental noise than is the internally mounted microphone and is therefore the recommended method. The approximation using the internally mounted microphone was developed as an alternative for circumstances in which placing the microphone in the medium was not feasible. Environmental noise degrades precision of both methods and is recognizable as increased scatter for replicate data points.

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