Related Experiment Video
Updated: Nov 18, 2025
10:03
Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel
Published on: October 5, 2018
8.5K
Geophysical water flows with constant vorticity and centripetal terms.
1Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
Annali Di Matematica Pura Ed Applicata
|February 11, 2021
Summary
Researchers found explicit solutions for 3D water waves with Coriolis and centripetal forces. Under constant vorticity, the rotating frame velocity field vanishes, but the free surface remains non-flat and time-independent.
Area of Science:
- Fluid dynamics
- Geophysics
- Oceanography
Background:
- Geophysical water wave equations model large-scale ocean and atmospheric flows.
- Coriolis and centripetal forces are crucial in rotating systems.
- Exact solutions are vital for validating numerical models and understanding complex phenomena.
Purpose of the Study:
- To derive explicit solutions for three-dimensional water flows using geophysical water wave equations.
- To analyze these solutions under the assumption of a constant vorticity vector.
- To investigate the behavior of the velocity field, pressure, and free surface in both rotating and fixed inertial frames.
Main Methods:
- Derivation of explicit solutions in Eulerian coordinates.
- Assumption of a constant vorticity vector.
- Analysis of solutions in a rotating frame and conversion to a fixed inertial frame.
Main Results:
- A family of explicit solutions to the geophysical water wave equations with full Coriolis and centripetal terms was derived.
- Under constant vorticity, the velocity field in the rotating frame vanishes.
- The free surface is time-independent, non-flat, and explicitly determined.
- In the fixed inertial frame, the velocity field is non-vanishing and the free surface remains non-flat and explicitly determined.
Conclusions:
- The derived solutions are the only ones possible under the constant vorticity assumption.
- These solutions provide exact and explicit representations of three-dimensional water waves.
- The findings offer valuable insights into fluid dynamics in rotating systems, relevant to geophysical flows.
Related Concept Videos
01:28Irrotational Flow
726
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:
726
01:20Velocity Potential
549
In steady, incompressible flow through a long, straight pipe with a uniform cross-section, the flow in the central region (far from the pipe walls) is irrotational. This irrotational nature means that fluid particles do not rotate around their axes, and a scalar function called the velocity potential, represented by ϕ, can be used to describe their movement. In irrotational flows, the velocity field V is defined as the gradient of the velocity potential:
549
01:28Euler's Equations of Motion
680
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...
680
01:27Steady Flow of a Fluid Stream
531
Consider a control volume, such as a pipe with solid boundaries, through which fluid flows and changes direction due to the impulse exerted by the resulting force from the pipe walls. In steady flow, the mass of fluid entering the control volume at a given time, t, with velocity v1, is equal to the mass leaving after infinitesimal time dt, with velocity v2.
During this process, the momentum of the fluid within the control volume remains constant over the time interval dt. By applying the...
During this process, the momentum of the fluid within the control volume remains constant over the time interval dt. By applying the...
531
01:12Equation of Continuity
9.7K
Fluid motion is represented by either velocity vectors or streamlines. The volume of a fluid flowing past a given location through an area during a period of time is called the flow rate Q, or more precisely, the volume flow rate. Flow rate and velocity are related—for instance, a river has a greater flow rate if the velocity of the water in it is greater. However, the flow rate also depends on the size and shape of the river. The relationship between flow rate (Q) and average speed (v)...
9.7K
01:23Plane Potential Flows
674
Plane potential flows simplify fluid motion by assuming the fluid to be irrotational and incompressible. These characteristics allow these flows to be described by a velocity potential function, ϕ, representing the flow speed in a given direction, and a stream function, ψ, that visualizes the flow path, both governed by Laplace's equation. These parameters help in estimating flow patterns, velocity distributions, and pressure fields around various hydraulic structures.
Uniform...
Uniform...
674