Related Experiment Video
Updated: Apr 12, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
10.2K
Algebraic instability in shallow water flows with horizontally nonuniform density.
1A. M. Obukhov Institute of Atmospheric Physics RAS, 109017 Moscow, Russia.
Summary
Nonhydrostatic effects significantly alter Rayleigh-Taylor instability, shifting final stages from collapse to algebraic instability. This simplified shallow water model realistically captures phenomena like the shallowing effect in fluid dynamics.
Area of Science:
- Fluid Dynamics
- Geophysics
- Plasma Physics
Background:
- Rayleigh-Taylor instability is crucial in various physical systems.
- Previous models often relied on hydrostatic approximations.
- Understanding nonhydrostatic effects is key to accurate instability prediction.
Purpose of the Study:
- To investigate the regimes and mechanisms of Rayleigh-Taylor instability.
- To analyze the influence of nonhydrostaticity in a shallow water model.
- To assess the model's capability in describing realistic fluid phenomena.
Main Methods:
- Utilized a nonhydrostatic shallow water model.
- Incorporated horizontally nonuniform density.
- Performed numerical simulations to test model predictions.
Main Results:
- Nonhydrostaticity critically influences instability dynamics.
- The tendency for collapse slows, transitioning to algebraic instability.
- The model accurately captures the shallowing effect, showing profile concavities.
Conclusions:
- Nonhydrostatic shallow water models offer realistic simulations of fluid instabilities.
- The study highlights the limitations of hydrostatic assumptions for certain regimes.
- The model's ability to capture effects like shallowing validates its utility.
Related Concept Videos
01:27Uniform Depth Channel Flow
821
Uniform depth channel flow keeps fluid depth consistent along channels such as irrigation canals. In natural channels, such as rivers, approximate uniform flow is often assumed. This condition occurs when the channel’s bottom slope matches the energy slope, balancing potential energy lost from gravity with head loss due to shear stress. This balance prevents depth changes along the channel length, resulting in a steady, uniform flow.Uniform flow in open channels with a constant cross-section...
821
01:17Steady, Laminar Flow Between Parallel Plates
1.0K
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.
1.0K
01:27Energy Considerations in Open Channel Flow
870
Open channel flow, where a fluid flows with a free surface exposed to the atmosphere, is primarily governed by gravitational and surface effects, distinguishing it from closed conduit or pipe flow. In open channels such as rivers, canals, and artificial channels, energy analysis provides valuable insights into flow behavior and the relationship between depth, velocity, and slope.Specific Energy and Flow DepthIn open channel flow, the specific energy, E, combines the gravitational potential...
870
01:18Uniform Depth Channel Flow: Problem Solving
693
To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
693
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
01:28Irrotational Flow
1.3K
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:
1.3K