TY - GEN
T1 - Stretched Amplitude Decaying Fourier Modes in the Jet Far-Field
AU - Hodžić, Azur
AU - Meyer, K. E.
AU - George, W. K.
AU - Velte, Clara M.
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - A framework is presented for decomposing the self-similar region of the round jet along the streamwise direction using an analytical series expansion deduced from the four dimensional (space-time) Proper Orthogonal Decomposition (POD) integral. A specific inner product weight function is introduced in order to deduce the Stretched Amplitude Decaying Fourier Modes. The inner product weight function, maps the POD kernel into a displacement invariant kernel. The SADFM are demonstrated to be orthogonal with respect to the weighted inner product and therefore constituting a basis for the weighted Hilbert space, Lw2(Ω,C3), over the domain Ω ⊂ R4. The SADFM allow for an Fast Fourier Transform (FFT) algorithm to be used along the streamwise inhomogeneous direction reducing the computational workload for the four-dimensional POD of the jet far-field. Applying a Galerkin projection to the governing equations using the SADFM provides additional insight into the far-field dynamics.
AB - A framework is presented for decomposing the self-similar region of the round jet along the streamwise direction using an analytical series expansion deduced from the four dimensional (space-time) Proper Orthogonal Decomposition (POD) integral. A specific inner product weight function is introduced in order to deduce the Stretched Amplitude Decaying Fourier Modes. The inner product weight function, maps the POD kernel into a displacement invariant kernel. The SADFM are demonstrated to be orthogonal with respect to the weighted inner product and therefore constituting a basis for the weighted Hilbert space, Lw2(Ω,C3), over the domain Ω ⊂ R4. The SADFM allow for an Fast Fourier Transform (FFT) algorithm to be used along the streamwise inhomogeneous direction reducing the computational workload for the four-dimensional POD of the jet far-field. Applying a Galerkin projection to the governing equations using the SADFM provides additional insight into the far-field dynamics.
UR - https://www.scopus.com/pages/publications/85119011874
U2 - 10.1007/978-3-030-80716-0_31
DO - 10.1007/978-3-030-80716-0_31
M3 - Conference contribution
AN - SCOPUS:85119011874
SN - 9783030807153
T3 - Springer Proceedings in Physics
SP - 231
EP - 236
BT - Progress in Turbulence IX - Proceedings of the iTi Conference in Turbulence, 2021
A2 - Örlü, Ramis
A2 - Talamelli, Alessandro
A2 - Peinke, Joachim
A2 - Oberlack, Martin
PB - Springer Science and Business Media Deutschland GmbH
T2 - 9th iTi Conference on Turbulence, iTi 2021
Y2 - 25 February 2021 through 26 February 2021
ER -