scholarly journals The Peregrine Breather on the Zero-Background Limit as the Two-Soliton Degenerate Solution: An Experimental Study

2021 ◽  
Vol 9 ◽  
Author(s):  
Amin Chabchoub ◽  
Alexey Slunyaev ◽  
Norbert Hoffmann ◽  
Frederic Dias ◽  
Bertrand Kibler ◽  
...  
Keyword(s):  
Free Water ◽  
High Amplitude ◽  
Finite Amplitude ◽  
Surface Boundary ◽  
Wave Amplification ◽  
Wave Flume ◽  
Degenerate Solution ◽  
Surface Boundary Conditions ◽  
Bose Einstein ◽  
Peregrine Breather

Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known as the degenerate two-soliton which also leads to high amplitude maxima. In this study, we report several observations of such multi-soliton with doubly-localized peaks in a water wave flume. The data collected in this experiment confirm the distinctive attainment of wave amplification by a factor of two in good agreement with the dynamics of the nonlinear Schrödinger equation solution. Advanced numerical simulations solving the problem of nonlinear free water surface boundary conditions of an ideal fluid quantify the physical limitations of the degenerate two-soliton in hydrodynamics.

Interaction of a deformable free surface with statistically steady homogeneous turbulence

2010 ◽  
Vol 658 ◽  
pp. 33-62 ◽  
Author(s):  
XIN GUO ◽  
LIAN SHEN
Keyword(s):  
Free Surface ◽  
Surface Deformation ◽  
Stokes Equations ◽  
Pseudospectral Method ◽  
Vertical Direction ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Surface Boundary Conditions

Direct numerical simulation is performed for the interaction between a deformable free surface and the homogeneous isotropic turbulent flow underneath. The Navier–Stokes equations subject to fully nonlinear free-surface boundary conditions are simulated by using a pseudospectral method in the horizontal directions and a finite-difference method in the vertical direction. Statistically, steady turbulence is generated by using a linear forcing method in the bulk flow below. Through investigation of cases of different Froude and Weber numbers, the present study focuses on the effect of surface deformation of finite amplitude. It is found that the motion of the free surface is characterized by propagating waves and turbulence-generated surface roughness. Statistics of the turbulence field near the free surface are analysed in detail in terms of fluctuations of velocity, fluctuations of velocity gradients and strain rates and the energy budget for horizontal and vertical turbulent motions. Our results illustrate the effects of surface blockage and vanishing shear stress on the anisotropy of the flow field. Using conditional averaging analysis, it is shown that splats and antisplats play an essential role in energy inter-component exchange and vertical transport.

Natural Convection in a Horizontal Layer of Water Cooled From Above to Near Freezing

1975 ◽  
Vol 97 (1) ◽  
pp. 47-53 ◽  
Author(s):  
R. E. Forbes ◽  
J. W. Cooper
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Natural Convection ◽  
Hydrodynamic Instability ◽  
Convective Heat Transfer Coefficient ◽  
Free Water ◽  
Ambient Air ◽  
Maximum Density ◽  
Surface Boundary ◽  
Initial Water

Natural convection in horizontal layers of water cooled from above to near freezing was studied analytically. The water was confined laterally and underneath by rigid insulators, and the upper horizontal surface was subjected to: (1) a constant 0C temperature, rigid conducting boundary, and (2) a free, water to air convection boundary condition, in which the convective heat transfer coefficient was held constant at values of 5.68 W/m2 · K and 284 W/m2 · K (1.0 and 50.0 Btu/hr ft2F) and the temperature of the ambient air was maintained at 0C. The ratios of the width to the depth of the rectangular water layers under consideration were W/D = 1, 3, and 6. Initially the water is assumed to be at a uniform temperature of either 4C or 8C, and then the upper surface boundary condition was suddenly applied. It was observed in all cases for which the initial water temperature was 4C, that the water remained stagnant and became thermally stratified. Heat transfer application of either of the surface boundary conditions to water initially at 8C produced large convective eddies extending from the bottom to the top of the layer of water. As the liquid layer cooled further, two distinct horizontal regions appeared, the 4C isothermal line separating the two. This produces a region of hydrodynamic instability in the fluid since the maximum density fluid (4C) is physically located above the less dense fluid in the lower portion of the cavity. The large eddies which appeared initially were confined to the hydrodynamically unstable region bounded by the 4C isotherm and the bottom of the cavity. The action of viscous shearing forces upon the stable water above the 4C isotherm produced a second “layer” of eddies. An alternating direction implicit finite difference method was used to solve the coupled system of partial differential equations. The paper presents transient isotherms and streamlines and a discussion of the effect of maximum density on the flow patterns.

Modeling Active Layer Depth of Permafrost Changing Surface Boundary Conditions

2020 ◽  
Author(s):  
MODI ZHU ◽  
Jingfeng Wang ◽  
Husayn Sharif ◽  
Valeriy Ivanov ◽  
Aleksey Sheshukov
Keyword(s):  
Boundary Conditions ◽  
Active Layer ◽  
Surface Boundary ◽  
Layer Depth ◽  
Surface Boundary Conditions

scholarly journals Energy Pile Field Simulation in Large Buildings: Validation of Surface Boundary Assumptions

2019 ◽  
Author(s):  
Andrea Ferrantelli ◽  
Jevgeni Fadejev ◽  
Jarek Kurnitski
Keyword(s):  
Boundary Conditions ◽  
Single Point ◽  
Ground Surface ◽  
Thermal Mass ◽  
Heat Equations ◽  
Outlet Temperature ◽  
Surface Boundary ◽  
Geothermal Heat ◽  
Soil Medium ◽  
Surface Boundary Conditions

As the energy efficiency demands for future buildings become increasingly stringent, preliminary assessments of energy consumption are mandatory. These are possible only through numerical simulations, whose reliability crucially depends on boundary conditions. We therefore investigate their role in numerical estimates for the usage of geothermal energy, performing annual simulations of transient heat transfer for a building employing a geothermal heat pump plant and energy piles. Starting from actual measurements, we solve the heat equations in 2D and 3D using COMSOL Multiphysics and IDA-ICE, and discover a negligible impact of the multiregional ground surface boundary conditions. Moreover, we verify that the thermal mass of the soil medium induces a small vertical temperature gradient on the piles surface. We also find a roughly constant temperature on each horizontal cross-section, with nearly identical values if the average temperature is integrated over the full plane or evaluated at one single point. Calculating the yearly heating need for an entire building we then show that the chosen upper boundary condition affects the energy balance dramatically. Using directly the pipes’ outlet temperature induces a 54% overestimation of the heat flux, while the exact ground surface temperature above the piles reduces the error to 0.03%.

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