Browsing NTNU Open by Author "Timokha, Alexander"
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Adaptive Lukovsky’s formulas for the resulting hydrodynamic force and moment owing to sloshing in an upright circular tank
Timokha, Alexander (Journal article, 2019)Lukovsky’s asymptotic formulas for the resulting hydrodynamic force and moment are derived as if they follow from the adaptive (infinitedimensional) multimodal theory of the liquid sloshing dynamics in an upright circular ... 
An inviscid analysis of the Prandtl azimuthal mass transport during swirltype sloshing
Faltinsen, Odd Magnus; Timokha, Alexander (Journal article; Peer reviewed, 2019)An inviscid analytical theory of a slow steady liquid mass rotation during the swirltype sloshing in a vertical circular cylindrical tank with a fairly deep depth is proposed by utilising the asymptotic steadystate wave ... 
Analytical approximate capillary surfaces
Timokha, Alexander; Tkachenko, Eugene (Journal article, 2018)Analytical approaches to hydrostatic capillary (meniscus) problem in infinite horizontal channel and axisymmetric container are developed. For these geometric cases, finding the capillary menisci reduces to freeboundary ... 
Damped steadystate resonant sloshing in a circular base container
Raynovskyy, IA; Timokha, Alexander (Journal article; Peer reviewed, 2018)To describe the damped resonant sloshing in a circular base container, the nonlinear modal equations by Faltinsen et al (2016 J. Fluid Mech. 804 608–45) are equipped with linear damping terms associated with the logarithmic ... 
Differential and variational formalism for acousticallylevitating drops
Chernova, MO; Lukovsky, IA; Timokha, Alexander (Journal article; Peer reviewed, 2017)We consider the most general problem of waves on the interface of two ideal fluids regarded as an ullage gas and a liquid, respectively. Separating the fast and slow time scales, we develop the differential and variational ... 
Multimodal method in sloshing
Lukovsky, I; Timokha, Alexander (Journal article; Peer reviewed, 2017)The multimodal method reduces the sloshing problem with free surface to a (modal) system of nonlinear ordinary differential equations. The method was originally proposed for nonimpulsive hydrodynamic loads. However, recently ... 
Nonlinear boundarylayer problems and laminar vortical stream generated by resonant sloshing in a circular base tank
Timokha, Alexander (Journal article; Peer reviewed, 2018)Suggesting a viscous incompressible liquid with laminar flows, nonlinear boundarylayer problems on the wetted tank surface (wall and bottom) of a rigid circularbase tank partly filled with a finite depth are derived ... 
On acoustic equilibria
Tkachenko, Eugene; Timokha, Alexander (Journal article, 2019)The present paper generalises mathematical theory of vibroequilibria onto the case of the acousticallydriven interface between ullage gas and liquid in a container 
Prandtl steady rotary current in an upright cylindrical container
Timokha, Alexander (Journal article; Peer reviewed, 2018)The quantifying of the experimentallyknown (Prandtl, 1949) steady rotary current during the swirltype sloshing is first given. The current is treated as the sum of the mean wave (pseudo) momentum through the meridional ... 
Resonant sloshing in a squarebase tank due to an angularandhorizontal periodic forcing
Timokha, Alexander (Journal article, 2016)Розробляється модальний метод для задачi про коливання рiдини у резервуарi квадратного перерiзу, який виконує перiодичнi горизон тальнi та кутовi рухи малої амплiтуди. Аналiз показує, що домiнан тна хвильова компонента ... 
Resonant steadystate sloshing in upright tanks performing a threedimensional periodic motion
Timokha, Alexander; Tkachenko, E.M. (Journal article, 2019)Analytical approaches to hydrostatic capillary (meniscus) problem in infinite horizontal channel and axisymmetric container are developed. For these geometric cases, finding the capillary menisci reduces to freeboundary ... 
Resonant SteadyState Sloshing in Upright Tanks: Effect of ThreeDimensional Excitations and Viscosity
Timokha, Alexander; Raynovskyy, IA (Chapter, 2018)Bearing in mind recent experimental and theoretical results showing that viscous damping can qualitatively affect resonant sloshing in clean tanks, the NarimanovMoiseev multimodal sloshing theory for an upright circular ... 
Resonant threedimensional nonlinear sloshing in a square base basin. Part 5. Threedimensional nonparametric tank forcing
Faltinsen, Odd Magnus; Lagodzinskyi, Oleksandr E.; Timokha, Alexander (Peer reviewed; Journal article, 2020)Assuming an inviscid incompressible liquid (with irrotational flows) partly filling a square base tank, which performs a smallamplitude sway/surge/pitch/roll periodic motion whose frequency is close to the lowest natural ... 
Resonant threedimensional nonlinear sloshing in a square base basin. Part 5. Threedimensional nonparametric tank forcing
Faltinsen, Odd Magnus; Lagodzinskyi, Oleksandr E.; Timokha, Alexander (Peer reviewed; Journal article, 2020)Assuming an inviscid incompressible liquid (with irrotational flows) partly filling a square base tank, which performs a smallamplitude sway/surge/pitch/roll periodic motion whose frequency is close to the lowest natural ... 
Resonant threedimensional nonlinear sloshing in a squarebase basin. Part 4. Oblique forcing and linear viscous damping
Faltinsen, Odd Magnus; Timokha, Alexander (Journal article; Peer reviewed, 2017)Faltinsen et al. (J. Fluid Mech., vol. 487, 2003, pp. 1–42) (henceforth, Part 1) examined an undamped nonlinear resonant steadystate sloshing in a squarebase tank by developing an approximate (asymptotic) Narimanov–Moiseevtype ... 
Sloshing in Upright Circular Containers: Theory, Analytical Solutions and Applications
Raynovskyy, Ihor; Timokha, Alexander (Book, 2020)This book presents mathematical fundaments and results on sloshing in an upright circular cylindrical tank with semianalytical solutions. The book outlines generic mathematical and physical aspects of the multimodal method, ... 
SteadyState Resonant Sloshing in an Upright Cylindrical Container Performing a Circular Orbital Motion
Raynovskyy, Ihor; Timokha, Alexander (Journal article; Peer reviewed, 2018)The nonlinear NarimanovMoiseev multimodal equations are used to study the swirlingtype resonant sloshing in a circular base container occurring due to an orbital (rotary) tank motion in the horizontal plane with the ... 
Steadystate sloshing in an orbitallyforced squarebase tank
Timokha, Alexander; Lahodzinskyi, O.E. (Journal article, 2019)The paper conducts a series of analytical studies on the resonant steadystate sloshing in a rigid square base container, which have been originated by Faltinsen & Timokha who derived and applied the NarimanovMoiseev—type ... 
The damped sloshing in an upright circular tank due to an orbital forcing
Timokha, Alexander; Raynovskyy, Ihor (Journal article; Peer reviewed, 2017)The nonlinear Narimanov—Moiseevtype modal system with linear damping terms is employed to study the damped steadystate resonant sloshing in an upright circular tank due to a prescribed horizontal orbital (elliptic) tank ... 
The NarimanovMoiseev multimodal analysis of nonlinear sloshing in circular conical tanks
Timokha, Alexander; Solodun, A.V. (Journal article, 2020)The chapter reports mathematical aspects of the Narimanov–Moiseev multimodal modelling for the liquid sloshing in rigid circular conical tanks, which perform smallmagnitude oscillatory motions with the forcing frequency ...