Exact Calculations for the Lagrangian Velocity

Exact Calculations for the Lagrangian Velocity

Bibliographic Details
Main Author: Schneider, Eduardo da Silva
Language:English
Published: Bowling Green State University / OhioLINK 2019
Subjects:
Mathematics
Applied Mathematics
Lagrangian velocity
random fields
Taylor series
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1555086598198833
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-bgsu15550865981988332021-08-03T07:10:18Z Exact Calculations for the Lagrangian Velocity Schneider, Eduardo da Silva Mathematics Applied Mathematics Lagrangian velocity random fields Taylor series We consider a homogeneous, stationary, and divergence free random velocity field U in R2to get a statistical description of some of its Lagrangian properties, for example, the Lagrangianauto-covariance, which is closely related to the mean-square displacement of one single particle ina turbulent flow. Velocity field U is written as a sum of finitely many Fourier modes, where eachFourier mode is characterized by an amplitude, a two-dimensional wave number, and a phase;all three can be random. We assume that random phases are independent and identically distributedand independent of other variables to get a general formula for Taylor coefficients of theLagrangian auto-correlation. This formula is a sum over many terms, the number of which dependson the number of Fourier modes and the degree of the derivative. We prove that odd orderderivatives of the Lagrangian auto-covariance vanish at t = 0 and the second order derivativeis negative definite with negative main-diagonal entries, so main components of the Lagrangianauto-covariance decay quadratically for small values of t > 0. Assuming that amplitudes andwave numbers are identically distributed and letting the number of Fourier modes go to infinitydramatically reduces the number of terms for Taylor coefficients. For remaining terms, we givean interpretation as interactions among wave numbers. Finally, by assuming isotropy, we provetheoretical results and provide more detailed expressions for Taylor coefficients in terms of wavenumber magnitudes. We also analyze convergence of the Taylor series for terms having the highestmoments of such wave number magnitudes. 2019-04-23 English text Bowling Green State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1555086598198833 http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1555086598198833 unrestricted This thesis or dissertation is protected by copyright: some rights reserved. It is licensed for use under a Creative Commons license. Specific terms and permissions are available from this document's record in the OhioLINK ETD Center.
collection NDLTD
language English
sources NDLTD
topic Mathematics
Applied Mathematics
Lagrangian velocity
random fields
Taylor series
spellingShingle Mathematics
Applied Mathematics
Lagrangian velocity
random fields
Taylor series
Schneider, Eduardo da Silva
Exact Calculations for the Lagrangian Velocity
author Schneider, Eduardo da Silva
author_facet Schneider, Eduardo da Silva
author_sort Schneider, Eduardo da Silva
title Exact Calculations for the Lagrangian Velocity
title_short Exact Calculations for the Lagrangian Velocity
title_full Exact Calculations for the Lagrangian Velocity
title_fullStr Exact Calculations for the Lagrangian Velocity
title_full_unstemmed Exact Calculations for the Lagrangian Velocity
title_sort exact calculations for the lagrangian velocity
publisher Bowling Green State University / OhioLINK
publishDate 2019
url http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1555086598198833
work_keys_str_mv AT schneidereduardodasilva exactcalculationsforthelagrangianvelocity
_version_ 1719455174139838464

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