Influence of initial velocity field on the formation of coherent structures in simple hydrodynamic flows

2001 ◽  
Vol 8 (4) ◽  
pp. 1180 ◽  
Author(s):  
A. R. Karimov ◽  
H. Schamel
Keyword(s):  
Velocity Field ◽  
Coherent Structures ◽  
Initial Velocity

A mathematical analysis of tsunami generation in shallow water due to seabed deformation

2011 ◽  
Vol 141 (3) ◽  
pp. 551-608 ◽  
Author(s):  
Tatsuo Iguchi
Keyword(s):  
Velocity Field ◽  
Shallow Water ◽  
Water Wave ◽  
Initial Velocity ◽  
Tsunami Generation ◽  
Wave Problem ◽  
Initial Displacement ◽  
Water Wave Problem ◽  
Submarine Earthquakes ◽  
Tsunami Model

In numerical computations of tsunamis due to submarine earthquakes, it is frequently assumed that the initial displacement of the water surface is equal to the permanent shift of the seabed and that the initial velocity field is equal to zero and the shallow-water equations are often used to simulate the propagation of tsunamis. We give a mathematically rigorous justification of this tsunami model starting from the full water-wave problem by comparing the solution of the full problem with that of the tsunami model. We also show that, in some cases, we have to impose a non-zero initial velocity field, which arises as a nonlinear effect.

scholarly journals Pollution Transport Patterns Obtained Through Generalized Lagrangian Coherent Structures

Atmosphere ◽  
2020 ◽  
Vol 11 (2) ◽  
pp. 168
Author(s):  
Peter J. Nolan ◽  
Hosein Foroutan ◽  
Shane D. Ross
Keyword(s):  
Velocity Field ◽  
Coherent Structures ◽  
Initial Conditions ◽  
Saddle Points ◽  
Chemical Species ◽  
Lagrangian Coherent Structures ◽  
Time Interval ◽  
Pollution Transport ◽  
Material Transport ◽  
Material Surfaces

Identifying atmospheric transport pathways is important to understand the effects of pollutants on weather, climate, and human health. The atmospheric wind field is variable in space and time and contains complex patterns due to turbulent mixing. In such a highly unsteady flow field, it can be challenging to predict material transport over a finite-time interval. Particle trajectories are often used to study how pollutants evolve in the atmosphere. Nevertheless, individual trajectories are sensitive to their initial conditions. Lagrangian Coherent Structures (LCSs) have been shown to form the template of fluid parcel motion in a fluid flow. LCSs can be characterized by special material surfaces that organize the parcel motion into ordered patterns. These key material surfaces form the core of fluid deformation patterns, such as saddle points, tangles, filaments, barriers, and pathways. Traditionally, the study of LCSs has looked at coherent structures derived from integrating the wind velocity field. It has been assumed that particles in the atmosphere will generally evolve with the wind. Recent work has begun to look at the motion of chemical species, such as water vapor, within atmospheric flows. By calculating the flux associated with each species, a new effective flux-based velocity field can be obtained for each species. This work analyzes generalized species-weighted coherent structures associated with various chemical species to find their patterns and pathways in the atmosphere, providing a new tool and language for the assessment of pollutant transport and patterns.

Resonance dynamics in compressible cavity flows using time-resolved velocity and surface pressure fields

2017 ◽  
Vol 830 ◽  
pp. 494-527 ◽  
Author(s):  
Justin L. Wagner ◽  
Steven J. Beresh ◽  
Katya M. Casper ◽  
Edward P. DeMauro ◽  
Srinivasan Arunajatesan
Keyword(s):  
Velocity Field ◽  
Shear Layer ◽  
Surface Pressure ◽  
Coherent Structures ◽  
Acoustic Waves ◽  
Mode Switching ◽  
Recirculation Region ◽  
Mean Flow ◽  
Time Resolved ◽  
Phase Velocities

The resonance modes in Mach 0.94 turbulent flow over a cavity having a length-to-depth ratio of five were explored using time-resolved particle image velocimetry (TR-PIV) and time-resolved pressure sensitive paint (TR-PSP). Mode switching was quantified in the velocity field simultaneous with the pressure field. As the mode number increased from one through three, the resonance activity moved from a region downstream within the recirculation region to areas further upstream in the shear layer, an observation consistent with linear stability analysis. The second and third modes contained organized structures associated with shear layer vortices. Coherent structures occurring in the velocity field during modes two and three exhibited a clear modulation in size with streamwise distance. The streamwise periodicity was attributable to the interference of downstream-propagating vortical disturbances with upstream-travelling acoustic waves. The coherent structure oscillations were approximately $180^{\circ }$ out of phase with the modal surface pressure fluctuations, analogous to a standing wave. Modal propagation (or phase) velocities, based on cross-correlations of bandpass-filtered velocity fields were found for each mode. The phase velocities also showed streamwise periodicity and were greatest at regions of maximum constructive interference where coherent structures were the largest. Overall, the phase velocities increased with modal frequency, which coincided with the modal activity residing at higher portions of the cavity where the local mean flow velocity was elevated. Together, the TR-PIV and TR-PSP provide unique details not only on the distribution of modal activity throughout the cavity, but also new understanding of the resonance mechanism as observed in the velocity field.

Experimental Analysis of Lagrangian Coherent Structures and Chaotic Mixing in Rayleigh-Benard Convection

2020 ◽  
Author(s):  
Masahito Watanabe ◽  
Yusuke Kitamura ◽  
Naoki Hatta ◽  
Hiroaki Yoshimura
Keyword(s):  
Velocity Field ◽  
Coherent Structures ◽  
Lagrangian Coherent Structures ◽  
Chaotic Mixing ◽  
Lagrangian Description ◽  
Two Dimensional ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract It is known that some fluid particles may be transported chaotically in Lagrangian description although the velocity field seems to be stable in Eulerian description. A typical example can be found in the system of two-dimensional Rayleigh-Benard convection with perturbed velocity fields, which has been investigated as a low dimensional mechanical model of fluid phenomena associated with natural convection in order to clarify the mechanism of fluid transport (see, for instance, [2]). In this study, we make an experimental study on the global structures of chaotic mixing appeared in the two-dimensional perturbed Rayleigh-Benard convection by analyzing Lagrangian coherent structures (LCSs), which correspond to the invariant manifolds of time-dependent mechanical systems. We develop an apparatus to measure the velocity field by Particle Image Velocimetry (PIV) and then show the LCSs which can be numerically detected from the experimental data by computing Finite-time Lyapunov exponent (FTLE) fields. Finally, we show the global structures of chaotic mixing appeared in the perturbed Rayleigh-Benard convection as well as the steady convection by experiments. In particular, we clarify how the LCSs are entangled with each other around the cell boundaries to carry out chaotic Lagrangian transports.

scholarly journals An example of self–acceleration for incompressible flows

2013 ◽  
Vol 31 (2) ◽  
pp. 149
Author(s):  
Jens Lorenz ◽  
Randy Ott
Keyword(s):  
Velocity Field ◽  
Initial Velocity ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Finite Energy ◽  
The Self ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Maximal Speed ◽  
The Cauchy Problem

In this paper we consider the Cauchy problem for the unforced Eulerand Navier–Stokes equations for incompressible flows. We give an example of a smooth initial velocity field of finite energy which is self-accelerating, i.e., the maximal speed increases for some time. The self–acceleration is due to the non–Bernoulli part of the pressure generated by the velocity field.

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