Related Experiment Video
Updated: Sep 24, 2025
10:08
Phase Behavior of Charged Vesicles Under Symmetric and Asymmetric Solution Conditions Monitored with Fluorescence Microscopy
Published on: October 24, 2017
9.3K
Convergence to precipitating quasi-geostrophic equations with phase changes: asymptotics and numerical assessment
Yeyu Zhang1, Leslie M Smith2,3, Samuel N Stechmann2,4
1School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, People's Republic of China.
Summary
Moist Boussinesq equations with phase changes show convergence towards precipitating quasi-geostrophic (PQG) equations. Numerical simulations indicate vertical velocity is proportional to decreasing Rossby and Froude numbers, supporting PQG dynamics.
Area of Science:
- Fluid dynamics
- Atmospheric science
- Oceanography
Background:
- Traditional quasi-geostrophic (QG) equations model dry atmospheric and oceanic dynamics.
- These models do not incorporate moisture and cloud processes.
- Precipitating quasi-geostrophic (PQG) equations were recently developed to include moist dynamics.
Purpose of the Study:
- To investigate the convergence of moist Boussinesq equations with phase changes to PQG equations.
- To determine if nonlinearities at cloud edges affect this convergence.
- To numerically assess the transition from moist Boussinesq to PQG dynamics.
Main Methods:
- Numerical simulations of moist Boussinesq equations with varying parameters (related to Rossby and Froude numbers).
- Analysis of vertical velocity and other imbalance measures.
- Quantification of these measures at specific time and parameter values.
Main Results:
- Vertical velocity magnitude was observed to be approximately proportional to the decrease in the ratio of Rossby and Froude numbers.
- This proportionality suggests a convergence towards PQG dynamics.
- Convergence was indicated at fixed and potentially later time points.
Conclusions:
- The study provides numerical evidence supporting the convergence of moist Boussinesq dynamics to PQG dynamics.
- This convergence is observed as the system approaches regimes governed by PQG equations.
- The findings advance the understanding of moist fluid dynamics in geophysical flows.
Related Concept Videos
01:06Divergence and Stokes' Theorems
2.1K
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
2.1K
01:28Navier–Stokes Equations
813
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...
813
02:39Phase Transitions: Vaporization and Condensation
19.0K
The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase...
19.0K
01:20Region of Convergence of Laplace Tarnsform
742
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
742
01:30Bernoulli's Equation for Flow Along a Streamline
1.1K
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:
1.1K
01:28Euler's Equations of Motion
590
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...
590