Related Experiment Video
Updated: Feb 17, 2026
09:37
Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole
Published on: August 26, 2019
6.2K
Nonlinear dynamics of an elliptic vortex embedded in an oscillatory shear flow
1Pacific Oceanological Institute of FEB RAS, 43, Baltiyskaya Street, Vladivostok 690041, Russia.
Chaos (Woodbury, N.Y.)
|December 3, 2017
Summary
This study numerically investigates chaotic regimes in elliptic vortex dynamics under time-periodic shear flow. Nonlinear resonance analysis reveals enhanced stability in regular dynamics regions when specific resonance zones overlap with critical points.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Chaos Theory
Background:
- Elliptic vortices are fundamental in fluid mechanics.
- Understanding vortex dynamics under external flows is crucial for predicting complex fluid behaviors.
- Nonlinear resonance overlaps theory provides a framework for analyzing chaotic phenomena.
Purpose of the Study:
- To numerically study the nonlinear dynamics of an elliptic vortex subjected to time-periodic linear external shear flow.
- To investigate the appearance of chaotic regimes and analyze nonlinear resonance overlaps.
- To explore the impact of perturbation frequency on stability regions and regular dynamics.
Main Methods:
- Numerical simulation of elliptic vortex dynamics.
- Application of nonlinear resonance overlaps theory.
- Analysis of phase portraits and stability regions under varying perturbation frequencies.
Main Results:
- For systems with a separatrix, the 1:1 nonlinear resonance significantly enhances the persistence of regular dynamics when its stability region occupies the critical point.
- Similar persistence of regular motion is observed for higher perturbation frequencies when stability islands reach the central elliptic point.
- Systems without a separatrix exhibit larger stability islands associated with nonlinear resonances.
Conclusions:
- Time-periodic shear flow introduces significant changes to vortex dynamics compared to stationary flow.
- Nonlinear resonances play a critical role in determining the stability and chaotic behavior of elliptic vortices.
- The findings highlight the importance of resonance phenomena in controlling regular versus chaotic dynamics in fluid systems.
Related Concept Videos
01:28Navier–Stokes Equations
2.4K
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
2.4K
01:28Euler's Equations of Motion
959
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform across...
959
01:18Newtonian Fluid: Problem Solving
1.0K
Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
1.0K
01:07Laminar and Turbulent Flow
11.2K
Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the...
11.2K
01:30Bernoulli's Equation for Flow Along a Streamline
1.5K
Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
1.5K
01:15Thin-Walled Hollow Shafts
596
In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
596