Mean flow generated by asymmetric periodic excitation in an annular channel

Abstract

Surface waves of a shallow liquid layer confined in an annular channel of length L~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\ ilde{L}}}$$\\end{document} are generated by periodic acceleration of the channel along its azimuthal direction. We show that if the oscillations are anharmonic, e.g., having the form of a saw tooth, a mean mass flow is generated and even the mean speed over one period is zero. The flow is studied both experimentally and numerically. In the experiment, the velocity field and surface deflection are derived from the frames of videos recorded with a Go-Pro Hero 4 camera with custom rectilinear lens. We show resonance curves of the mean square of the water surface deflection and of the averaged mass flow. Both curves show almost coinciding maxima for multiples of the fundamental resonance frequency f~r=c~0/(2L~),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\ ilde{f}}}_r=\ ilde{c}_0/(2{{\ ilde{L}}}),$$\\end{document} where c~0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\ ilde{c}}}_0$$\\end{document} is the shallow water wave velocity. The measurements are confirmed by numerical solutions of an integrated boundary layer model including inertia and dissipation.