wave refraction diagrams for the baltimore canyon … · mid-atlantic continental shelf. -wave...

$: WAVE REFRACTION DIAGRAMS FOR THE BALTIMORE CANYON … · mid-Atlantic continental shelf. -Wave refraction diagrams for a wide range of normally expected wave periods and directions$
NASA TECHNICAL

MEMORANDUM

COCN^«CO

NASA TM X-3423

WAVE REFRACTION DIAGRAMS FOR

THE BALTIMORE CANYON REGION OFTHE MID-ATLANTIC CONTINENTAL SHELF

COMPUTED BY USING THREE BOTTOM

TOPOGRAPHY APPROXIMATION TECHNIQUES

Lamont R. Poole

Langley Research Center

Hampton, Va. 23665 \

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, 0. C. • DECEMBER 1976

https://ntrs.nasa.gov/search.jsp?R=19770009733 2020-01-12T10:54:54+00:00Z

1. Report No.

NASA TM X-3^232. Government Accession No. 3. Recipient's Catalog No.

4. Title and Subtitle WAVE REFRACTION DIAGRAMS "FOR THE BALTIMORECANYON REGION OP THE MID-ATLANTIC CONTINENTAL SHELFCOMPUTED BY USING THREE BOTTOM TOPOGRAPHY APPROXIMATIONTECHNIQUES

5. Report Date

December 19766. Performing Organization Code

7. Author(s)

Lament R. Poole8. Performing Organization Report No.

L-1100U

9. Performing Organization Name and Address

NASA Langley Research CenterHampton, VA 23665

10. Work Unit No.

161-07-02-03

J1. Contract or Grant No.

12. Sponsoring Agency Name and Address

National Aeronautics and Space AdministrationWashington, DC 205 6

13. Type of Report and Period Covered

Technical Memorandum

14.'Sponsoring Agency Code

15.. Supplementary Notes

16. Abstract .

The Langley Research Center and Virginia Institute of Marine Science'waverefraction computer model was applied- to the Baltimore Canyon region of themid-Atlantic continental shelf. -Wave refraction diagrams for a wide range ofnormally expected wave periods and directions were computed by using' threebottom topography approximation techniques: quadratic least squares, cubicleast squares, and constrained bicubic interpolation. Mathematical or physi-cal interpretation of certain features appearing in the computed diagrams isdiscussed.

17. Key Words (Suggested by Author(s))

Wave refractionBottom topography approximationBaltimore Canyon region

18. Distribution Statement

Unclassified - Unlimited

Subject Category k8

19. Security Oassif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of. Pages

155

22. Price*

. $6.25

* For sale by the National Technical Information Service, Springfield. Virginia 22161

WAVE REFRACTION DIAGRAMS FOR THE BALTIMORE CANYON REGION

OF THE MID-ATLANTIC CONTINENTAL SHELF COMPUTED

BY USING THREE BOTTOM TOPOGRAPHY

APPROXIMATION TECHNIQUES

Lament R. Poole

Langley Research Center

SUMMARYV •

• r •Wave re-fraction diagrams were computed by applying the

Langley Research Center and Virginia Institute of Marine Science

wave refraction computer model to the Baltimore Canyon region of

the mid-Atlantic continental shelf. Diagrams were presented for a

wide range of normally expected wave periods and directions. For

each combination of period and direction, diagrams were computed

by using each of three commonly used bottom topography approxima-

tion techniques (quadratic least squares, cubic least squares, and

constrained bicubic interpolation), and all these diagrams are

presented with the exception of cases in which essentially identi-

cal diagrams resulted from the three techniques. Certain features

of the computed diagrams were discussed with respect to physical

or mathematical interpretation, but no conclusions were drawn.

INTRODUCTION

Man's increasing use of continental shelf regions of the

world has stimulated the development of analytical models to aid

in the study of the physical processes affecting offshore and

coastal activities. One such analytical tool is the wave refrac-

tion model, which describes the behavior of surface waves propa-

gating through areas of irregular bottom topography. The Langley

Research ;Center; (LaRC) and .the Virginia Institute o;f Marine'

Science. (VIMS) have, in a cooperative effort, developed a large-

scale -refraction model (ref. 1) for application.to the Virginian

Sea,.a region -of' th.e mid-Atlantic continenta'l-shelf from. Cape

Hatteras.to Cape Henlopen. Computer resource .requirements for

applying the;model to a large geographical region.were signifi-

cantly, reduced by the subsequent incorporation of a random-access

technique for modular storage and retrieval of bathymetry, d.ata

(re,f. -2). '• Recently, the model has been'-modified .to .employ,. ori

,'Optd.pn,. three commonly used techniques for approximating local .

ocean •bottom;topography. Two of these techniques.are-quadratic

least ;squares.and cubic least squares, both of whiph provide some .

smoothing of the discrete bathymetry data but do not 'insure con-

tinuity in the depth or its derivatives. The third .technique, .

constrained; bicubic interpolation, provides continuity without

smoothing.;:: Incorporation of all three techniques stemmed from a

small-scale refraction study (ref, 3) in :which it was concluded

that;, the best approximation technique for use in future .studies

could -.riot ;b'e determined without extensive comparison of, computed

results with; quantitative experimental data. In lieu of such a

comparison,; refraction diagrams can. be computed by using each of

the: techniques. Then more confidence can be placed in .the:cdm-

pute.d results' if no significant discrepancies exist among the

three diagrams. ,

. , The purpose of this paper -is to present wave refraction

diagrams computed by applying the LaRC-VIMS' model to an area of

the mid.-Atlantic shelf called the Baltimore Canyon region :after a

prominent regional'submarine geological feature. Extending from

near.Wachapreague Inlet, Virginia, to near Manasquan Inlet, New

Jersey, the region is of particular current interest with regard

to offshore petroleum deposits and is one of a series of model

regions which to'gether provide broadrscale refraction modeling

capability from Cape Hatteras to Montauk Point", Ne.w .York (ref. 4).

An,, immediate application of the computed diagrams is planned by

the Philadelphia District and the Coastal Engineering' Research .

2 : . - ; " - . • . - - " . - . - ' . . ; • . ; . • . ,

Center of the U.S. Army Corps of Engineers; these results will-be

used to furnish initial conditions for a fine-scale refractionstudy in the nearshore region off Ocean City, New Jersey.••'•-'•' -

, . . " " ' • »

: DATA INPUT . " - -'

The bathymetry data array for the Baltimore Canyon- regio.n1' was :

developed by first constructing a special transverse-.Mercator map

projection with a central meridian at 75° west, similar, to/the one

constructed for the Virginian Sea region. (See ref v:_1.pfo.r .;details.)The projection was then overlaid with a 0.5-nauti.cal.^raile ;:'sjquare '

grid pattern extending for 150 nautical miles from .north:'td south

and for 127 nautical 'miles from west to east. Depth values at the;r' • • • • *'•'<

76 200 nodes (300 rows by 25^ columns) of the square grid.pattern

were determined by using sounding charts and;'other data' i'h?'a .man- -

ner analogous to that used in developing :the. Virginian Seavvbathyin-

etry data grid (ref. 1). A three-dimensional computer-drawn-plot 'of the Baltimore Canyon region bathymetry data grid (with a verti-cal exaggeration of approximately 300~to 1) is shown in figure 1.:

The regional array was then divided into a series of smaller mod- •'-'•ules for use with the random-access data storage and retrieval- ' "technique described in reference 2. The module size.was selected ' •

as M2 rows by 32 columns to minimize computer cost,, resulting in : ;

a series of 72 overlapped bathymetry data modules. (See ref.- 2'

for sequencing and overlapping details.) As a final adjustment to

the input bathymetry data, the "-program input parameter for. tide

was set so that the input depth values would correspond to mean '

low water. • • ; - : - -

A range of wave direction and period was desired which would"5

provide meaningful refraction diagrams while being realistic from:

the standpoint of normally-occurring real-life wave conditions.

With these requirements in mind, the selected input wave direc-tions ranged from 0° (from due north) through 90° (from due east)to 160° (from due south). Input directions from the west were notdeemed significant for this study because of the limiting fetch for

3

'Cape May.

Delaware

Figure 1.- Three-dimensional computer-drawn plot of the

Baltimore Canyon region bathymetry data grid. Verti-cal exaggeration, 300 to 1.

physical wave generation. Within the selected direction range, '

input .directions were chosen at 22.5° increments (i.e., N, NNE,

NE, etc. ) as was done in the study presented in reference 1..

Input wave periods were selected in 2-second increments from 6 sec-onds to;' 16 seconds. On-the basis of results of'reference 1, wavesof•periods.less than 6 seconds were expected to undergo very little,if-any, refraction; thus, rejfrac-t-ion-:diagrams"~for these periods

would be of little meaning. It was also felt that waves of peri-

ods greater than- 16 seconds would occur so infrequently in nature

that their inclusion in this study was not justified. As a final

input, the initial wave height was fixed arbitrarily at 0.3 meter

for all cases since, according to linear wave theory, wave'height

does not affect the refraction pattern for a given combination of

wave period and direction.

; ; • , . WAVE.REFRACTION DIAGRAMS ' . ' ; . -

i ' ' r ,' a*

Wave refraction diagrams'for'the Baltimore .Canyon region were

computed for the input range of wave period and direction- by using

quadratic least squares, cubic least squares, and constrained

bicubic, interpolation techniques for approximating local bottom

topography. The initial separation distance between wave rays was

selected as 3 nautical miles to provide adequate overall resolu-

tion without cluttering the diagrams. Computations were required

to begin in deep water, which, for the purposes of this paper, was

considered 'to be a water depth greater than one-fourth the initial

wavelength for the particular wave period:being considered. (See

ref. 1 for discussion.) Tick marks were drawn along each computed

ray at 'points equally spaced in time, with the time increment

varied with .wave period to provide relatively uniform spatial reso-

lution among- cases of different periods. By connecting correspond-

ing tick marks o.n adjacent rays so that the connecting curve is

orthogonal to each.ray, wave crest patterns can be derived.

Computed- refraction diagrams are presented in figures 2 to 52

in the sequence given in table I. Diagrams computed for a wave

direction'of 0° and periods of 12, 14, and 16 seconds have been

omitted because only one or two rays met the deep-water condition

for initiating computations. Unless noted otherwise, each figure;,

consists of three parts: part (a) presents the diagram computed

by using the quadratic least squares technique for approximating .

bottom topography; part (b) presents the diagram computed by using

the cubic least squares technique; and part (c) presents the dia-

5

gram computed by using the constrained bicubic interpolation tech-

nique. When essentially identical diagrams resulted from the

three techniques, only the one computed by using the quadratic

least squares technique is presented. :

Some general comments are in order as an aid to potential

users in interpreting the various diagrams. Since the tick marks

along each ray denote equal time spacing, an increase in the spa-

tial density of tick marks as a ray approaches the shore indicates

decreasing wave phase speed. Convergence of a group of :neigh-

boring rays indicates an area of relatively high wave energy,;

whereas a sparsity of rays indicates relatively low energy. On

occasion, individual rays stop abruptly in an area of relatively

deep water (ray 23 in fig. 20(a), for example). Such ray; termi-

nations indicate failure to converge on a proper value fo;r local

ray curvature or calculation of a physically unrealistic value

for wave height and, as such, should be considered of no physical

significance. In several instances, individual rays undergo

abrupt changes in direction relative to the mean direction of

neighboring rays (ray 40 in fig. 32(c), for example). These

abrupt changes are induced by sharp gradients in the local bottom

topography, which are influenced, in turn, by the technique

selected for approximating the topography within the finite-mesh

bathymetry grid. Since use of the constrained bicubic interpola-

tion technique results in a surface which passes directly through

the bathymetry data points, sharp topography gradients tend to

occur more often with this technique than with the two least

squares techniques, both of which provide some smoothing .of the

data.

TABLE I.- SEQUENCE OF WAVE REFRACTION DIAGRAMS

Figure

2 ;3 .4

5 .6789101112

1314

1516

1718

19.20

21

22

2324

2526

27

Wave direction,

a, degrees

00

0

22 . 5 '

22.5

• ' • ' .22.5

22.522, 5

22.5

45

45

.45

, ' 45

'45 '

45

'.67 ..5

'.-'"•. ,67.5 .. ..67.5

67.5

'•;" 67.5

67.5

:• ; 90

90

, ' , 90

":;•: 90"

• ' ' 90

Wave period,

T, secondsa6a810a68

10

12

14

16

6

8

10

12

14

16

68

10

12

14

16

6

8

10

12

14

Figure

28

2930

. 3132

3334

-: 3536

3738

3940

41

42

4344

4546

4748

4950

5152

Wave direction,

a , degrees

90

112.5

112.5

112.5112.51 12.5

112. 5

135

135

135

135

135

135

157.5

157.5

157.5

157.5

157.5

157.5180

180

180

180,

180

180

Wave period,

T, seconds

16

6

8

1012- •

14 -.-

16 ,

6

,.(. 8

10: 3 1 •12

14

16

6

8'

10,1214

16

6

8

10

12

14 '

16

aOnly the diagram computed by using the quadratic least squarestechnique is given because no resolvable difference existed among dia-

grams computed by using the three approximation techniques.

75°|00' 74°|00'Y-axis, nautical miles

73°|00'

+•1 i imiiM1111ii i 111iii 11111111in11111111i i11 i

Figure 2.-- Wave refraction diagram. a = 0°; T = 6 seconds.

Bottom topography approximated by quadratic least squares

technique. • . : . : .


73°|00'

Figure 3-- Wave refraction diagram. a = o°; T = 8 seconds.


technique.

-. .:75°|00' 74°|00'

Y-axis, nautical.miles

73°|00'

•' . (a) Bottom topography approximated by quadratic

' ' • .•' least squares technique.

Figure-4.- Wave refraction diagrams, a = 0°; T = 10 seconds

10

75°00' 74°|00'Y-axis, nautical miles

73°|00'

40°

(b) Bottom topography approximated by cubic

least squares technique.

Figure 4.- Continued. .

11

75° 00' 74°|00'Y-axis, nautical miles

73°|00'

ra uI I I II I I I I II 11 II 11 II II I 11 I I MM I I I I I I I I I I II I 11 IMI

12

,(G) Bottom topography approximated by constrained

bicubic interpolation technique.

Figure 4.- Concluded.

74°|00'Y-axis, nautical miles

Figure 5.- Wave refraction diagram. a = 22.5°; T = 6 seconds.


technique.

13


73°00'

40° °g

(a) Bottom topography approximated by quadratic


Figure 6.- Wave refraction diagrams, a = 22.5°; T = 8 seconds


73°|00'



Figure 6.- Continued.

15

75°00' 74°|00'Y-axis, .nautical miles

73°|00'

,40°

- DELAWAREE, ^ BAY':'

16

(c) Bottom topography approximated by constrained

• bicubic interpolation, technique.

. , • Figure. 6.-, .Conclude.^.

75°00' 74°|00'Y-axis, nautical miles'

73°00'

40° °g



Figure 7.- Wave refraction diagrams, a = 22.5°; T = 10 seconds.

17


73°00'

111 111 I M I II 111 1 1111 111 I 11 II II I I I 1111 I M I III 111 I I I I 11 I I [ I I 11 I I I II I M I I I M 11 I I I I II I I I I 111 I II I 11 I [ I II I 111 M III I 11I . I - I I ~T~1* I ,1 - v r* *. ' » " l ~ *:' * \ L f. ^^—»^^^— . I ' H I >./ ^ 7"~* / j ^ * t S.K f

(b) Bottom topography approximated by -c.ubic

least .squares technique.

Figure 7.- Continued.. .

18


JTT

73°|00'

(c) Bottom topography approximated by constrained ...'

bicubic interpolation technique. -"..-'-' • . '.** .-i

Figure 7.- Concluded. • . _ '.-'' .;19


73°|00'

40°



Figure 8.- Wave refraction diagrams. a = 22.5°; T = 12."seconds

20


73°|00'

40° °G?




21

75°00' 74°|00'

Y-axis, nautical miles

73° 00'

(c) Bottom topography approximated by constrained.


. ; . : • • . . - • • Figure 8.- Concluded. ;

22


73°|00'


least squares technique. .

Figure 9-- Wave, refraction diagrams, a = 22.5°; T = 1 *J seconds

23

75° 00' 74°|00'


73°|00'

40°

24.

(b)' Bottom topography approximated by cubic

least squares technique.f

Figure 9.- Con t inued .

750100' 74°[00'Y-axis, nautical miles

73°|00'

•(c) Bottom topography approximated by constrained

• ;. bicubic interpolation technique.

. . - • ' • Figure 9 . - Concluded.

25

•>-75 000' . - - 74°|00'Y-axis, nautical niiles

73° 00'

r '* . . . -- i - •/••= . . ' - / - . • : - : - - . • •

i- ••»;*C£;)\Bottom;:tpp'O"graphy; approximated by quadratic

F r: -?'::-i->"V:;";. -:''i\";i s-t ;square,s technique.

Figure;^^^lâV^êâGtio^rdiagrams. a =22.5°; T = 16 seconds

26 /|S|:>::;S.:.;K • . :-

75°|00' 74°|00' '"Y-axis; nautical miles

73°|00' '

(:b) Bottom topography approximated by cubicleast squares technique.Figure 10.- Continued. "•/'•

27


73°|00'

28

(c) Bottom topography app>oximated by constrained


Figure 10.-' Concluded.

75c|00r ' . 74°|00' .Y-axis, nautical miles

73°|00'

(a-) Bottom topography approximated by quadratic - '

. '-'-:•.-':.'lea"s.t'.squares technique. ; • •

Figure 1 iv-^Wave^refraetion diagrams, -a = 45°; "T" =• 6'seconds.

29-

-- 75°|00' 74°|00'Y-axis, nautical miles

73°001

40°

'S,

30

:•' (b) Bottom topography approximated by cubic

:'.;-: . least squares technique.

: • : . . ; • Figure 11.- Continued.


73°00'

ra ut

'S,


"-.•".:.•/••• .-.bicubic interpolation technique.

••" V;f: .. '" Figure 11.- Concluded.

31

75°00' 74°|00' '


(a) Bottom topography approximated .by quadratic,^-. .- . . • ' " ' * : .''•"' ', ' ^f-

. -.-; ••---•-'.- least squares technique.; -.^/i "•.'•"-'.;;V:

Figure 12.-.'Wave refraction diagrams. a -= 45°; . T:,-='X8' "seconds

32 : -•-'•.-••"•• - - . ' - ' ' ' :'>>""' ' r.

75°00' 74°|00'


73°|00'

40° °E




33

••• 75° 00' 74°|00' v•Y-axis, nautical miles

73° 00'

T (c-). Bottom topography approximated by constrained- c';.:.. :;, ;-'. . bicubic interpolation technique. •[ • . ..

,- •'~y?:;: . .. Figure 12..- Concluded. ' • • ' " ' .

75°00' ' 74°|00'Y-axis, nautical miles

73°|00'

(a) Bottom topography approximated by quadratic •• '•'

. • ' ' least squares technique. . • " '.'"'.

Figure 13'-- Wave refraction diagrams. <* = 45°;. T .= 10 seconds.

35.


73° 00'

+i 1 1 1 1 1 1 1 1 1 1 1 1 M 11 |i 11 ii 1111| 111 M M 11 11 M M 111| i M 11 up i

36


least .squares, technique.

Figure .13.- Continued.


73°|00'

40° fl I MM 11111111111111111111111 I— 1 - M ' I I

: (c) Bottom-topography approximated by constrained *. - • . . , , «• * — , <f

.' " - " ' " '"" .bicubic interpolation technique,

i .'• ;' '. Figure 13-- Concluded.

37

75°00' 74°|00'

Y-axis, nautical miles73°|00'

40°



Figure 14.- Wave refraction diagrams, a = 45°; T = 12 seconds

38 "


73°|00'

40°00'


least squares technique.Figure 1M.- Continued.

39


73°|00'

40° °g

40

(c). Bottom topography approximated by constrained


. . . Figure 14.- Concluded.

75°00'

40°°El


en o> -jm

73°|00'



Figure 15.- Wave'refraction diagrams. a = 45°; T = 14 seconds.4-1

74°|00Y-axis, nautical miles

I

•» . (b.) Bottom topography approximated by cubic.;'"_...;-.••. •. •-•. least squares .technique.;* '•.•'. :-,'. Figure 15.- Continued.

. 75^00' 74°|00'Y-axis, nautical miles

73°|00'




75° 00' 74°|00'


40°



Figure 16.- Wave refraction diagrams. <*j= 450. T = 16 seconds

44


730|00'




75°|00' 740|00' '

Y-axis, nautical'miles

.73°|00'

(c) Bottom topography approximated by constrained,

bicubic interpolation technique. . -.



73°|00'

(a) Bottom topography approximated by quadratic " ."

least squares technique.- > . - ' - " • ; - - - •

Figure 1?.- Wave refraction diagrams, a = 67-5°; T =.6 seconds

,• " 75° 00' 74°|oo' : :Y-axis, nautical miles

73° 00'

,, (b) Bottom top.ography approximated ;by cubic

. . .least squares .technique. " -.

Figure 17..- Continued.

"48

75°l00' 74°|00'Y-axis, nautical miles

73°|00'

40°°gl




-75° 00' \ 74°|00'Y-axis, nautical miles

73°|00'

(a) Bottom,topography approximated by quadratic.- ;" - - - ' , . * . . . • - " '

•': " -.'.r- least squares technique. ' :

Figure 18.--Wave.refraction diagrams. a = 67-5°; "T.= 8 seconds,

50 > ''!-'••> " :


73°|00'

40° °g

(b) Bottom topography approximated ,,by cubic


Figure 18.- Continued. -

51


73° 00'

40°°gl

52

(c)'Bottom .topography approximated by constrained




73° 00'

m cn

(a) Bet-torn topography approximated by quadraticleast squares technique.

Figure 19. - Wave' refraction diagrams.' a = 67.5°; T = 10 seconds.

• - • • ' • • - . , ' 5 3

t.

'»- .Contlnu.,


73°|00'



' Figure 19.- Concluded.

55


01nr

73°|00'

(a) Bottom topography approximated by quadratic;-.-"-.

. least squares technique. ' .' -• : .

Figure 20.- Wave refraction diagrams, o = 67.5°.;. T =. 12.'.-seconds

5 6 , . " ' • • ' " ' ' , . - • - . • • • • . • , ; . ; . .

75° 00' '

40°°E


O!rn

73°00'

.. (b) Bottom topography approximated by .cubic'

least squares technique. ; .

Figure 20.- Continued. ' " '.'- .-'••-

57

58

iiiiSS-----,'•* ;?§::S1 ;§ ^ tec;

: -&&&&s&^:&$*;-i-',f'.,: "~ Concluded

r-;\'>:\%x^;^*.;rM:^^y .^:^§>^^^%::<^-:w>/;''.-,

^^

75°|00' 74°|00'Y-axis, nautical miles'

73°|00'

(a) Bottom topography approximated by"quadratic

. •;. •'• least squares 'technique. - . • :

Figure 21.- Wave refraction diagrams. a =• 67.5°; T .'= I1*' seconds.

. - . 59

• 73° 00'Y-axis, nautical''miles

60

(b) Bottom topography •approximated by cubicleast squares technique.

Figure 21 .'-.Continued.

75°00' 74°|00' . • ".Y-axis, nautical miles

73°|00'

(c) Bottom topography approximated By "constrained

bicubic interpolation technique.- - . .-r-:

• .Figure: 21 Concluded. ...

61

75900'" ' 74°|00'Y-axis, nautical miles

73°00'

Figur,e

62 "•

.'(a). Bottom topography approximated by quadratic •:•;.".'..'>".'>::S' ' least-squares technique. [

22;.'r':Wa.v;e 'refraction diagrams, a = 67.5°;- T = 16 seconds

75°00' 74C|00'Y-axis, nautical miles

73°|00'




63


73°|00'

40°




75°00' 74°|QO'Y-axis, nautical miles

73°00'

40°°FF



Figure 23.- Wave refraction diagrams, a = 90°; T = 6 seconds.

65

.75°|00' 74°|00'Y-axis, nautical miles

73°|00'

\* > 1 4 1 1- *V. i *—J,—4 1 I \ t-J

-' .(r ? \ ' \ 7. "r'. \ '.

\ f i , /t—i—i—*•)* j/ »—i—i—» •»- *,-*—i

66



Figure 23-.- Continued.


73°00'

V ' V ^ - • • .




67

75° 00' 74°|00'


73° 00'



Figure 24.- Wave refraction diagrams. a = 90°; T = 8 seconds

68


73°|00'

tn atTII ii i imp 11 mi 111 in i M ii i ii I M I I I 111 ii i MM 111 M 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 mi n 11 [ 111 m i n 11 n n »




69


73°|00'

40° °£

70




75°00' 740|00'Y-axis, nautical miles

73°|00'



Figure 25.- Wave refraction diagrams. a = 90°; T = 10 seconds.

71

75° 00' 740|00'


73°|00'

40°.

72





73°00'




7-3


73° 00'




74


73°|00'




75

75° 00' 74°|00'


73°|00'

76




75POO' 74°|00'Y-axis, nautical"mifes

73°00'




77

75° 00' .• ,74°|00' •L"Y-axi's,; nautical miles

73° 00'

en * ,o>

78





73°|00'

40° E

(c) Bottom topography approximated by constrained'



79

75° 00' 74°|00'


,4(0:




•80


73°|00'




81


73°00'

40° °g00' E

iiiiiiiiiimniiiiiiiiiiiim-N

54.9m\V

82


• .-' bicubic interpolation technique.



73°|00'

40°°B?



Figure 29.- Wave refraction diagrams. a = 112.5°; T = 6 seconds.

83

75° 00' 74°|00'


73°|00'




75°log' 74°|00'Y-axis, nautical miles

73°|00'

en 01

j 1 1 1 1 1 n •




85

74°00'Y-axis, nautical miles



Figure 30.- Wave refraction diagrams. a = 112.5°; T = 8 seconds

86

75°00' 740[00'Y-axis, nautical miles

73°|00'




87


73°|00'

40° °E





73°|00'

40°°E



Figure 31.- Wave refraction diagrams, a. = 112.5°; T = 10 seconds,

89

75? 00' 74°|00'


73°|00'

90



Figure 31-.- Continued.


73°|00'

re u> en o»




91

75° 00' 74°|OQ'


73°00'



Figure 32.- Wave refraction diagrams. a = 112.5°; T = 12 seconds

92

75° 00' 74°|00' .Y-axis, nautical miles

73°|00'

40°

( b ) . Bottom topography approximated by cubicleast squares- techri ique.Figure 32.- Con t inued .

93

74°iQQ'Y-axis, nautical miles

73°l00'

Cc) Bottom topography approximated by constrained

•'.','• bicubic interpolation technique,

•'„;. Figure 32.- Concluded.


73°|00'

•(a) Bottom topography approximated by quadratic

.,',.' least squares technique.

Figure 3 3...' .-Wave refraction diagrams. a = 112.5°; T = 14 seconds

:.';••?'•• • 95

75°00' 74°|OQ'


73°|00'

96



Figure 33-- Continued.

75°00' 74"|00'Y-axis, nautical miles

73°00'



Figure 33-- Concluded.97




Figure 3U.- Wave refraction diagrams, a = 142.5°; T = 16 second

98

75°|001 . 74°|00'Y-axis, nautical miles

mimiinii

73°|00'

(b) Bottom topography approximated by cubicleast squares technique.

:Figure 3.4 •- Continued.99


73°|00'

100



Figure 3^.- Concluded.

.75° 00' 74°|00'Y-axis, nautical miles

73°|00'

40°°E

_(a) Bottom topography approximated- by quadratic

least squares technique. .

Figure 35'.-"Wave, refraction diagrams, a = 135°; T = 6" "seconds.

101


73°|00'

40° °E



. Figure. 35.- Continued.

102


73°00'


bicubic interpolation technique.Figure 35-- Concluded.

103

75° 00' 74°|00'


73°|00'

ro to) en tn



Figure^36.- Wave refraction diagrams, a = 135°; T = 8 seconds

104


73°|00'

40" "gl




105


73°|00' ' .

(c) Bottom topography approximated by constrained-



106

75°JOO' 74°|00'Y-axis, nautical miles

73°00'




107

75°l00' 74°|00'Y-axis, nautical miles

73° 00'




.108

75°l00' . 74°|00'Y-axis, nautical miles

73°|00'




109


73° 00'


least squares technique. '


110 :


73°|00'




1 1 1


73°|00'

40°




.112

75°|00' 74°[00'


73°|00'



Figure 39.- Wave refraction diagrams, a = 135°; T = 14 seconds.

113

75°00' 74°|00'


73°|00'

114








115

75° 00' 74°|00'


73° 00'

40°°gTTTTTTTT

00' E




116

75°|00' 74°|00'


73°|00'




117


73°|00'



Figure 40.- Concluded. • .

118


73°|00'


• . least squares technique.

Figure 41.- Wave refraction diagrams. a = 157.5°; T = 6 seconds.

••'•• 119


73° 00'

40°°g1

120

(.b) Bottom topography approximated by cubic



75°00'

40°°E

74°|00'

Y-axis, nautical milesJim mm it

73° 00'

(c) Bottom topography approximated by constrained'

bicubic interpolation technique.:- .• • •'

Figure H'\.- Concluded. ' ' . '

121

'75° 00' 74°|00'


73100'



Figure 42.- Wave refraction diagrams, <* = 157.5°; T = 8 seconds

122 .


73°00'




123


73°|00'

40° °pra u>




124

75°|00' 74°|00'


73° 00'


least' squares technique.

Figure 43.- Wave refraction diagrams, a = 157.5°;- T =. 10 seconds,

125

75° 00'- 74°|00'


73°|00'

126

-.'. :(.b) Bottom topography approximated by cubic

'..',-;..;.,'; least squares technique.

:".'.-•;. Figure 43.- Continued.


73°|00'

40°°g

(c)-Bottom topography approximated by constrained

• .'•, bicubic interpolation technique.

;. ••• • ' Figure 43.- Concluded.

127

•75°00' 74°|00'Y-axis, nautical miles

73°|00'

(a) Bottom

Figure -44.-

128 .

topography approximated by quadratic ,

least.-squares technique. - -

Wave, refraction diagrams. a = 157.5°; T.-= 12 seconds

75°00' 74°|00'


73°00'




129


73°00'

I'3'O




75°00' 74°.|00' :Y-axis, nautical miles

73°l00'

; . .(a) Bottom topography approximated by quadratic

• •;' . " • least squares technique.

Figure--45VT Wave refraction diagrams. o = 157.5°; T = 14 seconds,

":'•'.' ' 131

132

•75° 00' 74°|00'Y-axis, nautical miles

73°|00'


bicubic interpolation technique. -; '


133


73°00'

40°


least squares technique. :

Figure 46.- Wave refraction diagrams. a = 157.5°; T = 16" seconds

134 • .


73°|00'



Figure ^6.- Continued.

135

75°mO' 74°|00'Y-axis, nautical miles

73° 00'

01 <n

136




75° 00' 74°|00'Y-axis, nautical

73°|00'miles

00'

39°00'

•-13mc

38°00'

.6|m

V



Figure 4?.- Wave refraction diagrams, a = 180°; T = 6 seconds.

137

75° 00' 74°|00'

Y-axis, nautical

73?|00'miles


least squares technique. • . -.-

Figure 4?.- Continued. . .

138

75°00' 74°|00'Y-axis, nautical

73°|00'miles

40°c

00'

39°00' :CAPE

•3"roc

t/f

'isX

38°00'

.6m 9n



Figure 4?.- Concluded.

139


73°|00'

40°°gl




140

75°00' . 74°|00'Y-axis, nautical miles

730|00'

(b)' Bottom topography approximated by cubic






Figure 48.- Concluded-.

142


730|0d'

*i1111111 111uH11 111111 i i1111111111111n i i i 11 i i i i t 1111

(a) Bottom topography approximated by quadratic- ' . '

least squares technique. . . ; ,


' 143


73°00'

.,(b). .Bottom topography approximated by cubic

.: least squares technique. :•: . '

Figure .49..- Continued. '. ''.'.'

•T44


40°c

00'

39°00' CAPE MA

•38°00'

E /

9i




145

40°'00'

39°00'

38°00'

TTTTTTTTT

= DELAWAREBAY

£APE

74°|00




Figure. 50.- Wave refraction diagrams. a = 180°; T = 12 se.conds

146 -


73°00'

(b) 'Bottom topography approximated by cubic




73°|00'

40° °F

148





73°|00'

(a) Bottom topography approximated by quadraticleast squares technique.


1,49


150





73°00'

f11 1 1 1 1 i i 1 1 1 1 1 1 1 1 1 1 1 i t 1 1 1 1 1 1 1 1 1 1 1 n 1 1 i i 1 1 1 1 1 1 1 1 1 1 1

(c) Bottom" topography approximated by constrained

'•bicubic interpolation technique.

. ' Figure 51.- Concluded.

151

75° 00' 740|00'

•Y-axis, nautical miles

73°|00'

40°e

00'

£ DtLAWAREBAY

39°00' tCAPE MA

38°00'

(a) Bottom topography approximated by quadratic ';'.

• . '.•'.• .least, squares technique.

Figure 52.- Wave refraction'diagrams. a = 180°; T = '16 seconds

152 : : ; : - " - •' • ' . ' ':'.' ' . : • ' -.


73°00'

40°°El




153

75° 00' 74°|00'


73°|00'

40°

154




REFERENCES

1. Goldsmith, Victor; Morris, W. Douglas; Byrne, Robert J.; and

Whitlock, Charles H.: Wave Climate Model of the Mid-

Atlantic Shelf and Shoreline (Virginian Sea) - Model Devel-

opment, Shelf Geomorphology, and Preliminary Results. NASA

SP-358, VIMS SRAMSOE No. 38, 1974.

2. Poole, Lament R.: Random-Access Technique for Modular Bathym-

etry Data Storage in a Continental-Shelf Wave-Refraction

Program. NASA TM X-3018, 1974. ' •• .

3. Poole, Lamont R.: Comparison of Techniques for Approximating1 Ocean Bottom Topography in a Wave-Refraction Computer, Model.

NASA TN D-8050, 1975.

4. Goldsmith, Victor: Shoreline Waves, Another Energy Crisis.

VIMS Contrib. No.'734 to First Annual Conference of the

Coastal Society (Arlington, Virginia), Nov. 1975. '

Langley Research Center .

National Aeronautics and Space Administration

Hampton, VA 23665

September 8r 1976 . { ' :

*U.S. GOVERNMENT PRINTING OFFICE: 1976 - 735-004/8

155

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

WASHINGTON. D.C. 2O546

OFFICIAL BUSINESS

PENALTY FOR PRIVATE USE «3OO SPECIAL FOURTH-CLASS RATEBOOK

POSTAGE AND FEES PAIDNATIONAL AERONAUTICS AND

SPACE ADMINISTRATION491

POSTMASTER : If Undeliverable (Section 158Postal Manual) Do Not Retur

"The aeronautical and space activities of the United States shall beconducted so as to contribute . . . to the expansion of human knowl-edge of phenomena in the atmosphere and space. The Administrationshall provide for the widest practicable and appropriate disseminationof information concerning its activities and the results thereof."

—NATIONAL AERONAUTICS AND SPACE ACT OF 1958

NASA SCIENTIFIC AND TECHNICAL PUBLICATIONSTECHNICAL REPORTS: Scientific andtechnical information considered important,complete, and a lasting contribution to existingknowledge.

TECHNICAL NOTES: Information less broadin scope but nevertheless of importance as acontribution to existing knowledge.

TECHNICAL MEMORANDUMS:Information receiving limited distributionbecause of preliminary data, security classifica-tion, or other reasons. Also includes conferenceproceedings with either limited or unlimiteddistribution.

CONTRACTOR REPORTS: Scientific andtechnical information generated under a NASAcontract or grant and considered an importantcontribution to existing knowledge.

TECHNICAL TRANSLATIONS: Informationpublished in a foreign language consideredto merit NASA distribution in English.

SPECIAL PUBLICATIONS: Informationderived from or of value to NASA activities.Publications include final reports of majorprojects, monographs, data compilations,handbooks, sourcebooks, and specialbibliographies.

TECHNOLOGY UTILIZATIONPUBLICATIONS: Information on technologyused by NASA that may be of particularinterest in commercial and other non-aerospaceapplications. Publications include Tech Briefs,Technology Utilization Reports andTechnology Surveys.

Details on the availability of these publications may be obtained from:

SCIENTIFIC AND TECHNICAL INFORMATION OFFICE

N A T I O N A L A E R O N A U T I C S A N D S P A C E A D M I N I S T R A T I O N

Washington, D.C. 20546

wave refraction diagrams for the baltimore canyon … · mid-atlantic continental shelf. -wave...

Documents