Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

Studies in Advanced Mathematics

Time-reversal symmetry in dynamical systems: a survey

Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems

There have been several, recent investigations devoted to the study of the ex-istence and uniqueness of solutions to the equations governing the flows of fluids of the differential type. As these equations are usually higher order partial differential equations than the Navier-Stokes equations, we need to address the issue of whether the “no slip” boundary condition is sufficient to have a well-posed problem. While this issue has been raised earlier (see Rajagopal, 1984; Rajagopal and Kaloni, 1989; Rajagopal, 1992 and Rajagopal and Gupta, 1984), given the critical role it plays in shaping the theory, it has not been accorded the importance it deserves. This question cannot be answered in any generality for fluids of the differential type of complexity n, for arbitrary n. However, if attention is confined to fluids of grade 2 or grade 3, we can indeed provide some definitive answers, while some partial answers are possible for fluids of grade n (Rajagopal, 1984).

On Boundary Conditions for Fluids of the Differential Type

Two‐dimensional time‐dependent flow in an axially symmetric liquid bridge of Si at zero g with flat ends at the melting temperature θM of Si driven by motions of the free, lateral surface is studied numerically. The system is energized by a ring heater H at temperature θH>θM that surrounds the midcircle m of the bridge. The radiation from H creates a ∇σS(δS is surface temperature), which in turn creates a ∇σ (σ is surface tension) that drives oscillations of its free surface and thermocapillary flow in the bridge. For aspect ratios A of (1)/(2) , (2)/(3) , and 1 it is found that as the relevant control parameter Δθ≡θH−θM is increased, the flow in the bridge bifurcates differently depending on A. For A= (1)/(2) and (2)/(3) the flow bifurcates from steady state to small‐amplitude periodic oscillations, breaking symmetry, to large‐amplitude, period‐tripled ones, to their subharmonics, then becomes aperiodic, and finally chaotic. Toroidal cells in the bridge oscillate to‐and‐fro along its axis as a compound p...

Bifurcations of numerically simulated thermocapillary flows in axially symmetric float zones

In zone refinement of silicon crystals, a molten zone of Si is held by surface tension between two solid, cylindrical rods. In a gravity‐free environment the fluid Si bridge is subjected only to force generated by the temperature gradient on its free surface caused by the ring heater. This Marangoni flow is simulated numerically in an axially symmetric, initially cylindrical domain with a free lateral surface by solving the time‐dependent Navier–Stokes–energy equations on this domain with appropriate boundary conditions. Asymmetric oscillations of the flow as well as the temperature of the fluid and the free surface were found for aspect ratios (length/radius) of 2.0, 1.5, 1.0, and 0.5.

A numerical study of Marangoni flows in zone-refined silicon crystals

where T is the stress tensor, /~ is viscosity, and ~1 and ~2 are material constants. The coordinates are (x, y) with the x-axis in the direction of motion along the flat sheet and the y-axis perpendicular to it. Then the xand y-components of velocity are u = cxf'(~) and v ~--(~c)1/2f(~), respectively, with u c x = v = O at y = 0 (hence f ( 0 ) = 0 , f ' ( 0 ) = 1), and with ~]=(c/~) l/2y. The kinetic viscosity is v = #/~ the density is ~o. In (1) the constant k = --(oq/#) c, where the sign of 0q (and hence that of k) can be either positive or negative depending upon the fluid. The sign of ~t is the subject of much controversy. Details regarding this may be found, for example, in a paper by FosoIcK & RAJAGOPAL [21. Existence and uniqueness of the solution (1 -e -'7) of (1), (2) for k = 0 were proved by McLI;oD & RAJAGOVAL [3] and TROY, OVERMAN, ERMENrROUT, & KEENER [5]. For -ec < k < 1, TROY et al. [5] also found an explicit one-parameter family of solutions

A New Family of Explicit Solutions for the Similarity Equations Modelling Flow of a non-Newtonian Fluid over a Stretching Sheet

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112082002195

Numerically computed multiple steady states of vertical buoyancy-induced flows in cold pure water

http://www.jstor.org/stable/pdfplus/2319394.pdf

Nicholas D. Kazarinoff

Papers

Bifurcations of numerically simulated thermocapillary flows in axially symmetric float zones

A numerical study of Marangoni flows in zone-refined silicon crystals

A New Family of Explicit Solutions for the Similarity Equations Modelling Flow of a non-Newtonian Fluid over a Stretching Sheet

Numerically computed multiple steady states of vertical buoyancy-induced flows in cold pure water

Squaring Rectangles and Squares