<s>[INST] This exercise requires critical application of the scientific method. Interfaces are ubiquitous in science and engineering because any composite material exhibits an interface between the individual elements. Defining pinholes as small holes with diameter \(\delta<<\lambda_{\mathrm{imp}}\), where \(\lambda_{\mathrm{imp}}\) is the impingement wavelength, researchers have obtained diverse results on the role of irregular interfaces in turbulent flows. Some claim that pinholes facilitate turbulent flow mixing [long dash-curled underline]; others vindicate the contrary [short dash-curled underline]. A peer reviewer believed that these _oppugned_ (disputed) claims are not justified because they quantify only pinhole contribution in terms of pinhole volume ratio \(\alpha\) while ignoring the significant wavelength-scale variation of the tangential surface variation \(\Delta\) over pinhole surfaces. He fiercely advocated use of \(\alpha^{\prime}\) that incorporates both pinhole volume ratio \(\alpha\) and surface roughness. The pinhole volume ratio \(\alpha\) is given in Eq. (8.29), and \(\Delta\) is defined in Eq. (8.28). Then, for any given \(\alpha\), prove or disprove the supposition of the peer reviewer[/INST]