Questions tagged [fluid-dynamics]
The fluid-dynamics tag has no usage guidance.
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Why does relative vorticity in spherical coordinates have an extra term as compared to the usual cartesian derivation?
With $u, v$ denoting the components of wind velocity along zonal (x) and meridional (y) direction, atmospheric (relative) vorticity is usually defined by
$$\zeta_z = \frac{\partial v}{\partial x} -\...
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Raindrop splash/splatter dynamics
I'm interested in the physics/dynamics of a drop of water (2-5 mm dia) dropped from a height (terminal velocity is the limit) on smooth hydrophobic surfaces. Specifically the largest diameter of ...
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How to explain "Vacuum Cleaner Effect" for upper level PV anomaly?
In Jonathan Martin's Book "Mid-Latitude Atmospheric Dynamics" there is a chapter dedicated to anomalies of potential vorticity (PV). The scenario shown in the image below depicts a situation,...
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Does air in the atmosphere get friction due to the planet's rotation?
Does air in the atmosphere suffer friction in some way due solely to the planet's rotation?
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What is the deeper difference between QG Omega equation and QG Height tendency equation?
The quasi-geostrophic $\omega$-Equation
is a diagnostic equation for $\omega$ (=dp/dt = vertical motion) in terms of geopotential. It is derived in a few steps by manipulating vorticity and ...
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Comparing expressions for Ertel Potential Vorticity and Quasi Geostrophic Potential Vorticity
In Meteorology there is a quantity called "Ertel Potential Vorticity" $q_e$ which is conserved considering isentropic flow ($\theta=const)$:
$$\frac{d}{dt}\left(\frac{1}{\rho} \vec \eta \...
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Why is one term missing in the derivation of continuity equation in isentropic coordinates?
In the book by Jonathan E. Martin "Mid-Latitude Atmospheric Dynamics - A First Course"
the continuity equation for isentropic coordinates is derived by applying conservation of mass:
$\...
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Manning's N vs. Drag Coefficient Cd values for NLCD land cover classes
I was trying to understand the difference between Drag coefficient Cd and Manning's N. There are many sources available online which provide values of Manning's N for different land covers such as ...
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How is Wind oriented in a Jet Streak?
Recently I found this tutorial video about Jet streaks (want to mention I'm only in second term so my knowledge is not advanced yet). Originally I was looking for the topic because of a particular ...
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Calculating Ekman transport and vertical velocity from wind stress τ of mesoscale cyclone
I'm working through problems in the Vallis 'big book' and I'm stuck on the following problem:
Consider a wind stress imposed by a mesoscale cyclonic storm (in the atmosphere) given by
τ = −Aexp{−(r/λ)^...
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Why are there different Notations of Vorticity Equation?
I'm a student of meteorology in first year. This time my question is not about a particular problem I have, but rather about teaching and learning: In a recent lecture on atmospheric dynamics we ...
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Geostrophic adjustment with shallow water equations
The linearized f-plane shallow water equations are:
$du'/dt - fv' = -g(d eta'/dx)$
dv'/dt + fu' = -g(d eta'/dy)
(d eta'/dt) + H((du'/dx)+(dv'/dy)) = 0
where g is ...
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Rossby waves in the atmosphere
I have trouble understanding the Rossby waves in the atmosphere.
Sometimes they are said to be caused by the jets moving from west to east. But the phase velocity of the waves is in the west direction ...
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Why air parcel is on a circular trajectory when considering Coriolis force
According to Coriolis force an air parcel is deflected in the absence of other forces by the acceleration (Holton, 4th Edition):
These equations lead to circular motion.
This figure is from a Matlab ...
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How can speed of geostrophic wind change when forces are always perpendicular to speed?
Equation for acceleration of an air parcel is
$$D \vec U/Dt = -2 \vec \omega \times \vec U -\frac{1}{\rho} \vec \nabla p + \vec g$$
Now, for geostrophic wind, U is parallel to the contour lines of ...
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How is centrifugal force identified in equations of fluid motion in the rotating reference system of earth?
I spent already days on the following: In one of my meteorology scripts the equations for conservation of momentum in the rotation reference system of earth are given by:
The apparent forces are in ...
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Compute upwind flux for gridded data
I'm trying to compute something called the "Drying Ratio" following: Eidhammer, 2018
The drying ratio is the ratio of the precipitation to the incoming vapor flux. So,
$DR = \frac{F_{in} - ...
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A problem of the 2-Layer hydrostatic model
The 2-layer hydrostatic model is like this
And the pressure of the two layers and the top are
and it is easy to find the horizontal gradient of $p_1$ and $p_2$
\begin{equation}
\begin{aligned}
\nabla ...
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Is continental drift a chaotic phenomenon?
Suppose that we reran Earth from two billion years ago changing the position of one atom. Would the continents drift to positions completely different from those today?
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What is the relationship between air pressure and temperature?
I'm trying to reconcile a paradox regarding air pressure and temperature.
On the one hand, compressing air heats it up, while expanding it cools it. So density and temperature are proportional.
On the ...
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Similarities and differences between lava flows and fluvial geomorphology (rivers)
How are active lava flows similar to fluvial geomorphology? You can search youtube for these dramatic videos of lava flows, and they all seem to look very similar to streams or rivers. I know that the ...
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How do you find the relationship between the angle a weather front makes with the ground and the temperatures and along front winds either side of it?
I am working through David Andrews' "An introductuion to atmospheric physics". (2nd Ed)
Question 4.8 concerns finding the relationship between the angle a weather front makes with the ground ...
Salamander
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What is "small layer thickness" defined as in terms of bulk Richardson number approaching gradient Richardson number?
In many sources (https://glossary.ametsoc.org/wiki/Bulk_richardson_number), bulk Richardson number is defined as an approximation to gradient Richardson number. The prior only approaches the ladder ...
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Can air be slowed down by Fricton? [closed]
Can wind/air that is moving at average speeds be slowed down by the cause of Friction? Also, Can Air bubbles in water be slowed down because of Friction? Please cite your sources.
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Deriving shallow water equations: why is the vertical velocity equal to the material derivative of the surface level?
I'm reading about the derivation of shallow water equations, and I have a hard time understanding why
$$ w(\eta) = \frac{D\eta}{Dt}$$
where $w$ is the vertical velocity, $\eta$ is the (top or bottom) ...
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Is COMSOL Multiphysics good for subduction CFD modelling? Are there alternatives?
As a beginner for CFD modelling of plate subduction, I heard comsol to be a good software. Can anybody suggests alternatives and the demerits of using COMSOL Multiphysics? Thank you.
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Vertical air speed
Assuming that the divergence varies linearly with the pressure between the surface
(1000 hPa) and the tropopause (200 hPa). Can someone tell me how do we calculate the vertical speed on the pressure ...
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Is it meaningful to assume static pressure to be constant along a streamline?
I am looking at Bernoulli's equation formulated in two dimensions, which reads
$$\frac{v^2}{2}+c_p\theta_0\pi+gz \equiv \mathrm{const.}$$
along a given streamline $\gamma$, where $v=|\mathrm{v}|$ for ...
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What is the simplest meteorological model to operate?
For teaching purposes I am looking for an atmospheric model that can be easily installed and the input data can be easily read and prepared.
Preferably I would like to run a global low resolution ...
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If the top layer of a large river freezes, is the remainder's rate of flow affected?
This question is a hypothetical, and has to do with the notion of cheap, modular turbines that can be sunk and anchored to a specific depth in a body of water. Each would not generate much power, but ...
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Barotropic vorticity equation
I came across the barotropic vorticity equation (below) in Sakamoto (2002) and I cannot figure it out. The notation is not clear to me. How can it be derived from the Navier-Stokes equation?
$$ \beta\...
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How far can an andesitic lava flow, and what is the velocity?
For an effusive volcanic activity, how far an andesitic lava can flow?
What is the velocity?
Eruption volume 0.2 km3 with 25 degree slope.
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Hydrology- flow accumulation
I'm not specialist in hydrology, and I would be very grateful if you answer my question:
What is flow accumulation in hydrology?
Why algorithms used to calculate it over a raster DEM don't take ...
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At what point are water droplets too small to make a rainbow?
This question asks How to tell if fog is made out of water droplets or ice crystals?
I know that ice fog makes a rainbow where fog does not.
Ice crystals aside: How does the water droplet size ...
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Algorithm for anisotropic porous media reconstruction
I have a series of micro-tomography images of a porous material (received from experimental partners) with a resolution 10 $\mu m$ with total size 1cm $\times$ 1cm. Porosity of the porous material ...
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Over what scales can we begin to apply fluid dynamics to accurately model properties of the mantle?
Over what size temporal/spatial scales do geophysicists and geodynamicists begin to apply fluid dynamics to model the mantle rather than elastic/plastic deformation theory?
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Godfrey's island rule (stream function in multiply connected domains)
In this paper, the authors detail the methods to calculate the stream function $\psi$ from velocity data in the case of the global ocean (i.e., multiply connected domains).
The general idea is to use ...
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Why would geostrophic theory be invoked in the tropics with regards to the MJO?
In this paper reviewing the Madden-Julian Oscillation, frequently geostrophic theory (or approximately geostrophic) is often invoked. However, for geostrophic theory to be invoked, $$Ro=\frac{U}{f_0L}&...
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Reasons for choosing LES in stead of RANS models?
In oceanography, is there any particular reason why choosing large eddy simulations in stead of RANS (regardless of the type of flow)? In both cases, 2d simulations would be used (shallow water model)....
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What forms do groundwater flow equations have when Dupuit supposition is not considered?
Near pumping wells or near/beneath a stream, the groundwater flow is not totally horizontal and the vertical component of groundwater movement at these points cannot be ignored in reality. Often, ...
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What is the difference between the Hydraulic diffusion equation and the Richards equation in groundwater dynamics?
What is the difference between the Hydraulic diffusion equation and the Richards equation in groundwater dynamics? I want also to understand the difference between the different storage coefficients (...
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What affects the surface characteristics of cumulus clouds?
I love looking at clouds. I love trying to describe them and compare what I see day to day.
I have dozens of questions about the things I’ve observed and I would really like to understand the physics ...
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comparing use of Laplace equation with diffusion equation to simulate flow of fluid/water through porous media?
What is the difference in using Laplace equation (say only in 1D) to simulate water flow in a porous media with that of using diffusion equation for same purpose?
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Link between different ways of modeling permeability
The most famous equation describing the permeability $k$ of a soil is the Kozeny-Carman equation:
$$k = \frac{\phi}{8}r^2 \approx \frac{\phi}{c}\left(\frac{V}{S}\right)^2$$
$\phi$: porosity
V: pore ...
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How to characterize flow of nonreactive tracer in a porous media?
About Tracer Experiment
This experiment is conducted by injecting a fluid with nonreactive species of certain concentration inside a column or core composed of sand. The injection of fluid can either ...
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Unrealistic solution for advection-diffusion-reaction PDE with heterogeneous porous media
About the code: I have a code which simulates concentration from advection-diffusion-reaction PDE in 2D space (X,Y) with time. The solution is obtained using fully implicit finite-difference method ...
user3153
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Shallow water height as vertical coordinate
In atmospheric physics we use often a variety of vertical coordinates, $z$ the height above some reference surface, or $r$ as distance from the planetary center.
However sometimes it simplifies the ...
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What is the difference between an inertial instability and a symmetric instability?
Inertial and symmetric instabilities are fluid instabilities present in atmosphere and ocean.
What are the difference between an inertial instability and a symmetric instability?
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Why does Coriolis determine the rotation direction of a cyclone but not my drain?
It is a common misconception that Coriolis is responsible for the direction the water swirls down a toilet, tub or sink drain. E.g. does a toilet flush the other way in the southern hemisphere? (If ...
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coriolis force in atmospheric/ocean modeling
The Coriolis force is not a real force, but depending on the reference system and how it does refer to an inertial system. Could this Coriolis force as widely used in atmospheric/climate modeling be ...
tom98765x