Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical reconstruction of isotropic turbulence spectra based on the
  Gaussian transform   The Random Particle Mesh (RPM) method used to simulate turbulence-induced
broadband noise in several aeroacoustic applications is extended to realise
isotropic turbulence spectra. With this method turbulent fluctuations are
synthesised by filtering white noise with a Gaussian filter kernel that in turn
gives a Gaussian spectrum. The Gaussian function is smooth and its derivatives
and integrals are again Gaussian functions. The Gaussian filter is efficient
and finds wide-spread applications in stochastic signal processing. However in
many applications Gaussian spectra do not correspond to real turbulence
spectra. Thus in turbo-machines the von K\'arm\'an, Liepmann, and modified von
K\'arm\'an spectra are more realistic model spectra. In this note we
analytically derive weighting functions to realise arbitrary isotropic
solenoidal spectra using a superposition of weighted Gaussian spectra of
different length scales. The analytic weighting functions for the von
K\'arm\'an, the Liepmann, and the modified von K\'arm\'an spectra are derived
subsequently. Finally a method is proposed to discretise the problem using a
limited number of Gaussian spectra. The effectivity of this approach is
demonstrated by realising a von K\'arm\'an velocity spectrum using the RPM
method.

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The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
21
The categories of this paper are: adap-org