(2.11) The following lemmas are related to the asymptotic behavior of the boundary layer terms for the left problem, whose proofs are similar to that of Lemma 2.1, and therefore they are omitted here.
The following two lemmas are concerned with the asymptotic behavior of the boundary layer terms for the left problem, whose proofs are essentially similar to that of Lemma 3.2 in [13] and thus are omitted here.
The following proposition concerns the asymptotic behavior of the boundary layer term, whose proof is substantially similar to that of Lemma 3.1 in [14].
We seek an asymptotic solution of the problem (2.1 - 2.2 2.1 - 2.2ofm (31). where,, ; and for, are coefficientheoformgular terms; are coefficients of boundary layer terms at ; are coefficients of boundary layer terms at ; and are left and right coefficients of internal transition terms at.
Next, we will construct the right boundary layer terms.
end{aligned} Here (bar{{U}}^{pm}) are regular terms, (L^{pm}), (W^{pm}), (Pi ^{pm}) being boundary layer terms, and (Q^{pm}) are interior layer terms.
For hydrodynamic entrance lengths of not less than eight equivalent diameters, data in the laminar region can be expressed by an emperical boundary layer type of equation which includes terms for the hydrodynamic entrance length and electrode length.
The deviation from the linear impedance is found to be a function of excitation amplitude and oscillating viscous boundary layer thickness, expressed in terms of the Strouhal number and the Shear number.
This paper presents the response to diffuse acoustic field (DAF) and turbulent boundary layer (TBL) excitations in terms of their joint acceptance.
