Turbulent wave attractors in large-aspect ratio domains.

<div>Ocean abyss is an example of a system with continuous stratification subject to large-scale tidal forcing. Owing to specific dispersion relation of internal waves, the domains bounded by sloping boundaries may support wave patterns with wave rays converging to closed trajectories (geometric attractors) as result of iterative focusing reflections. Previously the behavior of kinetic energy in wave attractors has been investigated in domains with comparable scales of depth and horizontal length. As the geometric aspect ratio of the domain increases, the dynamic pattern of energy focusing may significantly evolve both in laminar and turbulent regimes. The present paper shows that the energy density in domains with large aspect ratio can significantly increase. In numerical simulations the input forcing has been introduced at global scale by prescribing small-amplitude deformations of the upper bound of the liquid domain. The evolution of internal wave motion in such system has been computed numerically for different values of the forcing amplitude. The behavior of the large-aspect-ratio system has been compared to the well-studied case of the system with depth-to-length ratio of order unity.  A number of most typical situations has been analyzed in terms of behavior of integral mechanical quantities such as total dissipation, mean kinetic energy and energy fluctuations in laminar and turbulent cases. The relative mean kinetic energy (normalized by the kinetic energy of the liquid domain undergoing rigid-body oscillations with the amplitude of the wavemaker), may increase by order of magnitude as compared to low-aspect-ratio system.<br>It was shown previously, that in the case of aspect ratio close to unity, the transition to wave turbulence regime is associated with a cascade of triadic wave-wave interactions. Now it is shown that for large aspect ratios the energy cascade in the system is due to generation of superharmonic waves corresponding to integer (including zero) multiples of the forcing frequency. As forcing amplitude increases beyond certain value, an abrupt change is observed in behavior of relative mean kinetic energy and spectra, accompanied with appearance of additional harmonic components corresponding to half-integer (including 1/2) and integer multiples of the forcing frequency.  </div><div> </div>

PRESSURE AND STRESS ANALYSIS OF LIQUID-FILLED CYLINDRICAL TANK

During earthquakes, the liquid-filled storage tank generates hydrodynamic pressures, in addition to hydrostatic pressure, on the solid domain of the tank. The theoretical background of hydrodynamic pressure analysis, as well as the numerical simulation of the liquid-filled cylindrical concrete tank, is the focus of this paper. The Finite Element Method (FEM) modeling, along with Arbitrary Lagrangian-Eulerian and Fluid-Structure Interactions formulation, are used for simulating the seismic response of cylindrical concrete liquid-filled tank, fixed to the rigid foundation. The Loma Prieta accelerogram is utilized for recording the seismic ground motion. In the numerical study, two states are observed: 1) static condition where only hydrostatic pressure acts, and 2) seismic excitation where hydrodynamic pressure occurs. When exposed to an earthquake situation, the tank liquid gives the total pressure of the liquid domain. The dynamic analysis considers the pressure response of the liquid domain, as well as the stress response of the solid domain of the coupled system, i.e., liquid-filled cylindrical concrete tank.

Computational Evaluation of Stability in Slosh Dynamics of Tank Vehicles Using Zero Moment Point

Sloshing characterized by inertial waves has an adverse effect on the directional dynamics and safety of partially filled tank vehicles, limiting their stability and controllability during steering, accelerating or braking maneuvers. A mathematical description of the transient fluid slosh in a horizontal cylindrical tank should consider the simultaneous lateral, vertical and roll excitations assuming potential flows and a linearized free-surface boundary condition. While the determination of vehicle stability would require coupling this model to a dynamic roll plane model of a tank vehicle resulting in a computationally expensive analysis. Considering the need for a simpler method to predict roll stability for partially filled tank vehicles, we explore the Zero Moment Point of a liquid domain as a novel solution to this challenge. Numerical investigations are carried out in a three-dimensional partially filled tanks while tracking the movement of the liquid-air interface by employing the volume of fluid method in OpenFOAM. The center of Mass and Zero Moment Point were calculated from the computational results using analytical expressions. The movement of free surface is found to be in good agreement with available literature. The center of mass of the liquid domain was traced as a practical means to quantify the slosh in the tanker. The analyses are performed for different fluid fill heights at varying speeds. The results suggest that the roll stability of tank vehicles can be efficiently analyzed using the zero moment point with significantly lower computational effort.

Drag coefficient of a liquid domain with distinct viscosity in a fluid membrane

We calculate the drag coefficient of a circular liquid domain in a flat fluid membrane surrounded by three-dimensional fluids on both sides. The coefficient of a rigid disk is well known, while that of a circular liquid domain is also well known when the membrane viscosity inside the domain equals the one outside the domain. As the ratio of the former viscosity to the latter increases to infinity, the drag coefficient of a liquid domain should approach that of the disk of the same size in the same ambient viscosities. This approach has not yet been shown explicitly, however. When the ratio is not unity, the continuity of the stress makes the velocity gradient discontinuous across the domain perimeter in the membrane. On the other hand, the velocity gradient is continuous in the ambient fluids, whose velocity field should agree with that of the membrane as the spatial point approaches the membrane. This means that we need to assume dipole singularity along the domain perimeter in solving the governing equations unless the ratio is unity. In the present study, we take this singularity into account and obtain the drag coefficient of a liquid domain as a power series with respect to a dimensionless parameter, which equals zero when the ratio is unity and approaches unity when the ratio tends to infinity. As the parameter increases to unity, the sum of the series is numerically shown to approach the drag coefficient of the disk.

Heat Capacity of Nanoconfined Liquid: A Molecular Dynamics Simulation

Equilibrium molecular dynamics (EMD) simulations aiming to investigate the effect of confinement gap thickness on constant volume molar heat capacity (Cv) of the confined liquid in nanoscale have been carried out by simultaneously controlling the density and temperature of the liquid domain. Simplified Lennard-Jones (LJ) molecular model is used to model the system where the liquid is entrapped between two flat solid surfaces separated by a distance varying from 0.585 nm to 27.8 nm. Molar heat capacity of the bulk liquid has been evaluated using fluctuation formula which matches greatly with the NIST data and published literatures. But in case of confined liquid, molar heat capacity is observed to vary significantly with the gap thickness. For a specific range of gap thickness, molar heat capacity of the confined liquid is found higher than that of the bulk. But molar heat capacity of the nanogap confined liquid becomes independent of the gap thickness and approaches to that of the bulk liquid as gap thickness is greater than this specific range (6.14 nm for 100 K temperature of the confined liquid).

Drag force on a liquid domain moving inside a membrane sheet surrounded by aqueous medium

We compute the drag on a circular and liquid microdomain diffusing in a two-dimensional fluid lipid bilayer membrane surrounded by a fluid above and below. Under the assumptions that the liquids are incompressible and the flow is of low Reynolds number, Stokes’ equations describe the flow in the two-dimensional membrane as well as in the surrounding three-dimensional fluid. The expression for the drag force on the liquid domain involves Fredholm integral equations of the second kind, which we numerically solve using discrete collocation method based on Chebyshev polynomials. We observe that when the domain is more viscous than the surrounding membrane (including the rigid domain case), the drag force is almost independent of the viscosity contrast between the domain and the surrounding membrane, as also observed earlier in experiments by other researchers. The mobility also varies logarithmically with Boussinesq number${\it\beta}$for large${\it\beta}$. On the other hand, for a less viscous domain the dimensionless drag force reduces with increasing viscosity contrast, and a significant change in the drag force, from that when there is no viscosity contrast or when the domain is rigid, has been observed. Further, the logarithmic behaviour of the mobility no longer holds for less viscous domains. Our method of computing the drag force and diffusion coefficient is valid for arbitrary viscosity contrast between the domain and membrane and any domain size (subject to${\it\beta}\geqslant 5$).