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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 Load the data For example for temperature Load CBSta9Summer.mat 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/ ************************** 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 "as is" 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 "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) -> -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)