A new class of approximate analytical solutions of the Pridmore-Brown equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00359446" target="_blank" >RIV/68407700:21230/22:00359446 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1063/5.0098473" target="_blank" >https://doi.org/10.1063/5.0098473</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/5.0098473" target="_blank" >10.1063/5.0098473</a>
Alternative languages
Result language
angličtina
Original language name
A new class of approximate analytical solutions of the Pridmore-Brown equation
Original language description
There is only a limited amount of known analytical solutions to the Pridmore-Brown equation, mostly employing asymptotic behavior for a certain frequency limit and specifically chosen flow profiles. In this paper, we show the possibility of transformation of the Pridmore-Brown equation into the Schrödinger-like equation for the case of two-dimensional homentropic mean flow without critical layers. The corresponding potential that depends on the mean flow profile can then be approximated by a quartic polynomial, leading to a triconfluent Heun equation whose solution based on the triconfluent Heun functions is generally known. The quality of this approximation procedure is presented for the case of symmetric polynomial flow profiles for various values of polynomial order and the Mach number. A more detailed example is then shown for a quadratic mean flow profile, where the solution is accurate up to the third order of the Mach number.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10307 - Acoustics
Result continuities
Project
<a href="/en/project/GA22-33896S" target="_blank" >GA22-33896S: Advanced methods of sound and elastic wave field control: acoustic black holes, metamaterials and functionally graded materials</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Physics
ISSN
0022-2488
e-ISSN
1089-7658
Volume of the periodical
63
Issue of the periodical within the volume
8
Country of publishing house
US - UNITED STATES
Number of pages
9
Pages from-to
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UT code for WoS article
000844402500006
EID of the result in the Scopus database
2-s2.0-85137102434