# Problem set 3 ```Problem set 3 – Brunt-Vaisala Frequency and Potential Energy
Goal – understand by B-V frequency means and what PE means
The Data
You are going to work with two shallow stations from the Bay Mouth.
CBSta9Summer.mat CBSta9Winter.mat
The location of the data columns are in DataColumns.m
And the station from the past problems
Check the Data
Steps
For example for temperature
Summertemp= CBSta9Summer(:,8)
And salinity
Summersal= CBSta9Summer(:,9)
And pressure (actually depth in this case)
Summerpres= -CBSta9Summer(:,7)
Note the data had depth as minus and we need positive pressure so I added the negative.
So now you can plot T and S vs Depth(pressure) and work with them
Plot the data. Does it look ok?
Do the same for the ATL station.
Brunt-Vaisala Frequency
Look at gsw_Nsquared (N2 is usually used to denote BV frequency). What does the function need?
[N2, p_mid] = gsw_Nsquared(SA,CT,p,{lat})
The units are per second squared
The frequency is f=sqrt(N2)/2pi
The period is 2pi/sqrt(N2)
Plot the buoyancy frequency (gsw_Nsquared Brunt-Vaisala frequency squared) for each of the three
stations. Assume temp is Conservative Temp and assume sal is Absolute Salinity.
Now plot the period.
Discuss the frequency (sqrt of N2)
Potential Energy Calculation
PE = weight x distance
Recall that weight = mass x gravity
So PE = mgh where m = mass (kg), g = 9.8 m/s2 and h = distance in meters above some surface.
So if you lift a 1 kg bowling ball 1 meter the Potential Energy is 1x1x9.8 = 9.8 kg m2/s2
The units are Joule (J) or Newton-Meter (SI base units)(Force x Distance)
It turns out that the equation by Simpson, Hunter and Morris is very useful
[Insert equation here]
Discuss equation
Given that equation and the two coastal stations and the PAPA Station calculate PE and discuss
Note I’m getting data from http://www.ccpo.odu.edu/~jlblanco/bmc/
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The following Matlab function calculates the PE for a given water column
%calculate potential energy anomaly given density
%reference:function [PE] = poteng(den,P,depth)
function [PE] = poteng(den,P, depth)
% poteng
Potential Energy Anomaly
%===========================================================================
% poteng
%
% USAGE: [PE] = poteng(den,P,depth)
%
% DESCRIPTION:
%
Calculates the potential energy anomaly from the equation,
%
%
PE = 1/density times the depth integral of the ....
%
% INPUT: (all must have same dimensions MxN)
%
den
= density [kg m-3]
%
Depth of sample (negative number)
%
depth = depth of water column considered (positive)
%
% OUTPUT:
%
PE = Potential Energy Anomaly [Joules per cubic meter]
% NOTE: if you do not divide by the depth you will have J per square meter.
%
% AUTHOR: Larry Atkinson 23/2/99 [email protected]
%
% DISCLAIMER:
%
This software is provided &quot;as is&quot; without warranty of any kind.
%
%
% REFERENCES:
%
J. H. Simpson, D. G. Hughes, and N.C.G. Morris. 1977. The relation of
seasonal
%stratification to
%
tidal mixing on the continental shelf. in &quot;A Voyage of Discovery, George
Deacon, 70th %
%
Anniversary, Volume suppliment of Deep Sea Research (Ed.
Martin Angel). Pergamon Press, Oxford, p %
327-340.
%
%=========================================================================
%make vector of incremental depth (0 -1 -2 -3) -&gt; -0.5 -1.5 -2.5 ...)
DepthInc=Depth-.5;
%Get depth averaged density, rhobar
rhobar=sum(den)/length(den)
%calculate PE
PE=(1/depth)*sum((den-rhobar).*P*9.8)
```