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Link to Full Text ~ .......... ~ ~ - - -- .. ~~ -- .... ..... .., - .. - ... ...., .... IX. ADYNAMIC HESEHV01H SIMULATION MODEL-DYHESM:5 i\ 311 c. transverse and longitUdinal direction playa secondary role and only the variations) ." I in the vertical enter lhe first order balances of mass, momentum and energy. 1/ I Departures from this Stilte of horizontalisopyc'nalsare possible, but these \ tI l A DYNAMIC RESERVOIR SIl\olULATION MODEL ­ enter only as isolated events or as \I/eak pe.!lurbatiQ.D.S. In both cases the.•net eJJ;cJ,J CI DYRESM: 5 is e~plured wi(h a parame!efizalion of their inp,ut (0 the vertical s(rUelure"iiild , ) I comparison of the model prediction and field data must thus be confined to ~ ~ .....of.............,.calm when the structure is truly one-dimensional. lorg 1mberger and John C.. Pattetsun .. ~ ,. The constraints imposed by ~uch a one-dimer.:Jional model may best be University of Western Australia quantified by defining a series of non-dimensional llUmbers. The value of the Nedlands, Western Australia Wedderburn number :) LV =.i.!!.. h (.J" I I '( 14.2 • L- '7 y(l .. n, (I) , \ ..,' I / 1. INTRODUCTION where g' is an effective reoufed gravity across the thermocline, h the depth of the mixed layer, L the basin scale, and u· the surface shear velocity, is a measure of """·".',j<}·,t-·;~·'",,,"~~,'ti The dynamic reservoir simulation model, DYRESM, is a one-dimensional the activity within the mixed layer. Spigel and Imberger (I980) have shown thah, numerical model for the prediction of temperature and salinity in small to medium for W > 00) the departure fmm one-dimensionality is minimal and for I ':I­ sized reservoirs and Jakes. The model was constructed toiorm a suitable basis for 0(11/ L) < W< 0(1) the departure is severe but may be successfully parameter- r 17 I ized. For W < O(h/L) the lake ove!1urns,- " • I, I a more general water quality model. The requirements imposed by this aim are J':~I made by Imberger (1978), who shows that for both substances with a fast tumo,ter Inflows do not lead to severe vertical motions in the bulk of the reservoir I lime such as phytoplankton and for conservative substances such as salt, the mix­ provided the internal Froude number ing mechanisms within the reservoir must be modeled accurately. Not only must a -- .mOdelbe.capable of predicting, the~v~ Y~rlieal tri!illifer--!!.t:.J!1.!!~.'0!~"~~ ~roi~ U <1 and the subsequent flow processes, but it must also be capable of F; = .Jg'H (2) Iresolving individual mixing regioos. - - -.----. This is a great departure from what has been assumed to date. Previously it I has been generally accepted that once a partkular reservoir model was capable of where U is the inflow velocity, g' the reduced gravity between the surface reser­ being tuned to correctly predict the vertical temperature profiles over a particular voir Water and the inflow and H the reservoir depth. study period, that this then constituted a reliable model for the purposes of water The outflow dynamics..is governed by a similar Froude number criterion I quality modeling. However, as discussed in Fischer et al., (1979) this is not the case since gif'f~r~I]t paraml;t~r~are dependent on different mixing Qro.9~sses fQ[ f~ = Q their. dis~ributio!l. g,I/2Hs/2 < 1 (3) The problem confronting the modeler is thus difficult. On the one hand the model should be widely applicable and cheap to run, and on the other it must cap' where Q is the outflow discharge and g' the reduced gravity between the surface ture the mixing induced by the small ·scales of motion. The marriage of these and bottom water. seemingly conflicting aims requires careful consideration of not only the concept I Laslly, the earth '5 rotation will not lead to vertical motions if J but also the architecture ora proposed--model. Although increasing availability oi' I . computing power has led to an increased potential for application of two or three- dimensional reservoir models, the required !]§.Ql!Jlio_1h. down to centimeters and g'8 minutes, is not currently possible within the context of long term simulations, and f 2B 2 < (4) I aor.e-dimensional model appears to be the only realistic option. 7 l F • I' -~ >Thelli.Qng stratification normally found in 2.m.all to lUe.t!ium sized reservoirs where g'is the effective reduced gravity over the depth 8, the scale bf the ~lucity A r may be used to advantage. strong stratiJicallon of the water inhibits vertical .toncell1ral.ious~ I ,IS the Coriolis parameter and B is the maximum width of the lake. - I~ c motions and reduces the turbulence to intermittent bursts. For such lakes the I~"··"'·:'I • ~ ~ (-t1I'IIll(hl InKI "l AIl"lt'U!IL'I'I~ ~ III'" • nllllWI '>lOll ::.~J ' 'lill \u ,I. I 1".I,f,I"'- 1Jt,lh\ JO.HI ri • •_,:, ...... ___ I' 4' ••:->4 J ""., '- ' L t t' . " -\~;:fi'l!f~.$$'- rt~~ i~lX~) 1l'~ '~~";. ~~"" ~~.L_~·~." ~"~'~.:. .. .. 1' "'_ ....... .. '.. r ~~- >t-....-,...:.-.;,._-:.~,. _~~,:~~~-_.;_:~'>:~....--.-. _.;,.._~. ~~,._.~,,--, ~-::""· _-~---c-"i -~ ~"_., ~~. "-~. ~ ~;;.~r't."": .:.:~-r:_',:~" ·?>-,-<~~~':;4.14>4$i.,:j;;'~~,4:t.~;. tf"''''''. __ ... __ ....... ..l .. , ....... -Q,'- "" - r, . ,':'-",'-':' ,;;:/-',) . ~ ~ ~ 312 JOHG IMBEHGEH AND JOHN C. PAT'l'E.\SON IX. A DYNAMIC HESEHVOm SIMULATION MODEL-DYRESM:5 313 Within these constraints DYRESM yields an llccurate descriplion of the 2. DY.R.E~M MAIN PROGRAM dynamics governing the verlical structure in a lake. It must, however, always be emphasized that superimposed on the structure predicted by DYRESM there are I 12[£'h&~ The model DYRESM is cocstructed as a main program with :mbroutines \ mixini which have only a second order influence on the vertical slruc­ which separately model each of the -e.hY~'!!..PJ~~se~ .of inflow, withdrawal, mixed !tures, but which are the first order mechanisms for transporting subslances hor- layer dynamics, and vertical transport in the hypolimnion. In addition, thm'e are a .~. I izontally. These find their origins in _~.!Wan~~~ .b~~timt al!..<!.£Q.oHng at the edge of. number of service subroutines which provide maintenance of the layer sllslem !he.1,!~-e, c!ir~t ~ nd .Shd.~iillL.bY~ ri.Q~ ')' r surt1!ce runoff. sheiterinu mountain. .. (volumes, positions, etc.). and provide calculations of physical propertk,s which are and boundary mixing in the hypolimnion, Only the influence of these processes frequently required such as density. The functions of the main program are the;,'e­ on the one-dimensional structure is modeled by DYRESM, A separate perturba­ fore those of input/output, the calculation of fixed parameters. and control over tion scheme is required to reveal their influence on horizontal varialions in n reser­ timing of the calls to the various process subroutines. voir. The firslorder vertical structure computed with DYRESM may in future investigations be used to compute such hgrizontul traosQoftprocesses. These may The question of how frequently the process. subroutines should be called \ D t natu.rally arises, For-.!!lost purposes., a ,gailY pl1(diction of th~JhermaLstruc;tur.e..is.I." be modeled with a simplified three-dimensional model using the one-dimensional ~uffl~i~.nl~ 'yasi~ ~of vertical structure as the mean density field. and the time the model is set to this value. Since the 1 inflow and outflow volumes change only slowly~ generally over a few days at least, I' <k Even the one-dimensional problem is oot simple. A uniform gr:rt model this basic lime step is also suitable for lhese processes, and Ihe appropriate subroll- . which resolves lhese fine scales over the whole depth would require a large tines are cal1ed~..93jJy. On the other hand, the mixed layer dynamics covers number of mesh points and computation would be slow, to say nothing about scales very much shorler than one day, and e.ven thOu.g.h. dailY. ave.r.aged meteoro-j problems of stability and numerical diffusion. Even if local compaction of a wider logical inputs ... e mo!)~!v used, the mixed layer model subroutines need to be grid were employed. which introduces its own problems. the model at any instant ~alled more frequently tQ m~tch the response-of the'diurna"ideepening. would have only an estimate of where the compaction was required for each pro­ cess,and since several processes may occur at different positions simultaneously, Thus the model incorporates ,two time steps; a fixed basic giep 0: ~>ne day and ) v' little advantage would be gained. a ~ariable. syeb-d:illK. time st~PJorJ1!e_ mixing algorllhm. The length of this sub- .I 2lliL9y'ar~~r...baur I: I I I dally step IS determmed by the dynamiCs and ranges between i!nJ I' t -;lith these considerations in mind. the model DYRESM was dey'eloped by ~elye. ho.!:'~!Jf averaged data is used, This procedure allows small time steps Jl.-/, Imberf: "r et al. (1978) with a different approach to the task. Concentrating on 4' when the dynamics so require; in less critical periods, the time step expands "paraJTI.I:!~erizatioJLQL th~'physical proSS&~k~Lrather than numerical solution of the without loss in accuracy. appropriate differential eq'uations, DYRESM makes use of a layer concept, in which the reservoir is modeled as a ,.System..of !!.orizoo.taLJ<lYers_of uniform pro", DYRESM is then organized in the fOllowing way (see Flowchart 2.0. The per!y..~ These layers move up and down, adjusting their thickness in accordance main program inputs the fixed data; physical dimensions, volume and area as a with the volume-:depth relationship, as inflow and withdrawal increase and decrease function of depth, physical properties of the inflowing streams, locations of the the reservoir volume.
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