c8bf7d06-dec5-4743-99ad-31207fc622c620210810131319636wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS2224-34291991-874710.37394/232011http://wseas.org/wseas/cms.action?id=40063420213420211610.37394/232011.2021.16https://wseas.org/wseas/cms.action?id=23298Ivan V.KazachkovNizhyn Mykola Gogol State University, Dept of Information Technology and Data Analysis 16600, UKRAINEBased on the earlier developed mathematical model of the complex flow due to the double rotations in two perpendicular directions, the stability analysis is performed in the paper. The Navier-Stokes equations are derived in the coordinate system rotating around the two perpendicular different axes, the vertical one of them is arranged on some distance from the other axis of rotation, the horizontal axis is directed along the tangential line to the circle of the vertical rotation. The two centrifugal and Coriolis forces create the unique features in high oscillating flow, with localities of the stretched liquid, due to their action varying by the circumferential cylindrical coordinate in the channel flow. Stability analysis for the complex rotational flow under double rotations creating strongly varying mass forces and stretching of the liquid is considered at first8102021810202162727https://wseas.com/journals/mechanics/2021/a145111-002(2021).pdf10.37394/232011.2021.16.7https://wseas.com/journals/mechanics/2021/a145111-002(2021).pdf10.37394/232013.2020.15.20Ivan Kazachkov. Mathematical Modelling and Computer Simulation of the Flow in Thin Gap Channel due to Alternating Volumetric Mass Forces, WSEAS Transactions on Fluid Mechanics, 2020, Vol. 15, pp. 202-212. Ivan Kazachkov, Kujtim Hyseni, Mohammad Al Fouzan, Yevgen Chesnokov, Development and application of device with double rotation turbine, Proc. 3rd Int Conf. on Innovative Studies of Contemporary Sciences.- Tokyo, Japan, February 19-21, 2021. https://www.openhazards.com/topics-hurricanes https://www.rt.com/usa/269614-vortex-damlake-texoma/ 10.1103/physrevlett.91.104502Andersen A., Bohr T., Stenum B., Rasmussen J.J., Lautrup B. Anatomy of bathtub vortex, Phys. Rev. Lett., Vol.91, 2003, pp. 104502-1−4. Hasslberger, Josef, Understanding Water Power, EXPLORE!, Vol.4, 1993, No.1. Sorokodoum E., Vortex heat-generators, New Energy Technologies, March-April, 2(5), 2002, pp. 17-18. 10.1002/ceat.270150412Pascal Belleville, Lhadi Nouri and Jack Legrand, Mixing Characteristics in the Torus Reactor, Chem. Eng. Technol., 1992, No.15, pp. 282–289. Smits A., Auvity B. & Sinha M., TaylorCouette flow with a shaped inner cylinder, Bull. Am. Phys. Soc., 45(9), 2000, pp. 37. 10.1051/epjconf/201714302044Darina Jasikova, Michal Kotek, Milos Muller, Vaclav Kopecky, Cavitation bubble interaction close to ultra-hydrophobic surface, WSEAS Transactions on Fluid Mechanics, 2016, Vol. 11, pp. 166-172. Ishan Varma, Ranjith Maniyeri, Numerical Study of Flow in a Centrifugal Blower, WSEAS Transactions on Fluid Mechanics, 2018, Vol. 13, pp. 1-9. Gladkov S.O., Bogdanova S.B., On distribution of speeds and pressures near the surface of rotating discs, WSEAS Transactions on Fluid Mechanics, 2019, Vol. 14, pp. 8-14. 10.37394/232013.2020.15.12Taha El Amine Terki Hassaine, A. Seddini, H. Bouchelkia, Overall performance of a centrifugal vaned diffuser Pump for different flow rates, experimental and numerical comparisons, WSEAS Transactions on Fluid Mechanics, 2020, Vol. 15, pp. 121-130. 10.37394/232013.2021.16.5Salman Shahid, Abdul Qader Hasan, Sharul Sham Dol, Mohamed S. Gadala, Mohd Shiraz Aris, Effects of Near-Wall Vortices on Wall Shear Stress in a Centrifugal Pump Impelle, WSEAS Transactions on Fluid Mechanics, 2021, Vol. 16, pp. 37-47.