Implementatin f the Wave Radiatin Stress Gradient as a Frcing fr the ADCIRC Hydrdynamic Mdel: Upgrades and Dcumentatin fr ADCIRC Versin 34.12 Richard A. Luettich, Jr. University f Nrth Carlina at Chapel Hill Institute f Marine Sciences 3431 Arendell St. Mrehead City, NC 28557 Jannes J. Westerink Dept. f Civil Engineering and Gelgical Sciences University f Ntre Dame Ntre Dame, IN 46556 May 18, 1999 Cntractrs Reprt Prepared fr the DEPARTMENT F THE ARMY Castal Engineering Research Center Waterways Experiment Statin US Army Crps f Engineers Vicksburg, MS 39180
CNTENTS TABLE F CNTENTS 1 FRMULATIN 2 ACTIVATING WAVE RADIATIN STRESS GRADIENTS IN ADCIRC VERSIN 34.12 2 FRMAT F THE RADIATIN STRESS GRADIENT INPUT FILE 8 REFERENCES 9 1
FRMULATIN It is well knwn that nnlinearities in the mmentum balance f surface gravity waves result in mmentum being transferred frm the surface wave frequency t lw frequency. Specifically, waves whse amplitude and perid are cnstant in time generate mmentum at zer frequency (steady) via what has been termed radiatin stresses (e.g., Lnguet-Higgins and Stewart, 1964). Newtn s secnd law f mtin requires that gradients in these radiatin stresses must be balanced by a steady frce and cnsequently wave setup r setdwn and lngshre currents result (Massel, 1989; Dean and Dalrymple, 1991). If we assume that the wave field changes slwly in time, the radiatin stress gradients can be included in the mmentum balance f lng wave mdels such as ADCIRC (Luettich et al, 1992, Westerink et al, 1994, Luettich and Westerink, 1999). In this case the mmentum equatins are mdified frm thse given by Eqs. (25,26) in Luettich et al. (1992) t: U + U U + V U fv = t x x x V + U V + V V + fu = t x x y L N M L N M b g Q 1 L N bζ αηg Q 1 L N M ps + g P + M + + + + H M x D x B x R τ sx τ bx ζ αη x ρ ρ ρ ps + g ρ P + H M + D + B + R + τ sy y y y y τ by ρ ρ All variables are as defined in Luettich et al, (1992), with the exceptin f the radiatin stress gradient terms which are defined as: R x 1 ρ L NM S x xx S + y xy QP and R y 1 ρ L NM S x xy S + y where S xx, S yy, S xy = S yx are the radiatin stresses, presumably cmputed frm a shrt wave mdel. It is imprtant t nte that the stress gradients must be cmputed using a crdinate system that is riented in the same directin as the lng wave mdel, which is likely t be different than that used fr the shrt wave mdel. yy QP Q P Q P ACTIVATING WAVE RADIATIN STRESSES IN ADCIRC VERSIN 34.12 The radiatin stress gradients R x and R y appear as external frcing terms in the lng wave mmentum equatins and must be input t the calculatin in much the same was as the wind stress terms τ sx ρ and τ sy ρ. Therefre, in ADCIRC we have bundeled these terms with the wind stresses. If desired, radiatin stress gradients are read in at a specified time interval frm a frt.23 file during the curse f the simulatin. The parameter NWS lcated in the master input parameter file (frt.15) cntrls whether ADCIRC will attempt t read meterlgical (wind and pressure) frcing (frm frt.22 r frt.200 series files), radiatin stress frcing (frm a frt.23 file) r bth. The parameter RSTIMINC in the master input parameter 2
file (frt.15) cntrls the time interval between radiatin stress values. This may be assigned a value that is different frm the parameter in the master parameter file (frt.15) that cntrls the time interval between meterlgical input values (WTIMINC). The parameter NWS is lcated n line 16 f the frt.15 file and may have the fllwing values: NWS = 0 NWS = 1 NWS = 2 NWS = 3 N wind stress, wind velcity, pressure r radiatin stress gradient frcings are used. Wind stress and pressure are read in at all grid ndes frm an input file (frt.22) at a wind time interval that is equal t the mdel time step. It is assumed that the first values in the frt.22 file crrespnd t the beginning f the mdel run (i.e., the cld start time). If the mdel is ht started, initial values in the frt.22 file will be skipped until the mdel ht start time is reached. Units f input stress are (length/time) 2 - which is actually stress/reference density f water - and f pressure are length f water which is actually pressure/reference density f water/acceleratin f gravity. In bth cases length must match the units used in the grid. If a ln, lat crdinate system is used in the grid, length units are assumed t be meters. Wind stress and pressure are read in at all grid ndes frm an input file (frt.22) at a wind time interval that is nt equal t the mdel time step. It is assumed that the first values in the frt.22 file crrespnd t the beginning f the mdel run (i.e., the cld start time). If the mdel is ht started, initial values in the frt.22 file will be skipped until the mdel ht start time is reached. Interplatin in time is used t synchrnize the stress and pressure fields with the mdel time step. Units f input stress are (length/time) 2 - which is actually (frce/area)/reference density f water - and f pressure are length f water which is actually (frce/area)/reference density f water/acceleratin f gravity. In bth cases length must match the units used in the grid. If a ln, lat crdinate system is used in the grid, length units are assumed t be meters. The wind time interval (WTIMINC) must be specified in the input parameter file (frt.15). Wind speed and directin (10 m) are read in frm a US Navy Fleet Numeric frmat file (frt.22) that prvides data n a Cartesian grid at a wind time interval that is nt equal t the mdel time step. Velcity is interplated in space nt the ADCIRC grid. Based n the specified beginning time f the run, ADCIRC will attempt t lcate the prper place t begin in the frt.22 file. Interplatin in time is used t synchrnize the velcity fields with the mdel time step. The unit f wind speed is meters/sec and f wind directin is degrees clckwise frm Nrth. Directin references the directin the wind is blwing frm. N pressure infrmatin is read in and therefre it is assumed that the surface pressure gradient is zer. Several parameters describing the fleet numeric wind file, including the wind time interval (WTIMINC) and the beginning time f the run must be specified in the input parameter (frt.15) file. Garret s frmula is used t cmpute wind stress frm wind speed and directin. 3
NWS = 4 NWS = -4 NWS = 5 NWS = -5 Wind velcity (10 m) and pressure (surface) are read in frm a PBL frmat file (frt.22) at a subset f ADCIRC grid ndes at a wind time interval that is nt equal t the mdel time step. It is assumed that the first values in the frt.22 file crrespnd t the beginning f the mdel run (i.e., the cld start time). If the mdel is ht started, initial values in the frt.22 file will be skipped until the mdel ht start time is reached. Interplatin in time is used t synchrnize the velcity and pressure fields with the mdel time step. Units f velcity are knts and f pressure are Pascals = Newtns/m 2. Velcity references the directin the wind is blwing tward. The wind time interval (WTIMINC) must be specified in the input parameter file (frt.15). Garret s frmula is used t cmpute wind stress frm velcity. Wind velcity (10 m) and pressure (surface) are read in frm a PBL frmat file (frt.22) at a subset f ADCIRC grid ndes at a wind time interval that is nt equal t the mdel time step. This ptin is different frm NWS = 4 because it is assumed that the first values in the frt.22 file crrespnd either t (i) the beginning f the mdel run (i.e., the cld start time) if the run has been cld started r (ii) the ht start time if the mdel has been ht started. Regardless f whether the mdel is cld started r ht started, ADCIRC will nt skip any values at the beginning f the frt.22 file. Interplatin in time is used t synchrnize the velcity and pressure fields with the mdel time step. Units f velcity are knts and f pressure are Pascals = Newtns/m 2. Velcity references the directin the wind is blwing tward. The wind time interval (WTIMINC) must be specified in the input parameter file (frt.15). Garret s frmula is used t cmpute wind stress frm velcity. Wind velcity (10 m) and pressure (surface) are read in at all grid ndes frm an input file (frt.22) at a wind time interval that is nt equal t the mdel time step. It is assumed that the first values in the frt.22 file crrespnd t the beginning f the mdel run (i.e., the cld start time). If the mdel is ht started, initial values in the frt.22 file will be skipped until the mdel ht start time is reached. Interplatin in time is used t synchrnize the velcity and pressure fields with the mdel time step. Units f velcity are length/time and f pressure are length f water. Velcity references the directin the wind is blwing tward. In bth cases length must match the units used in the grid. If a ln, lat crdinate system is used in the grid, length units are assumed t be meters. The wind time interval (WTIMINC) must be specified in the input parameter file (frt.15). Garret s frmula is used t cmpute wind stress frm velcity. Wind velcity (10 m) and pressure (surface) are read in at all grid ndes frm an input file (frt.22) at a wind time interval that is nt equal t the mdel time step. This ptin is different frm NWS = 5 because it is assumed that the first values in the frt.22 file crrespnd either t (i) the beginning f the mdel run (i.e., the cld start time) if the run has been cld started r (ii) the ht start time if the mdel has been ht started. Regardless f whether the mdel is cld started r ht started, ADCIRC will nt skip any values at the beginning f the frt.22 file. Interplatin in time is used t synchrnize the velcity and pressure fields with the mdel time step. Units f velcity are length/time and f pressure are length 4
NWS = 6 NWS = 10 NWS = 11 f water. Velcity references the directin the wind is blwing tward. In bth cases length must match the units used in the grid. If a ln, lat crdinate system is used in the grid, length units are assumed t be meters. The wind time interval (WTIMINC) must be specified in the input parameter file (frt.15). Garret s frmula is used t cmpute wind stress frm velcity. Wind velcity (10 m) and pressure (surface) are read in frm an input file (frt.22) that prvides data n a Cartesian grid (either in ln,lat r lineal crdinates cnsistent with the grid) at a wind time interval that is nt equal t the mdel time step. Velcity and pressure are interplated in space nt the ADCIRC grid. It is assumed that the first values in the frt.22 file crrespnd t the beginning f the mdel run (i.e., the cld start time). If the mdel is ht started, initial values in the frt.22 file will be skipped until the mdel ht start time is reached. Interplatin in time is used t synchrnize the velcity and pressure fields with the mdel time step. Units f velcity are meters/sec and f pressure are Pascals = Newtns/m 2. Velcity references the directin the wind is blwing tward. The wind time interval (WTIMINC) must be specified in the input parameter file (frt.15). Garret s frmula is used t cmpute wind stress frm velcity. Wind velcity (10 m) and pressure (surface) are read in frm a sequence f SFLUX type files frm the Natinal Weather Service AVN meterlgical mdel that prvides data n a Gaussian ln/lat grid at ne time per file. The first data set is fund in file frt.200 and crrespnds either t (i) the beginning f the mdel run (i.e., the cld start time) if the run has been cld started r (ii) the ht start time if the mdel has been ht started. The secnd data set is fund in file frt.xx1 where XX1=200+WTIMINC/3600 and WTIMINC is the time interval in secnds. The third data set is fund in file frt.xx2 where XX2=200+2*WTIMINC/3600. Succeeding data sets are fund in similarly named files. Fr example, if the time between meterlgical files is 3 hurs, WTIMINC=10800 and met files shuld be named frt.200, frt.203, frt.206, frt.209, Velcity and pressure are interplated in space nt the ADCIRC grid. Interplatin in time is used t synchrnize the velcity and pressure fields with the mdel time step. Units f velcity are meters/sec and f pressure are Pascals = Newtns/m 2. Velcity references the directin the wind is blwing tward. The wind time interval (WTIMINC) must be specified in the input parameter file (frt.15). Garret s frmula is used t cmpute wind stress frm velcity. Nte, the SFLUX files are assumed t have been generated by the UNPKGRB1 prgram. Prir t versin 34.05, it was assumed that these files were in binary grib frmat. Starting with versin 34.05 it is assumed that these files are in ASCII tabular frmat. Nte, if the mdel is ht started, it must be dne at a time that crrespnds t a wind file time, (e.g., an even multiple f WTIMINC). Wind velcity (10 m) and pressure (surface) are read in frm a sequence f files frm the Natinal Weather Service ETA-29 meterlgical mdel that prvides data n an ETA grid at ne day per file. Within each day data is prvided every 3 5
NWS = 100 NWS = 101 NWS = 102 NWS = 103 NWS = 104 hurs beginning at 3:00Z and ending at 24:00Z. Fr a mdel ht start, file frt.200 must cntain data frm the day befre the ht started s that the 24:00Z fields can be used as initial meterlgical cnditins fr the mdel run. Fr a cld start, the initial cnditins are assumed t be at rest and therefre the frt.200 file is nt used. The first day f data after ether a cld r a ht start is fund in file frt.201, the secnd day f data in file frt.202, the third day f data in file frt.203, etc. Velcity is cnverted t frm the ETA crdinate system t an East, Nrth crdinate system and all fields are interplated in space t the ADCIRC grid. Interplatin in time is used t synchrnize the velcity and pressure fields with the mdel time step. Units f velcity are meters/sec and f pressure are 100*Pascals = 100*Newtns/m 2. Velcity references the directin the wind is blwing tward. The wind time interval is assumed t be 3 hurs (WTIMINC=10800) and therefre is nt read in the input parameter file (frt.15). Garret s frmula is used t cmpute wind stress frm velcity. Nte, the input files are assumed t be in binary. Nte, the mdel must always be started at the beginning f a day. (e.g., 0:00Z). Radiatin stress gradients are read in frm a PBL frmat file (frt.23) at a subset f ADCIRC grid ndes at a radiatin stress time interval that is nt equal t the mdel time step. It is assumed that the first values in the frt.23 file crrespnd either t (i) the beginning f the mdel run (i.e., the cld start time) if the run has been cld started r (ii) the ht start time if the mdel has been ht started. Therefre, regardless f whether the mdel is cld started r ht started, ADCIRC will nt skip any values at the beginning f the frt.23 file. Interplatin in time is used t synchrnize the radiatin stress fields with the mdel time step. Units f radiatin stress gradient are (length/time) 2 - which is actually (frce/area)/ reference density f water. Length must match the units used in the grid. If a ln, lat crdinate system is used in the grid, length units are assumed t be meters. The radiatin stress time interval (RSTIMINC) must be specified in the input parameter file (frt.15). Radiatin stress gradients, wind stress and pressure are read in. Radiatin stress described fr NWS = 1. Radiatin stress gradients, wind stress and pressure are read in. Radiatin stress described fr NWS = 2. Radiatin stress gradients and wind speed and directin are read in. Radiatin stress input is as described fr NWS = 100. Wind velcity input is as described fr NWS = 3. Radiatin stress gradients, wind velcity and pressure are read in. Radiatin stress described fr NWS = 4. NWS = -104 Radiatin stress gradients, wind velcity and pressure are read in. Radiatin stress described fr NWS = -4. 6
NWS = 105 Radiatin stress gradients, wind velcity and pressure are read in. Radiatin stress described fr NWS = 5. NWS = -105 Radiatin stress gradients, wind velcity and pressure are read in. Radiatin stress described fr NWS = -5. NWS = 106 Radiatin stress gradients, wind velcity and pressure are read in. Radiatin stress described fr NWS = 6. NWS = 110 Radiatin stress gradients, wind velcity and pressure are read in. Radiatin stress described fr NWS = 110. NWS = 111 Radiatin stress gradients, wind velcity and pressure are read in. Radiatin stress described fr NWS = 111. Depending n the value f the NWS parameter, the fllwing additinal parameters must be set in the frt.15 file: NWS = 0 N further meterlgical r radiatin stress parameters are required. NWS = 2, 4, -4, 5, -5, 6, 10 line 23: WTIMINC where, WTIMINC = time in secnds between data in the met file NWS = 3 line 23: IREFYR,IREFM,IREFDAY,IREFHR,IREFMIN,REFSEC line 24:NWLAT,NWLN,WLATMAX,WLNMIN,WLATINC,WLNINC, WTIMINC where, IREFYR = year f the start f the simulatin IREFM = mnth f the start f the simulatin IREFDAY = day f the start f the simulatin IREFHR = hur f the start f the simulatin IREFMIN = minute f the start f the simulatin REFSEC = secnd f the start f the simulatin NWLAT = number f latitude values in the met file NWLN = number f lngitude values in the met file WLATMAX = maximum latitude (deg) f data in the met file (< 0 suth f the equatr WLNMIN = minimum lngitude (deg) f data in the met file (< 0 west f the Greenwich meridian) WLATINC = latitude increment (deg) f data in the met file (must be >0) WLNINC = lngitude increment (deg) f data in the met file (must be >0) WTIMINC = time interval in sec between data in the met file. 7
NWS = 11 N further meterlgical r radiatin stress parameter are required. WTIMINC is assumed t be 10800 sec. NWS = 100, 111 line 23: RSTIMINC where, RSTIMINC = time in secnds between data in the radiatin stress gradient file NWS = 102, 104, -104, 105, -105, 106, 110 line 23: WTIMINC, RSTIMINC where, WTIMINC = time in secnds between data in the met file RSTIMINC = time in secnds between data in the radiatin stress gradient file NWS = 103 line 23: IREFYR,IREFM,IREFDAY,IREFHR,IREFMIN,REFSEC line 24:NWLAT,NWLN,WLATMAX,WLNMIN,WLATINC,WLNINC, WTIMINC, RSTIMINC where, RSIMINC = time in secnds between data in the radiatin stress gradient file all ther values as in NWS = 3 FRMAT F THE RADIATIN STRESS GRADIENT INPUT FILE The frmat fr the frt.23, radiatin stress gradient file, is the fllwing: I, RSX2(I),RSY2(I).. # I, RSX2(I),RSY2(I). # where, I = nde number in the ADCIRC grid where the radiatin stress gradient is being specified RSX2(I) = R x in units f (length/time) 2 where length must match the units used in the grid. If a ln, lat crdinate system is used in the grid, length units are assumed t be meters RSY2(I) = R y in units f (length/time) 2 where length must match the units used in the grid. If a ln, lat crdinate system is used in the grid, length units are assumed t be meters A data line must have the frmat I8, 2E13.5 A data line is repeated fr as many ADCIRC grid ndes as desired 8
A line cntaining the # symbl in clumn 2 indicates the radiatin stress gradients beginning n the fllwing data line apply t the next time increment. At each time increment, every nde that is nt explicitly referenced by a data line is assumed t have a radiatin stress gradient f zer. If the mdel is cld started, the first data crrespnd t the beginning time f the mdel run. If the mdel is ht started the first data crrespnd t the ht start time. Subsequent data sets (separated by # lines) are prvided every RSTIMINC secnds. Data must be prvided fr the entire mdel run, r the run will crash. REFERENCES Dean, R.G. and R.A. Dalrymple, 1991, Water Wave Mechanics fr Engineers and Scientists, Wrld Scientific, New Jersey, 353p. Lnguet Higgins, M.S. and R.W. Stewart, 1964, Radiatin stress in water waves; a physical discussin, with applicatins, Deep-Sea Research, 11:529-562. Luettich, R.A. Jr., J.J. Westerink and N.W. Scheffner, 1992, ADCIRC: An Advanced Three- Dimensinal Circulatin Mdel fr Shelves, Casts and Estuaries, Reprt 1: Thery and Methdlgy f ADCIRC-2DDI and ADCIRC-3DL, DRP Technical Reprt DRP-92-6, Department f the Army, US Army Crps f Engineers, Waterways Experiment Statin, Vicksburg, MS., Nvember 1992, 137p. Westerink, J.J., R.A. Luettich, Jr. and N.W. Scheffner, 1994, ADCIRC: An Advanced Three- Dimensinal Circulatin Mdel fr Shelves, Casts and Estuaries, Reprt 2: Users Manual fr ADCIRC-2DDI, DRP Technical Reprt DRP-92-6, Department f the Army, US Army Crps f Engineers, Waterways Experiment Statin, Vicksburg, MS., January 1994, 156p. Luettich, R.A., Jr. and J.J. Westerink, 1994, Elemental Wetting and Drying in the ADCIRC Hydrdynamic Mdel: Upgrades and Dcumentatin fr ADCIRC Versin 34.XX, Cntractrs Reprt, department f the Army, US Army Crps f Engineers, Waterways Experiment Statin, Vicksburg, MS, March 11, 1999, 8 p. Massel, S.R., 1989, Hydrdynamics f Castal Znes, Elsevier, Amsterdam, 336p. 9