N PS ARCHIVE 1968 PAQUIN, J. A LABORATORY EXPERIMENT ON SURFACE WAVE ATTENUATION DUE TO UNDERWATER TURBULENCE by James Edward Paquin DUDLEY KNOX LIBRARY CHQ0L UNITED STATES NAVAL POSTGRADUATE SCHOOL THESIS A LABORATORY EXPERIMENT ON SURFACE WAVE ATTENUATION DUE TO UNDERWATER TURBULENCE by James Edward Paquin December 19 6 8 Tlva> docwnzivt kai bzzn approved &ol pubtic K.Q.- Iza&e. and talz; -LU duVLcbution u> unturuXzd. LIBRARY c^uom NAVAL POSTGRADUATE SCHOOL MONTEREY. CALIF. 93940 A LABORATORY EXPERIMENT ON SURFACE WAVE ATTENUATION DUE TO UNDERWATER TURBULENCE by James Edward Paquin Lieutenant, United States Navy B.S., United States Naval Academy, 1962 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN OCEANOGRAPHY from the NAVAL POSTGRADUATE SCHOOL December 1968 ABSTRACT The attenuation of surface waves caused by underwater turbulence was investigated in a wave-tank experiment. The waves studied (frequencies ranging from 1.2 to 12.3 Hertz) were strongly attenuated by a zone of grid-generated turbu- lence. This attenuation depended on the length of the turbulent region, and on the frequency of the incident wave. The equation governing attenuation was: u u ~ax h = h e o where h is wave height, h is undisturbed wave height, x is the length of the turbulent region, and a is an attenuation coefficient proportional to the cube root of frequency. It was also noted that the waves were shifted in phase as they passed through the turbulence, and that the magnitude of this shift increased with frequency. The quantitative results of the experiment were obtained from measurements of nearly sinusoidal waves. They were confirmed, qualitatively, for a continuous spectrum of waves by measurement of a wind-gener- ated model sea surface. LIBRARY NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIF. 93940 TABLE OF CONTENTS Section Page 1. INTRODUCTION 11 Objective 11 Outline of Experiment 12 2. EQUIPMENT 13 Wave Tank 13 Wave Generator 15 Turbulence Generator 15 Wave Probe Design and Calibration 17 Anemometer Function and Calibration 22 3. SPECTRA OF THE PADDLE-DRIVEN WAVES 26 4. TURBULENCE SPECTRA 38 5. ATTENUATION OF WAVES DUE TO TURBULENCE 4 0 6. PHASE SHIFT IN THE TURBULENT ZONE 54 7. ATTENUATION OF WIND-DRIVEN WAVES 57 8. SUMMARY AND CONCLUSIONS 59 BIBLIOGRAPHY 60 LIST OF TABLES Table Page 1 Typical Values of Energy Losses 41 LIST OF ILLUSTRATIONS Figure 1. Schematic Diagram of Wave Tank 2. Turbulence Generator 3. Wave Probe Circuit 4. Typical Wave Probe Calibration Curve 5. Dynamic Calibration of Wave Probes 6. Typical Anemometer Calibration Curve 7. RMS Height Distribution for Paddle-Driven Waves at Probe #1 and #2 8. Spectral Analysis for a 1.2 Hertz Wave 9. Spectral Analysis for a 1.8 Hertz Wave 10. Spectral Analysis for a 2.4 Hertz Wave 11. Spectral Analysis for a 3.1 Hertz Wave 12. Spectral Analysis for a 3.5 Hertz Wave 13. Spectral Analysis for a 4.0 Hertz Wave 14. Spectral Analysis for a 4.1 Hertz Wave 15. Wave Attenuation due to Distance 16. Velocity Distributions in the Turbulent Region for a 3.1 Hertz Wave 17. Effect of Turbulence on 1.2 Hertz Wave 18. Effect of Turbulence on 1.8 Hertz Wave 19. Effect of Turbulence on 2.4 Hertz Wave 20. Effect of Turbulence on 3.1 Hertz Wave 21. Effect of Turbulence on 3.5 Hertz Wave 22. Effect of Turbulence on 4.0 Hertz Wave Page 14 16 18 19 21 23 27 29 30 31 32 33 34 35 37 39 42 43 44 45 46 47 Figure Page 23. Effect of Turbulence on 4 . 1 Hertz Wave 48 24. Percent Wave Attenuation due to Turbulence 49 25. Attenuation of Waves due to Turbulence Plotted as a Function of Number of Wavelengths in the Turbulent Region 51 26. Phase Shift Versus Frequency 55 27. Attenuation of the Model Sea Surface 58 ACKNOWLEDGMENTS The author wishes to express his sincere appreciation to Drs. H. Medwin and T. Green III for their guidance and assistance in completing this project. A LABORATORY EXPERIMENT ON SURFACE WAVE ATTENUATION DUE TO UNDERWATER TURBULENCE 1 . Introduction Objective The objective of this experiment was to determine, quantitatively, the effect that a zone of underwater turbu- lence has on a gravity wave which passes through it. P. Groen [l954, p . 7 J predicted that a decay in ampli- tude and an apparent increase in period of swell would occur after a gravity wave train passed through a turbulent region, and that this effect is related to external turbulence, that is, turbulence which is produced independently of the wave. Groen further predicted that this effect depends on both wavelength of the waves and characteristic wavelength of the turbulence. Groen also states that gravity waves may be affected by self-produced or internal turbulence. This will not be considered in this paper. T. P. Barnett Q.968] states that one of the possible drawbacks of the present scheme of predicting generating and dissipation of ocean waves is the neglect of some un- known dissipative mechanism. Since his scheme did not account for external turbulence, the interactions between waves and turbulence may provide the needed explanation for loss of wave energy. 11 Because of the difficulties of precise measurement of waves and turbulence at sea, this possible energy dissi- pation was studied in a laboratory experiment. Outline of Experiment A wave tank equipped with wave and turbulence generat- ing devices was used to produce the desired experimental conditions. A traveling surface wave was generated at one end of the tank and absorbed by a porous beach at the opposite end. The wave passed through a zone of turbulence, produced by an oscillating grid in the center of the tank bottom. The effect of the turbulent region on the wave was evaluated by wave height measurements taken with two resistance-type probes located on each side of the turbu- lent region. Measurements of turbulent velocities were taken with a constant temperature anemometer. 12 2 . Equipment Wave Tank Dimensions of the rectangular-shaped wave tank used in this experiment are shown in Figure 1. A false bottom installed in the tank isolated the driving mechanism for the oscillating grid and prevented it from generating currents which might advect turbulence beyond the desired region. The false bottom was stepped down in the center of the tank (Figure 1) to accomodate the grid which was supported by four metal rods. Since the turbulence generator was located entirely below the false bottom, no equipment penetrated the water's surface except the chain drive for the turbulence generator. A false side of the tank prevented this chain from inter- fering with the wave as it traveled down the tank. The effective depth for the higher-frequency waves generated was the depth of the false bottom, approximately 12 centimeters. When lower frequency waves were generated, the false bottom was removed, allowing currents to form. The effect of these currents on the experiment appeared to be negligible. Only deep-water waves were studied to avoid compli- cations resulting from the effects of reflection of shallow- water waves which would occur in the stepped-down region. (Deep-water, in this experiment, refers to waves whose ratio of depth to wavelength is greater than or equal to one-half.; 13 A A * >H J J* C CO E- 4) > cO :«: Cm O E CO U hO CO •H Q o •H CD X! o CO •H 14 Wave Generator Waves were generated at one end of the tank by a flat aluminum paddle driven by a variable-speed motor. The period of the wave generated depended on the speed of the motor; the wave height depended on the stroke length of the paddle. The equipment used provided two paddle-stroke lengths and continuous changes of motor speed. Turbulence Generator Turbulence was generated by a vertically-oscillating grid located in the center of the wave tank just above the false bottom. Various screening materials were tried for the grid, but it was found that only screening with a large, solid surface-to-hole ratio would generate turbu- lence strong enough to disturb the near-surface area of the water. The grid screen used for this experiment was woven of metal strips one centimeter wide, set one centimeter apart across the width of the grid and two centimeters apart lengthwise. The grid was oscillated by apparatus located beneath the false bottom of the tank (Figure 2) . All moving parts of this apparatus were lubricated by the water which surrounded them. A frame, connected to the grid by four bolts which penetrated the bottom of the tank, was moved up and down by a piston driven through a crankshaft. A chain drive connected the crankshaft (through the false side) to an electric motor located just above the tank. 15 1*— 6" 0 o E 0 0 support and bearing assembly for drive- shaft flange-attaches to false bottom moving piston drive gear for shaft frame to support rods that pene- trate the false bottom 6" V slot for grid frame (not to scale) \ \ false bottom turbulence gener- ating grid slot for attachment of arm to Diston driving arm Fig. 2 Turbulence Generator 16 Wave Probe Design and Calibration Resistance-type wave probes were used to measure wave height outside the turbulent zone. The probes operate on the principle that two parallel wires immersed in water, so that the plane of wires is parallel to wave crests, will have a resistance that is a function of the depth of immer- sion. A block diagram of the probe circuit is shown in Figure 3. The power supply is an audio oscillator. The probe, which consists of two wires supported by an insulat- ing block, is in parallel with one leg of a balanced bridge circuit. As the water level varies on the wires, the AC signal from the audio oscillator is amplitude mod- ulated. The bridge output is amplified, and then converted by a demodulator from an amplitude-modulated AC signal to a varying DC signal. This signal can then be recorded on magnetic tape, strip chart or other suitable recorder. Static calibration of the wave probes was accomplished by changing the depth of immersion of the probes and plotting the water level versus the DC output of the probe circuit. Figure 4 shows a typical plot of output versus water level. The magnitude of the linear range for the probes used was in excess of 7 centimeters. Since the wave heights generated were all less than this value, the static response of the probes imposed no significant restrictions on the experiment. Dynamic calibration of the wave probes was more diffi- cult to accomplish than static calibration. The probe and a rod, graduated in millimeters, were placed in the wave tank 17 Audio Osc. Hewlett Packard Model 200 AB Amplifier Hewlett Packard Type 2470A ImJULUUUJuuJ insulated - support ~~ ^rffjprrrrrr 6212 5Z •H •H .p a •p o 0) o a u 30a 24< 18CU 1204 60. Probe #2 .114 x Probe #1 .15^ 2SS mv 12 3 4 5 6 depth of immersion in centimeters Fig. 4-Typical Wave Probe Calibration Curve 19 in such a position that water level could be read on the rod. When waves were generated in the tank, the difference between the maximum and minimum reading on the rod gave the wave height. In order to facilitate reading the wave height from the rod, a strobe light was used to "stop" the wave train. The light flashed at the same frequency as the wave, illum- inating only one phase of the wave and thus, eliminating the effect of the moving wave on the visual reading. Waves of various frequencies were generated and wave height was recorded both visually and from the DC calibrated probe circuit. The ratio of probe wave height to actual (visual) wave height was computed and plotted as a function of fre- quency as in Figure 5. The ideal ratio of voltage output to wave height was obtained from the static calibration and is shown as the value at zero frequency in Figure 5. As shown in the figure, height response was excellent for frequencies up to 4 Hz and was still fairly good at 26 Hz. The absence of readings between 4 and 26 Hz is due to the limitations of the wave generators. (Frequencies 4 Hz and lower were generated by the afore-mentioned generator; the 26 Hz wave is a capillary wave of much lower amplitude generated by a fan.) 20 u 0) ■P •h e •H (0 d C 0) o o a to u a> a) t, a Q) W OrH t. o .12- .lia — .10* -♦— 0 1 tf* I ideal response -^from static calibration 5 26 27 frequency in Hertz I , •P •H O O t-\ Q) > 15 10 kC 12 3 4 5 anemometer output in volts Fig. 6-Typical Anemometer Calibration Curve 23 anemometer is the sum of the mean fl©W and fluctuation: u = u + u* where U is mean flow velocity, U* is the time varying fluc- tuation and U is the flow at any instant. The anemometer senses the magnitude of U and thus, in most applications, the turbulent fluctuations can be obtained by subtracting the mean flow. In this experiment, however, U is zero, or very nearly so. Therefore, since the anemometer senses only the magnitude of U (U* when U is zero) , as U* changes direction, the output of the anemometer remains a positive voltage and thus does not give a true velocity profile. As a result, there is a tendency for the instrument to double the frequency of the fluctuations. A second drawback in the use of the anemometer in this experiment affects the magnitude of velocities in the tur- bulent region. The anemometer probe is most sensitive to the component of flow velocity perpendicular to the film. When flow in the tank reverses, it passes back over the posterior of the probe. The probe, therefore, influences the flow physically. When measureing this altered flow, the probe is also measuring a flow velocity moving in a direction opposite from the flow direction it has been calibrated to measure. When probe orientation was reversed in a constant flow of known unidirectional velocity, probe response was measured 24 at 20 to 25% of the true value for velocities of five to six cm/sec. Because of this reduced sensitivity, the probe tended to respond primarily to velocities in one direction; however, the response in the opposite direction is great enough to make interpretation of the probe output very un- certain. 25 3 . Spectra of the Paddle-Driven Surface Waves The spectral energy of the waves produced by the wave generator was strongest at the frequency of oscillation of the paddle. However, Figure 7, which is a plot of root- mean-square height distribution versus frequency, shows that there was also energy at the second and third har- monics of the paddle frequency. The distribution of wave height with frequency was determined as follows: 1. The wave generator was run until a steady state was approximated (i.e., until the waves in the tank no longer increased in height) . 2. Wave height was measured at the two probe positions when no turbulence was being generated. 3. The outputs of the two probes were recorded on a PI 6200 magnetic tape recorder operating at .375 inches per second . 4. The tape was then played back at 3.75 inches per second and the output was analyzed with a General Radio Company Type 1900 Wave Analyzer. (The tape was played back at ten times recorded speed so that waves of 1 Hz and greater could be measured since the effective low frequency limit of the analyzer is 10 Hz.) In an application where the signal measured is broad band (i.e., for study of the turbulence spectrum) the meter of the wave analyzer indicates the value of the instantaneous 26 r-{ CN ■=*te **: 0) CD XI X 0) o O CO u Ch •H Q< (X O c 4-> ■P CO cO •p •H (0 (0 3 > t~. CO crt •H £ > (0 C\J CO CD X O f-. Ou P CO CO CD > CO 35 c > •H Q I O U sO Oh • iH » < » « » ■ . 1 F 1 o to CM rH vO -* CM O -CO vO -4- rH rH rH fH rH CM vO 0) JO o u Q-, CM ir\ O CM to CM — T- o r to vO — i — — T- CM vO • o^ N ■P u -* 0) • X CD CM > C CO •H 25 >> tSJ O ■P CM c *H •• 0) CD r-\ 3 cr X a) CM ti • ■O fr. rH 05 U o CO •H to rH cd a < rH • CO -P tSJ o •P a> fn a a> CO -d- X • CM c ♦H to • ^ bO O •H c fc CM CO • 3 rH cr a) SJs^aajxxiTW ut ^q3T8H aAB,\\ 29 CO x> o M a, o cn -J- O vO O to UN un O UN un -J- O -J- ITS CN r ' O un on <\i O CNi — i — un -T— o irv v£) on to un SJa^amfTTTw "T aq9T«H ^A«M rH UN O • (V O U fa • CV r-i • rH — 1 1 ■ ■ ■ i -* r UN vO on to N •P U >> o C n fa o vO un un O u^ UN o UN ON O on un O c\i > tSJ •P U CD to U O cm CO •H n •-I g ctj H ■P O CD a en o •H fa UN UN saa^amixiTW UT Vj2"F8H 9ahjv\ 30 O to cm =*fc 0) x» o -* u • £ r> c^ cm CM 15~ cm "35 cm- ?5" cm to cm sja^auiiixxw ut: cmSiaH aAUM o >» > O CO fl 25 0) 3 N cr •P 0) U b «> fe w -* • CM cd U o «H m •H m >> rH cd 4 ta rH « Cd U 0) •P X t* ® G Cu •H CO >» O O rH a a> • 3 b0 cr •H a) fe k fe saa^aiuxxxTW UT V^T^H sabm 31 o o (V CV a> x> o u a. o 1 1 — r ■ 1 ■ —t -■ 1 r » i *> vO -4- o u (V O CM r^\ O r"N tsi •P U a> c •H O C a> cr JH o c cr ■COnO -*CVOtOvO -± CO N •P 0) X CO & cm w •H CO rH CO c CO •P o a> cu CO b0 •H 32 o o CM 0) .a o u a. CM CM • to cm o vO cm to -* o -± cn c> cm CM (V MO CM to gja^awTiiTW t*T cvq3j8H ©ab^ • 4- cm i N •P I ^ 0) X CM • C ■CO -H >> O G a> rH 3 • cr -4- a> u > cd 3= N -P M a> CO U o «m W •H (0 t>» rH CO UN * ** CM 0) •8 u Ol, MO ON to o MD CM ■CO -4- O VD -* cn py CM CM CM iH CM <0 9 -4- N •P u (0 CM X to C O c CD cr a> CO M •P O a) a CO CM rH •H sj8^aaiT-[-[Tw uf iq3f9H sabm 33 r^ BJe^araxxifw ui ^qSf^H ©ab^ to o sO o cs o -4- to ir\ cv CM Os v£> c\ k^ o t-\ N P u CD EC O • c 9 O-tH > CTJ >» ^ O C M 0) P ITS 3 m • -\ t> X h fe ir\ • c*~\ (0 *h O «m « •H 10 >» rH crj C < v/\ • rH O crj rH M N P P o m 0) 0) a ox CO • c^- c CN. •H rH >* • o W) C •H u-\ 0) Cn • 3 f*\ cr o m fe saa^aaifXTTW ^1 ^qSf^H sabm 34 o o CM 4) St O U CM O to H ■P U o X G •H MD CM O C 0) O 0) o o CM SJaiaraiTTTfw uf ^3x9h 9ai?m CM O u CM O to CM 4 CM N rH +3 0) o to a •H c 0) cr o 0) • k o O CM SJ8^aoif[TTW UI m^TsH sab^ 4) > CO 3= N •P u a en ho •H 35 used is this experiment. Figure 15 shows the per cent wave attenuation as a function of frequency caused by this 1.2-meter distance. Figure 15 illustrates that attenuation due to distance between the probes was small. In most cases, the fundamental frequency of the waves was only slightly affected; however, the second and third harmonics were significantly reduced in height with distance, that is, the wave became more nearly sinusoidal with distance from the source. The greater attenuation of the high-frequency components is as expected; however, the large amount of scatter in the values obtained makes it difficult to assign a good relationship between frequency and attenuation in this case. 36 o -to -vO --* CD > cd 5== Cm O ^ o C CD 3 CT a> o u •H O fc e: «h o c iH E O cd M E p cd u c tc cd a> a: E T5 cd C T> -o o u c O -H 3 ox: fc c/) E-< o <1 0 4 c\j x X X 0 o G x 0 ir\ CV to -* o o (V v\ CV O t)0 vO -4- rH iH r-H cv 01 CD J=> o u Q-, c CD CD 4-5 CD PQ CO s: P hO CD .H CD > cd cm O M CD U CD a CD CO cd CD M o CD Q •P CD > cd CD O C cd 4-3 CO •H Q O P CD Q C o •H P cd B CD -P P cd faO •H Fx< 37 4 . Turbulence Spectra Typical spectra measured with the constant temperature anemometer are shown in Figure 16 for the case of waves, waves and turbulence, and turbulence alone. The velocities shown were measured at a point in the center of the turbu- lent zone, two centimeters below the surface with the probe in a position such that the anemometer was most sensitive to velocities perpendicular to a vertical plane in line with the wave crests. Other similar turbulence spectra were measured at six equally-spaced positions at depths of one and three cm. The drawbacks noted in Section 4 make interpretation of the spectra difficult; however, Figure 16 shows signifi- cant turbulent energy at all wave frequencies used. The curve for waves alone indicated that the probe sensed the orbital velocities of the wave and its harmonics, and that the high frequency portion of the spectrum of waves and turbulence was almost identical to the spectrum of turbu- lence alone. The low-frequency portion of the turbulence spectrum showed a marked increase in energy at the funda- mental frequency of the wave. 38 i-H c 3 o X> r-H a) fa CTJ CO 3 •H 0) 4-> 0) O c O C O T3 a H C 0) ■P Ctf Cfl rH •H 3 3 CO (0 £> O 0) a> & u > > •H (TJ aj 4-5 O 5 s to ■P (-. CD c •H >. O c a a> c o •H hO a> 4-> C a> X) cd a> X! > 4-> aj c •H N 4-> CO Jh C vO hi) •H o o -oo vO UT\ c^n cv oas/uio ut iC^xooxay\ 39 5 . Attenuation of Waves due to Turbulence Attenuation of waves due to turbulence was determined by comparing the two wave probe outputs which were recorded while turbulence was being generated. Some typical results of this comparison are presented in Table 1. Wave energy per unit surface area was calculated from the following relationship : E = 1/8 dgH2 d = density g = acceleration due to gravity H = wave height Other comparisons of attenuation due to turbulence are shown in Figures 17 to 23. Figure 24 is a plot of percent attenuation versus frequency on a log-linear graph. The points which are marked by dashed circles represent measurements of waves which were of sufficient wavelength to undergo a shoaling effect as they passed over the turbu- lence generator (in runs with the false bottom removed). The points that fall on the straight vertical line were com- pletely attenuated. Because of the additional effects which shoaling might introduce, the points circled by a dashed line cannot be con- sidered good data points for quantitative turbulent attenua- tion measurements. They do indicate qualitatively that atten- uation is less at lower wave frequencies . 40 TABLE 1 TYPICAL VALUES OF ENERGY LOSSES (Energy density in Ergs/cm ) Loss Due to Loss Due to Distance Turbulence and Distance Freq. (Hz) Energy Density Probe #1 Probe #2 % Loss of Energy Energy Density Probe#l Probe#2 % Loss of Energy 3.1 372 356 .43 347 18.1 94.8 * 6.2 5.63 1.55 72.6 45.4 .24 99.6 ** 9.3 .01 .00 — .04 .00 — 3.5 1148 1127 .18 1750 38.1 98.0 * 7.0 59.3 34.5 40.8 60.2 .00 — **10.5 16.5 1.31 92.2 1.59 .00 — 4.0 1018 870 14.5 986 60.00 93.9 * 8.0 22.1 10.6 52.0 21.3 .00 — **12.0 .02 .00 84.8 .00 .00 __ * second harmonic ** third harmonic 41 cm CM CD O m O CM to vO -T — CM O to vO CM =tfc CD X> o u Oh CM vO 0 • > r^ CO M P ■P u -d- U CD • > C CM O o • a rH o 0) 3 o cr c 0 CD m rH fa 3 X) u B E-" Cm O P O CD Cm «m W vO • c- c*\ r-4 • N •H -P fa -± U • CD CM e •H CM >> • O rH c o On -4- O u^ -* O O O CM 1 ITN. — r o ir\ saaasuifXTTW UT V-l^T^H 9A^M ir\ vO o to N ■P €) u > CD CO IT ^ c tS3 •H •P m J>» CD O X c cr CD U to c o CD O C CD rH X) =tfc (1) o M PL, LT\ cn. LfN c\j -4- vO to O O -d- cn O cv O cv ir\ ir\ N -P U CD X C •H c CD cr a> O P o co «h W to W) •H SJ9^aai"f[Xi]^ ui ^q2i9Lj 9ai=m 43 cv O o r~\ i 04 to • cfl N •P M 3C CV CO c o 0) o c CD rH J3 vO ir\ cv (J) -Q O o vO CV to -d- o -* c^ r^s CM cv 04 vO cv to -d r-i rH cv to N 1 *> -J- u 0) cv o c cr CD O •P o 0) Cm cm O bfl •H 44 cm o M fa r^ o o -4- CM vO cn. N •P U 0) X a •H t>» O C! crj IS) .p u 3C o tO \Q -* CM Ot0\£> J- rH rH iH r-\ ,-| "^ CM o -co vO U0 o o — ■»- to O tO vO -* CM O "CO vO rH rH rH rH rH saaasaiTITTW UT h^TsH SA^M — i— CM CM c^\ •p $-. o c rH x> o •p o 3 cr a> u tr\ r^ O vO cv to -* c^ c^n cv CV O CM ^O cv to eaaaaurniTW UT ^M^T9H ©A1BM 0) o u Oh -4- O vO 14^ o to • u\ r*\ N a) o CO N ■P M 0) UN C o o c 0> iH 3 o •P o W CM •H 46 o o o •,. CM O o CM 0) S3 o u P-, o o o CM -4 CM CM to UN CM i-4 rH On NO C*\ sja^amfXTTW UT VJ3TaH ©ab^ to N ■P U (0 tsi ■P ac O d> o C 0) o o X> o -J- O -4- • •CO CM CM to O N ■P t- 0> c •H o c a> cr «H o p o a) O CV (V CM r-i r-i •oo — J— SJS^aoifllTW UI ^^T9H 9A*M o O to CO JO o u Oh -*- o Cr\ CV to ■P u 0) X a •H >►> O a 0) cr CD , J N P u CO X c •H c cr CD (h o en CV "OO -* O VD CV cn CV CV CV rH iH •00 0) > 2s N P CO x o a> o c CO JO u Eh 7 4 :©. ;©: G> Fundamental X Second Harmonic ^ Third Harmonic &, x: ^ i^ 0 0 0 10 20 30 40 Attenuation in per cent 50 60 70 SO 90 100 Fig. 24 Percent Wave Attenuation due to Turbulence 49 The length of the turbulent region used in this experi- ment was essentially the same for all data runs. The waves, however, were of various wavelengths and thus, their exposure to the turbulence differed. A high-frequency wave had more wavelength exposed to the turbulence at any one time than a low-frequency wave. This unequal exposure to the turbulence has been compensated for in Figure 25 where frequency is the abscissa and . . , the fractional change of height per wave- length, is the ordinate. where: H ■ h-h, h = height of the incident wave corrected for attenuation due to distance by multiplying the value obtained at the first probe by (1-b) where b is the percent attenuation due to distance alone for that frequency. h. = height of the wave after passing through the turbulent region. Ax = length of the turbulent zone, and L = wavelength .A h /h Figure 25 suggests that the relationship between log ^zfr* and log (frequency) is linear. Assuming this to b© so, a least squares fit to the points results in a line given approximately by the equations log 10axA/h -I l09 £ + 2-10 (1) so W 0) i-H C o •H (0 c d) E 30 25 • 20 . 15 - 10 3 7 " 6 • 5 • 4 - 3 . 2. O © fundamental X second harmonic 1 1 i 2 3 4 5 Frequency in Hertz 6 7 3 9 Fig. 2 5 Attenuation of Waves Due to Turbulence Plotted as a Function of Number of Wavelengths in the Turbu- lent Region 51 which can be written *h.£*Kf-5 (2) h L 3 where K has units of time to the^f ive-thirds power and a numerical value of approximately 1.26. If the waves are assumed to be in deep water, then: L = 2ttfz and equation (2) can be written as: 1r ■ f 2lTKfV3 (3) If Ah and ax are allowed to become very small, equation (3) can be written in differential form: dh = dx 21TK fl/3 (4) h g Integrating both sides of equation (4) yields: h = hQ e"ax (5) where h is the initial height of the wave and a is an 21? K .c / j u attenuation coefficient which is equal to f t and has g units of reciprocal length. This relation may be expressed in terms of energy density as follows: 1 ^ v2 E = g- dgh where d is fluid density and E is energy per unit area. 52 Substituting equation (5) : 1 j *_2 «~2 ax E = - dgh^ e 8 ° or where E = E e o -2ax E = - dgh 2 o 8 o a. tf * < £ %b i/t ,\^ £>& Y* ,/3 ,&* (6) 53 6 . Phase Shift in the Turbulent Zone The fundamental frequency of the wave trains experienced a phase shift upon passing through the turbulent region. This shift was not measured for second and third harmonics because of the limitations in the measuring technique. Phase shift was measured by recording the output of both probes on a two-channel strip chart recorder. Waves alone were measured initially; the turbulence generator was then turned on and the outputs of the two probes were compared with respect to their phase relationship both before and after passing through turbulence. Firure 26 is a plot of frequency versus phase shift and frequency versus phase shift per number of wavelengths pass- ing through the turbulent region at any one time. Figure 26 shows that at the lowest frequency measured, the phase shift was negative. At higher frequencies the phase shift was positive and increased with frequency. Assuming that the frequency of the waves remained con- stant as they travelled the length of the tank, the observed phase shift implies that both the wavelength and the phase speed of the waves changed as they passed through the turbu- lent region and that this phase change increased in magni- tude with frequency. It was observed visually, particularly for the higher frequency waves, that as the waves entered the turbulent region, they steepened considerably at first and were then reduced in height and steepness in the 54 9 0) 10 CO a to xi 6 c 4) a> > o (0 c cfl o ■H hO 0) u .p c 0 CO 3 *hX> •H .p p CD •H 4J bfl 0) ^ CO o cfl U XJXJ 0-, 4-5 O CO c cfl •H T3 Cfl U C •H c •H X! CO CU CO cfl XI Ou, % 0 e© -4- JL C> CM f£ r-4 >» O C CD 3 cr o CD • U -* fc. + (0 to o CD • CO > r^ c + cfl +5 •H Si o *-, a iH ■* ^tfc cv a) *tfc o 0) c x> 0) a> o X) .H L, o d ^ ■P c cu o c -a iH o c (d 03 03 CO CO 0) 0) CO > > > •H (X) ctf CO o 5 * s c 0 X 0 0 -3- C»-\ CV iH O gaa^aurpiTTW ux ^qSian sab;/; SWH 58 8 . Summary and Conclusions This experiment showed that underwater turbulence had the following effects on surface waves: 1) Wave height decreased as a result of attenuation by turbulence for all frequencies measured (1.2 to 12.3 Hz) according to the formula v, - v, ~~ax n = n e o 9*fTTC 1/3 where a is an attenuation coefficient equal to f g 2) The waves studied were shifted in phase by turbu- lence; below 1.5 Hertz, this shift was negative and became positive above 1.5 Hertz. 3) Measurements using a model sea surface indicate, qualitatively, that a continuous spectrum of waves experiences attenuation in much the same manner as the nearly sinusoidal waves of this experiment. 59 BIBLIOGRAPHY 1. Groen, P. On the Behavior of Gravity Waves in a Turbulent Medium, with Application to the Decay and Apparent Period Increase of Swell. Staatsdrukkeri j- En Uitgeveri jbedri jf / ' S-Gravenhage , 1954. 2. Barnett, T. P. On the Generation, Dissipation, and Prediction of Ocean Wind Waves , Journal of Geophysical Research , Vol. 73, No. 2, January 1968. 60 INITIAL DISTRIBUTION LIST No. Copies 1. Defense Documentation Center 20 Cameron Station Alexandria, Virginia 22314 2. Library Naval Postgraduate School 1 Monterey, California 93940 3. Naval Weather Service Command 1 Washington Navy Yard Washington, D. C. 20390 4. Dr. H. Medwin 6 Department of Physics Naval Postgraduate School Monterey, California 93940 5. Director, Naval Research Laboratory 1 Attn: Tech. Services Info. Officer Washington, D. C. 20390 6. Commander Naval Ships Systems Command 1 Attn: Code 0 0VIK Washington, D. C. 20390 7. Prof. N. E. Boston 1 Department of Oceanography Naval Postgraduate School Monterey, California 93940 8. Dr. T. Green ill 3 Department of Oceanography Naval Postgraduate School Monterey, California 93940 9. W. Smith 1 Department of Physics, Room 022 Naval Postgraduate School Monterey, California 93940 10. Department of Oceanography 3 Code 5 8 Naval Postgraduate School Monteres, California 93940 61 11. Department of Meteorology Code 51 Naval Postgraduate School Monterey, California 93940 12. Oceanographer of the Navy The Madison Building 732 N. Washington Street Alexandria, Virginia 22314 13. Naval Oceanographic Office Attn: Library Washington, D. C. 20390 14. National Oceanographic Data Center Washington, D. C. 20390 15. Director, Maury Center for Ocean Sciences Naval Research Laboratory Washington, D. C. 20390 16. James E. Paquin US NROTC Unit Oregon State University Corvallis, Oregon 62 UNCLASSIFIED Security Classification DOCUMENT CONTROL DATA -R&D ini\ i lassification ot title, body ot abstract and indexing annotation must be entered when the overall report is classified) 1 originating activity [Corporate author) Naval Postgraduate School Monterey, California 93940 2a. REPORT SECURITY CLASSIFICATION UNCLASSIFIED 2fc. GROUP 3 REPORT TITLE A LABORATORY EXPERIMENT ON SURFACE WAVE ATTENUATION DUE TO UNDERWATER TURBULENCE 4. DESCRIPTIVE NOTES (Type ot report and.inclusive dates) Thesis 5 AuTHORiSI (First name, middle initial, last name) James Edward Paquin, Lieutenant, United States Navy REPORT DATE December 1968 la. CONTRACT OR GRANT NO. b. PROJ EC T NO 7a. TOTAL NO OF PAGES 61 7b. NO. OF REFS 2 9a. ORIGINATOR'S REPORT NUMBER(S) 9fc. OTHER REPORT NOISI (Any other numbers that may be assigned this report) 10 DISTRIBUTION STATEMENT Distribution of this document is unlimited. 11. SUPPLEMENTARY NOTES 13. ABSTRACT 12. SPONSORING MILITARY ACTIVITY Naval Postgraduate School Monterey, California The attenuation of surface waves caused by underwater turbulence was investigated in a wave-tank experiment. The waves studied (frequencies ranging from 1.2 to 12.3 Hertz) were strongly attenuated by a zone of grid-generated turbu- lence. This attenuation depended on the length of the turbulent region, and on the frequency of the incident wave The equation governing attenuation was : h = h e o •ax where h is wave height, h is undisturbed wave height, x is the length of the turbulent region, and a is an attenuation coefficient proportional to the cube root of frequency. It was also noted that the waves were shifted in phase as they passed through the turbulence, and that the magnitude of this shift increased with frequency. The quantitative results of the experiment were obtained from measurements of nearly sinusoidal waves. They were confirmed, qualitatively, for a continuous spectrum of waves by measurement of wind-generated model sea surface. DD,F. 0RM 1473 NOV 65 I "T / Sj S/N 01 01 -807-681 1 (PAGE 1 63 UNCLASSIFIED Security Classification A-31408 UNCLASSIFIED Security Classification KEY WORDS TURBULENCE ATTENUATION OF SURFACE WAVES WAVES SURFACE WAVES I . DD ,F„°o1"„1473 S / N 0 1 0 I - 9 0 7 - 6 1 ■? t BACK 64 UNCLASSIFIED Security Classification flora = SHELF BINDER - Syracuse, N. Y. ■ Stockton, Calif. Maboratorve> .,„*«->« i V , \\\ \ WW »»'