Short wave stability of homogeneous shear flows with variable topography.pdfVIP

Appl. Math. Mech. -Engl. Ed., 35(5), 541–548 (2014) Applied Mathematics DOI 10.1007/s10483-014-1811-7 and Mechanics c Shanghai University and Springer-Verlag Berlin Heidelberg 2014 (English Edition) Short wave stability of homogeneous shear flows with variable topography∗ Hua-shu DOU (), V. GANESH (Faculty of Mechanical Engineering Automation, Zhejiang Sci-Tech University, Hangzhou 310018, P. R. China) Abstract For the stability problem of homogeneous shear flows in sea straits of arbitrary cross section, a sufficient condition for stability is derived under the condition of inviscid flow. It is shown that there is a critical wave number, and if the wave number of a normal mode is greater than this critical wave number, the mode is stable. Key words hydrodynamic stability, shear flow, variable bottom, sea strait Chinese Library Classification O35 2010 Mathematics Subject Classification 76E05 1 Introduction The stability of homogeneous and stratified shear flows of an inviscid fluid to infinitesimal normal mode disturbances has been studied extensively[1−2]. These studies are mostly restricted to rectangular cross sections. However, sea straits have rarely rectangular cross sections. The stability analysis of homogeneous and stratified shear flows in sea straits of arbitrary cross section was initiated in Ref. [3], while a more general theory for transversely uniform, time- dependent, and stratified flows in a channel with an arbitrary cross section was studied in Ref. [4]. For the homogeneous shear flow