... TECHNICAL REPORT NO. 51 = C FISHERIES RESEARCH BOARD OF CANADA ..".

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1 ... r..". = C FISHERIES RESEARCH BOARD OF CANADA TECHNICAL REPORT NO

2 FISHERIES RESEARCH BOARD OF CANADA Technical Report.s FRB Technical Reports are research documents that <lrc of sufficient importance to be preserved, but which for some reason are not suitable for scientific publication. No restriction is placed on subject matter and the series should reflect the broad research interest of FRB. These Reports can be cited in publications, but care should be taken to indicate their manuscript status to prevnt erroneous implications being drawn from data and analysis that may be preliminary. Some of the material in these Reports will eventually appear in scientific publication. Inquiries concerning any particular Report should be directed to the issuing FRB establishment which is indicate.:! on the titie page.

3 FISHERIES RESEARCH BO!\RD OF CANADA TECHNICAL REPORT NO. Sl Surface Transport Charts for the North Pacific Ocean by W. Percy Wickett J.A. C. Thomson and L. V. Pienaar FISHERIES RESEARCH BOARD OF CANADA Biological Station, Nanaimo. B.C. Hay. 1968

4 Surface Transport Charts for the North Pacific Ocean, W. Percy Wickett l J.A.C. Thomson 2 and L.V. Pienaar 2 by Fisheries Research Board of Canada Biological Station, Nanaimo, B.C. Introduction Monthly charts of surface transport vectors (synoptic pilot charts) for the North Pacific Ocean can be drawn using the 22 years of meridional and zonal components given in Fofonoff (1960, 1961), in Fofonoff and Dobson (1963). in Fofonoff and Ross (1962) and in Wickett (1966, 1967). Such charts are a useful tool for recognizing annual differences in ocean conditions. The card output containing the above numerical output can serve as data input to a computer and plotter to make available, quickly and easily. a long series of charts. The problem was to plot on an azimuthal projection centered on the North Pole, similar to that used for meteorological charts, rather than to plot on a rectangular grid. The Fortran program, VECTR, written for use on an IBM 1130 computer with on line plotter uses as input two matrices calculated by die program for Pofonoff' s analysis (Froese. 1963). as modified by this laboratory. The matrices used contain (1) the calculated zonal component of surface transport and (2) the meridional component of surface transport for data points lying between 1l0oW longitude and 115 E longitude and 6etween 20 0 N latitude and 60 0 N latitude. The program establishes an arbitrary location as the North pole and plots latitude as a radius from the pole (scale is 0.15" per degree). Longitude is defined by calculating the value of the angle THETA in radians such that 180 longitude equala 270 in polar terms. Ipacific Oceanographic Group 2Computations and Theoretical Population Studies Group

5 - 2- With the data point defined. the meridional component (scaled by 0.04) is added with sign retained to the radius. The zonal component 1s then used to calculate a new angle (THETA 1) in radians; nteta 1 - zonal component Umes 0.04 divided by radius (corrected). A correction value is then applied to the new radius which is defined as the radius times the exsecsnt of THETA 1. The new radius and angle thus define the location of the end of the vector of surface transport. The above procedure expresses closely the surface transport vector in terms of a rectangular grid starting from a point defined by polar coordinates. Since the vector should be considered as a measure of transport at the grid points, the plotted output stresses the starting point or data point rather than the end of the vector. A year I s data (12 charts) takes 60 minutes to run on the computer and plotter. 11le following pages. give monthly vectors on an adml.1nthal equidistant projection centred on the North Pole. The 'Plotter output is photographed through a plastic overlay carryirg the coastline and grid of latitudes and longitudes. Ocean Station lip" is indicated by a black dot. The vectors are point values at the asterisks which form the origins of the vectors. Certain cautions concerning the numerical output must be kept in mind. namely. that the monthly mean pressure values used as the original input may give values of transport different from mean transport calculated from daily pressure values. and the calculated values of transport have not been checked against observations at sea. Charts for the remaining years in the series are being produced as time permits. Acknowledgement We are indebted to the Extended Weather Forecast Division of the U. S. Weather Bureau for supplying copies of Mean Monthly Sea Level Pressure Data cards each month.

6 - 3 - FofonoH, N.P. MSS, Transport computations for the North Pacific Ocean Fish. Res. Bd. Canada, HS Rept. Oceanogr. and Limnol., NOB. 77, 78, 79, pp. MSS Transport Computations for the North Pacific O=ean Th.!.2. Nos. 85, pp. Fafanaff, N.P., and F.W. Dobson. MSS, Transport Computations for the North Pacific Ocean, , Nos. 149, 150, l51, 152, 153, 164. FofouoH, N.P. and C.K. Ross. MS, Transport Computations for the North Pacific Ocean, Ibid. No pp. Froese, C. MS, Computation of mass transport in the ocean from atmospheric pressure data. Fortran I program for IBM 1620 computer. lli!!..:., No pp. Wickett, W. Percy. MSS, Fofonoff Transport Computations for the North Pacific Ocean , Ibid., Nos , 92 pp. MSS Transport Computations for the North Pacific Ocean, Technical Report No pp. Wickett, W. Percy, J.A.C. Thomson and L.V. Pienaar, Surface Transport Charts for the North Pacific Ocean, Technical Rept. No. 52, 27 pp.

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APPH 4200 Physics of Fluids

APPH 4200 Physics of Fluids APPH 42 Physics of Fluids Problem Solving and Vorticity (Ch. 5) 1.!! Quick Review 2.! Vorticity 3.! Kelvin s Theorem 4.! Examples 1 How to solve fluid problems? (Like those in textbook) Ç"Tt=l I $T1P#(