Design of 2-D recursive filters having approximately circularly symmetric variable magnitude characteristics

2003 ◽  
Author(s):  
S. Fallah ◽  
V. Ramachandran ◽  
C.S. Gargour
Keyword(s):  
Recursive Filters ◽  
Symmetric Variable

scholarly journals Variable-Order Fractional Models for Wall-Bounded Turbulent Flows

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 782
Author(s):  
Fangying Song ◽  
George Em Karniadakis
Keyword(s):  
Fractional Derivative ◽  
Turbulent Flows ◽  
Fractional Order ◽  
Variable Order ◽  
Universal Curve ◽  
Reynolds Stresses ◽  
Continuous Change ◽  
Mean Velocity ◽  
Symmetric Variable ◽  
Fractional Models

Modeling of wall-bounded turbulent flows is still an open problem in classical physics, with relatively slow progress in the last few decades beyond the log law, which only describes the intermediate region in wall-bounded turbulence, i.e., 30–50 y+ to 0.1–0.2 R+ in a pipe of radius R. Here, we propose a fundamentally new approach based on fractional calculus to model the entire mean velocity profile from the wall to the centerline of the pipe. Specifically, we represent the Reynolds stresses with a non-local fractional derivative of variable-order that decays with the distance from the wall. Surprisingly, we find that this variable fractional order has a universal form for all Reynolds numbers and for three different flow types, i.e., channel flow, Couette flow, and pipe flow. We first use existing databases from direct numerical simulations (DNSs) to lean the variable-order function and subsequently we test it against other DNS data and experimental measurements, including the Princeton superpipe experiments. Taken together, our findings reveal the continuous change in rate of turbulent diffusion from the wall as well as the strong nonlocality of turbulent interactions that intensify away from the wall. Moreover, we propose alternative formulations, including a divergence variable fractional (two-sided) model for turbulent flows. The total shear stress is represented by a two-sided symmetric variable fractional derivative. The numerical results show that this formulation can lead to smooth fractional-order profiles in the whole domain. This new model improves the one-sided model, which is considered in the half domain (wall to centerline) only. We use a finite difference method for solving the inverse problem, but we also introduce the fractional physics-informed neural network (fPINN) for solving the inverse and forward problems much more efficiently. In addition to the aforementioned fully-developed flows, we model turbulent boundary layers and discuss how the streamwise variation affects the universal curve.

scholarly journals Implementation of a 3-D-Var system for atmospheric profiling data assimilation into the RAMS model: initial results

2013 ◽  
Vol 6 (2) ◽  
pp. 3581-3610
Author(s):  
S. Federico
Keyword(s):  
Relative Humidity ◽  
Data Assimilation ◽  
Initial Conditions ◽  
Weather Prediction ◽  
Wind Profiler ◽  
Short Term ◽  
Recursive Filters ◽  
Data Assimilation System ◽  
Rams Model ◽  
Assimilation System

Abstract. This paper presents the current status of development of a three-dimensional variational data assimilation system. The system can be used with different numerical weather prediction models, but it is mainly designed to be coupled with the Regional Atmospheric Modelling System (RAMS). Analyses are given for the following parameters: zonal and meridional wind components, temperature, relative humidity, and geopotential height. Important features of the data assimilation system are the use of incremental formulation of the cost-function, and the use of an analysis space represented by recursive filters and eigenmodes of the vertical background error matrix. This matrix and the length-scale of the recursive filters are estimated by the National Meteorological Center (NMC) method. The data assimilation and forecasting system is applied to the real context of atmospheric profiling data assimilation, and in particular to the short-term wind prediction. The analyses are produced at 20 km horizontal resolution over central Europe and extend over the whole troposphere. Assimilated data are vertical soundings of wind, temperature, and relative humidity from radiosondes, and wind measurements of the European wind profiler network. Results show the validity of the analysis solutions because they are closer to the observations (lower RMSE) compared to the background (higher RMSE), and the differences of the RMSEs are consistent with the data assimilation settings. To quantify the impact of improved initial conditions on the short-term forecast, the analyses are used as initial conditions of a three-hours forecast of the RAMS model. In particular two sets of forecasts are produced: (a) the first uses the ECMWF analysis/forecast cycle as initial and boundary conditions; (b) the second uses the analyses produced by the 3-D-Var scheme as initial conditions, then is driven by the ECMWF forecast. The improvement is quantified by considering the horizontal components of the wind, which are measured at a-synoptic times by the European wind profiler network. The results show that the RMSE is effectively reduced at the short range (1–2 h). The results are in agreement with the set-up of the numerical experiment.

Some error bounds for K-iterated Gaussian recursive filters

2016 ◽  
Author(s):  
Salvatore Cuomo ◽  
Ardelio Galletti ◽  
Giulio Giunta ◽  
Livia Marcellino
Keyword(s):  
Error Bounds ◽  
Recursive Filters

Approximation of 2-D separable denominator recursive filters

2005 ◽  
Author(s):  
B. Lashgari ◽  
L. Silverman ◽  
J. Abramatic
Keyword(s):  
Recursive Filters ◽  
Separable Denominator

Systolic recursive filters

1988 ◽  
Vol 35 (8) ◽  
pp. 1067-1068 ◽  
Author(s):  
W. Luk ◽  
G. Jones
Keyword(s):  
Recursive Filters

DESIGN OF RECURSIVE FILTERS

Geophysics ◽  
1970 ◽  
Vol 35 (2) ◽  
pp. 247-253 ◽  
Author(s):  
Raymundo Aguilera ◽  
J. CL. Debremaecker ◽  
Salvador Hernandez
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Minimum Phase ◽  
Recursive Filter ◽  
Recursive Filters ◽  
The Time Domain

Recursive filters are inherently more efficient than purely transverse or purely regressive ones. They can be computed in the frequency domain by a series of simple operations. The roots of the denominator must be computed and the moduli less than unity replaced by their inverses. If such an operation is also performed on the numerator, the resultant recursive filter is minimum phase. The same method can be used to construct a deconvolution operator in the time domain, starting with the autocorrelation. Two examples are given which show the efficiency of the method.

An adaptive lattice algorithm for recursive filters

1980 ◽  
Vol 28 (1) ◽  
pp. 110-111 ◽  
Author(s):  
D. Parikh ◽  
N. Ahmed ◽  
S. Stearns
Keyword(s):  
Recursive Filters ◽  
Lattice Algorithm

Design of recursive filters to simulate clutter for the evaluation of radar MTI processors

1983 ◽  
Vol 19 (2) ◽  
pp. 47 ◽  
Author(s):  
D.C. Cooper ◽  
P. Rogers
Keyword(s):  
Recursive Filters
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