Related Experiment Video
Updated: Mar 22, 2026
09:17
Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods
Published on: April 23, 2018
11.3K
Tricritical spiral vortex instability in cross-slot flow
Simon J Haward1, Robert J Poole2, Manuel A Alves3
1Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan.
Physical Review. E
|April 15, 2016
Summary
Fluid flow in cross-slot devices exhibits symmetry at low Reynolds numbers (Re). Above a critical Re, a symmetry-breaking bifurcation leads to spiral vortices, with transition order dependent on the device
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Microfluidics
Background:
- Cross-slot devices are used to study fluid mixing and instabilities.
- Understanding flow behavior is crucial for optimizing device performance.
Purpose of the Study:
- To investigate fluid flow dynamics in cross-slot devices with varying depth-to-width ratios (α).
- To characterize the transition from symmetric to asymmetric flow regimes and the development of vortex structures.
Main Methods:
- Numerical simulations of fluid flow.
- Analysis of flow symmetry and stability.
- Application of Landau theory to describe order parameters.
Main Results:
- At low Reynolds numbers (Re), flow is symmetric with a distinct interface between streams.
- A critical Reynolds number, Re(c)(α), dependent on α, triggers a symmetry-breaking bifurcation.
- Spiral vortex structures emerge, with transition order changing from second- to first-order beyond α ≈ 0.55.
- Vortex stretching at the stagnation point drives the observed instability.
Conclusions:
- The depth-to-width ratio (α) significantly influences the stability and transition dynamics of cross-slot flow.
- The study reveals a progression in transition order, explained by a sixth-order Landau potential.
- Vortex stretching is identified as the primary mechanism for instability onset.
Related Concept Videos
01:17Steady, Laminar Flow Between Parallel Plates
982
Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
982
01:28Irrotational Flow
1.2K
Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:
1.2K
01:24Turbulent Flow
861
Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid's velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent...
861
01:22Couette Flow
1.3K
Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
1.3K
01:16Bernoulli's Equation for Flow Normal to a Streamline
1.4K
Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines. However, the...
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines. However, the...
1.4K
01:30Bernoulli's Equation for Flow Along a Streamline
1.6K
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:
1.6K