Free surface lump wave dynamics of a saturated superfluid 4 He film with nontrivial boundary condition at the substrate surface

2020 ◽  
Vol 95 (9) ◽  
pp. 095209
Author(s):  
Abhik Mukherjee
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Substrate Surface ◽  
Wave Dynamics ◽  
Lump Wave

scholarly journals Computing Effective Hamiltonians of Coupled Electromagnetic Systems

2021 ◽  
Author(s):  
Shaolin Liao ◽  
Lu Ou
Keyword(s):  
Boundary Condition ◽  
Dispersion Relation ◽  
Normal Modes ◽  
Computational Procedure ◽  
Hamiltonian Matrix ◽  
Effective Hamiltonian ◽  
Electromagnetic System ◽  
Wave Dynamics ◽  
Potential Applications ◽  
Free Port

In this paper, we present an efficient procedure to compute the effective Hamiltonian matrix of a coupled electromagnetic system consisting of subsystems that are coupled to a discrete number of channels through couplers. Each subsystem is described by its own effective non-Hermitian Hamiltonian and the corresponding Quasi-normal Modes (QNMs), while the coupler connecting the subsystems and the channels is described by the scattering matrix, which is equivalent to the transfer matrix, in terms of port vectors defined for the coupler. Due to the constraints imposed by the QNMs of the subsystems and the wave dynamics of the channels, as well as boundary condition constraints, constraint-free port vectors need to be chosen efficiently and they follow two rules: 1) port vectors forming loops with couplers; 2) port vectors of couplers with most constraints or with less freedom. With the constraint-free port vectors chosen, the effective Hamiltonian matrix of the coupled electromagnetic system can be obtained by imposing the boundary condition constraints. After the effective Hamiltonian is obtained, the eigenvalues, eigenvectors and dispersion relation of the coupled electromagnetic system, as well as other quantities such as the reflection and transmission, can be calculated. A 2D interstitial square coupled MRRs array is used as an example to demonstrate the computational procedure. The computation of the effective Hamiltonian matrix of a coupled electromagnetic system has many potential applications such as MRRs array, coupled Parity-Time Non-Hermitian electromagnetic system, as well as the dispersion relation of finite and infinite arrays.

scholarly journals A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion

2019 ◽  
Vol 475 (2224) ◽  
pp. 20180642 ◽  
Author(s):  
H. Alemi Ardakani ◽  
T. J. Bridges ◽  
F. Gay-Balmaz ◽  
Y. H. Huang ◽  
C. Tronci
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Variational Principle ◽  
Stream Function ◽  
Fluid Motion ◽  
Two Dimensional ◽  
Euclidean Group ◽  
Fluid Sloshing ◽  
Pressure Boundary Condition ◽  
Vessel Motion

A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and the vessel motion is represented by a path in the planar Euclidean group. Novelties in the formulation include how the pressure boundary condition is treated, the introduction of a stream function into the Euler–Poincaré variations, the derivation of free surface variations and how the equations for the vessel path in the Euclidean group, coupled to the fluid motion, are generated automatically.

Large-eddy simulation of free-surface turbulence

2001 ◽  
Vol 440 ◽  
pp. 75-116 ◽  
Author(s):  
LIAN SHEN ◽  
DICK K. P. YUE
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Large Eddy Simulation ◽  
Surface Boundary ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Similarity Model ◽  
Scale Similarity ◽  
Surface Turbulence ◽  
Free Surface Turbulence

In this paper we investigate the large-eddy simulation (LES) of the interaction between a turbulent shear flow and a free surface at low Froude numbers. The benchmark flow field is first solved by using direct numerical simulations (DNS) of the Navier–Stokes equations at fine (1282 × 192 grid) resolution, while the LES is performed at coarse resolution. Analysis of the ensemble of 25 DNS datasets shows that the amount of energy transferred from the grid scales to the subgrid scales (SGS) reduces significantly as the free surface is approached. This is a result of energy backscatter associated with the fluid vertical motions. Conditional averaging reveals that the energy backscatter occurs at the splat regions of coherent hairpin vortex structures as they connect to the free surface. The free-surface region is highly anisotropic at all length scales while the energy backscatter is carried out by the horizontal components of the SGS stress only. The physical insights obtained here are essential to the efficacious SGS modelling of LES for free-surface turbulence. In the LES, the SGS contribution to the Dirichlet pressure free-surface boundary condition is modelled with a dynamic form of the Yoshizawa (1986) expression, while the SGS flux that appears in the kinematic boundary condition is modelled by a dynamic scale-similarity model. For the SGS stress, we first examine the existing dynamic Smagorinsky model (DSM), which is found to capture the free-surface turbulence structure only roughly. Based on the special physics of free-surface turbulence, we propose two new SGS models: a dynamic free-surface function model (DFFM) and a dynamic anisotropic selective model (DASM). The DFFM correctly represents the reduction of the Smagorinsky coefficient near the surface and is found to capture the surface layer more accurately. The DASM takes into account both the anisotropy nature of free-surface turbulence and the dependence of energy backscatter on specific coherent vorticity mechanisms, and is found to produce substantially better surface signature statistics. Finally, we show that the combination of the new DFFM and DASM with a dynamic scale-similarity model further improves the results.

Coupled Dynamic Analysis of a Moored Spar Platform in Time Domain

2010 ◽  
Author(s):  
M. D. Yang ◽  
B. Teng
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Dynamic Analysis ◽  
Time Domain ◽  
Surface Boundary ◽  
Spar Platform ◽  
Mooring Lines ◽  
Coupled Dynamic Analysis ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition

A time-domain simulation method is developed for the coupled dynamic analysis of a spar platform with mooring lines. For the hydrodynamic loads, a time domain second order method is developed. In this approach, Taylor series expansions are applied to the body surface boundary condition and the free surface boundary condition, and Stokes perturbation procedure is then used to establish corresponding boundary value problems with time-independent boundaries. A higher order boundary element method is developed to calculate the velocity potential of the resulting flow field at each time step. The free-surface boundary condition is satisfied to the second order by 4th order Adams-Bashforth-Moultn method. An artificial damping layer is adopted on the free surface to avoid the wave reflection. For the mooring-line dynamics, a geometrically nonlinear finite element method using isoparametric cable element based on the total Lagrangian formulation is developed. In the coupled dynamic analysis, the motion equation for the hull and dynamic equations for mooring lines are solved simultaneously using Newmark method. Numerical results including motions and tensions in the mooring lines are presented.

scholarly journals Charge Response of Jellium Surface through Ripplons

1982 ◽  
Vol 35 (2) ◽  
pp. 147
Author(s):  
J Mahanty
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Boundary Conditions ◽  
Surface Plasmons ◽  
Density Profile ◽  
External Source ◽  
Equilibrium Density ◽  
Response Properties ◽  
Surface Response ◽  
Dispersive Limit

The feasibility of explaining the charge response properties of a jellium surface through excitation of ripplon modes on the electron fluid is examined. It is demonstrated that for a sharp equilibrium density profile the response to the field of an external source through ripplons is different from that through surface plasmons, although in the non-dispersive limit they become identical despite the radical difference in the boundary conditions associated with the two types of excitation. It is suggested that because a free surface is more likely to satisfy the boundary condition for ripplons than for surface plasmons, the surface response properties would be determined more through the excitation of ripplons.

scholarly journals The Prediction of Hull Gesture and Flow Around Ship Based on Taylor Expansion Boundary Element Method

2019 ◽  
Vol 26 (2) ◽  
pp. 198-211
Author(s):  
Jiaye Gong ◽  
Yunbo Li
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Boundary Element Method ◽  
Flow Field ◽  
Boundary Element ◽  
Taylor Expansion ◽  
Surface Condition ◽  
Control Point ◽  
Surface Boundary ◽  
Element Method

Abstract Based on the potential flow theory and traditional boundary element method (BEM), Taylor expansion boundary element method (TEBEM) is introduced in this paper for the prediction of the flow field around ship, as a result, hull gesture and pressure distribution on hull surface are obtained. By this method, dipole strength of every field point is expanded in Taylor expansion, so that approximately continuous hull and free surface boundary condition could be achieved. To close the new equation system, the boundary condition of tangent velocity in every control point is introduced. With the simultaneous solving of hull boundary condition and free surface condition, the disturbance velocity potential could be obtained. The present method is used to predict the flow field and hull gesture of Wigley parabolic hull, Series 60 and KVLCC2 models. To validate the numerical model for full form ship, the wave profile, the computed hull gesture and hull surface pressure of KVLCC2 model are compared with experimental results.

Experimental Study of the Impact of a Vibrating Wire on Free Abrasive Machining as Correlated to the Modeling of Vibration Subject to an Oscillating Boundary Condition

2020 ◽  
Vol 143 (5) ◽  
Author(s):  
Liming Li ◽  
Imin Kao
Keyword(s):  
Boundary Condition ◽  
Material Removal ◽  
Substrate Surface ◽  
Abrasive Machining ◽  
Vibrating Wire ◽  
Fracture Formation ◽  
Oscillating Boundary ◽  
The Impact ◽  
Brittle Material Removal ◽  
Free Abrasive

Abstract In this paper, we study experimentally the impact of a vibrating wire on the free abrasive machining (FAM) process in removing material from the surface of brittle materials, such as silicon. An experimental setup was designed to study the FAM process on silicon substrate surface by using a slurry-fed wire with a periodic excitation. An analytical solution of a wire moving axially, subject to an oscillating boundary condition with damping from abrasive slurry, was derived based on the partial differential equation of motion. Experiments were conducted on the apparatus using a wire with an oscillating boundary. It was found that the amplitudes of vibration were larger at the side of the oscillatory boundary, which caused more FAM interaction near the edge of the oscillatory boundary with larger material removal that was measured and validated. Furthermore, experiments were conducted to elucidate the effectiveness of brittle material removal using FAM with abrasive grits: (i) under dry condition, (ii) with water, and (iii) with abrasive slurry. Experimental results showed that the vibration of wire resulted in plastic deformation on the surface of silicon wafer. The abrasive grits in slurry driven by a vibrating wire generated material removal through observable grooves and fractures on the surface of silicon due to FAM in just a few minutes. The grooves from FAM process is an outcome of brittle machining through fracture formation and concatenation, generated by the indentation of abrasive grits on the silicon surface.

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