Solitary internal waves in the Celtic Sea

Solitary internal waves in the Celtic Sea

Prog. Oceanog. Vol. 14, pp. 431-441, 1985. Printed in Great Britain. 0079--6611/85 $0.00 + .50 Pergamon Press Ltd. Solitary Internal Waves in the Ce...

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Prog. Oceanog. Vol. 14, pp. 431-441, 1985. Printed in Great Britain.

0079--6611/85 $0.00 + .50 Pergamon Press Ltd.

Solitary Internal Waves in the Celtic Sea R. D. PINGREE and G. T. MARDELL Institute of Oceanographic Sciences, Brook Road Wormley, Godalming, Surrey, U.K. Abstract-An examination is made of tidally generated high frequency internal wave trains propagating from the shelf-break of the Celtic Sea and Armorican shelf. The waves propagate on-shelf after maximum off-shelf tidal streaming at speeds of about 70 cm s-1 giving a wavelength between successive tidal disturbances of 30km. As the waves travel on-shelf they are advected by the barotropic tide and can take on a solitary wave form.

1. INTRODUCTION INTERNAL waves near the shelf-break of the Celtic Sea and Armorican shelf can be conveniently categorised into high frequency internal waves (with periods of 15 mins to 1 hr) and longer period oscillations at the semidiurnal tidal frequency though, of course, these categories only represent part of the complete internal wave spectrum. The longer period waves usually have a marked first and second baroclinic mode which is particularly conspicuous at spring tides. At thermistor chain mooring 069 (Figs 1 and 2) the higher frequencies tend to occur as the thermocline is both depressed and broadened and these effects become more marked at spring tides. Both high and low frequency components generated during spring tides at the shelf-break, propagate on-shelf with comparable phase speeds with finite amplitude effects for the short waves nearly matching the rotational effects for the longer waves. However, the group velocity for the longer waves is strongly influenced by rotation resulting in a group velocity which is only about 40% of the phase speed of the internal tide at these latitudes. Thus about 100km on-shelf the sernidiurnal internal tide can show maximum amplitudes several days after spring tides. In this paper the on-shelf propagation of the higher frequency internal waves from the shelfbreak of the Celtic Sea and Armorican shelf is examined. Disturbances at the shelf-break can develop into a series of internal solitary waves. Such waves are able to emerge from collisions with other solitary waves unchanged in form (WITTING, 1982) and because of their elementary particle-like behaviour ZABUSKY and KRUSTAL (1965) coined the word "soliton" to describe them. Noteworthy studies of propagating internal wave trains in other regions include those of HAURY, BRISCOE and ORR (1979) in Massachusetts Bay and ZIEGENBIEN (1969) near the Strait of Gibraltar.

2. METHODS AND RESULTS Three experiments were performed to investigate the on-shelf propagation of internal waves and are described briefly under separate headings. 431



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FIG. 2. Thezmistor chain record 069 at a position (47°41.8'N, 6°18.2'W, sea Fig. I) about 25 k m on-shelf from the shelf-break. The bottom mixed layer was about 12°C and this contour has been omitted. Note the marked difference in character in the record between neaps and springs (22.7.82).

Solitary internal waves in the Celtic Sea


2.1. General survey over a broad region The broad positions of internal wave trains encountered along the track of the RV Frederick Russell in the Celtic Sea are shown plotted in Fig. 3. The waves could be identified both in the echo-sounder (33 khz) records (Fig. 4) and in the SeaSoar sections (Fig. 5). The SeaSoar is a towed undulating recorder measuring temperature, conductivity, chlorophyll a fluorescence, oxygen and pressure (COLLINS, POLLARD and SUCHEN, 1983; FASHAM, PUGH, GRIFFITHS and WHEATON, 1981). The recorder has the capability of measuring each parameter 16 times a second and was cycled up and down from near surface, 2 m, to 80 m every 4 mins. At a towing speed of 8 knots the thermocline region at mid depths is sampled every 500 m, so wavelengths of less than 1 km are not resolved and are perhaps even aliased. Whilst the scatter in Fig. 3 is considerable, the plotted positions of the internal wave trains suggest that these waves are generated near the shelf-break (200 m contour) approximately 2 hr after H.W. Plymouth, which corresponds to local maximum off-shelf tidal streaming, and travel on-shelf about 25-30 km in a tidal period. 2.2. Repeated sections over a limited shelf region The positions of internal wave trains encountered whilst making repeated sections of the shelf-break are shown in Fig. 6. The arrows represent the finite length of the high frequency



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110 FIG. 4. Echo-sounder records showing displacement of the thermocline in selected regions. (a) Internal waves (observed whilst steaming) propagation on-shelf in the direction 015°N (as observed by ship's radar) from the shelf-break region (200 m contour on the far right). The position of these internal waves corresponds to point 4 in Fig. 6. (b) Internal waves propagation past a fixed C.T.D. station 47°52'N 6°29'W (27.7.83). The scale is approximate since these waves were not observed by radar. Their arrival time from the shelf-break region corresponds to point 14 in Fig. 6. (c) Internal waves taking on a solitary wave aspect. These waves were propagating in the direction 350°N and the progress of leading wave on the left is shown plotted in Fig. 7 (near vertical lines show C.T.D. dips). internal disturbances and the time for which they were observed. The orientation of the lines depends upon whether the ship was steaming on-shelf or off-shelf. Some repeated C.T.D. stations were also made in this same area and the arrival times of internal waves recorded by the measurements have also been plotted in Fig. 6 (points 10, 12, 13, and 14). In addition two further points (22 and 12) are indicated as triangles. These

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FIG. 5. (a) SeaSoar section of temperature (~C) and chlorophyll a (mgm -a) fluorescence (16.7.83) showing the structure of the internal tide along'the first leg of the track shown in the upper left of Fig. 3. The thermocline is noticeably depressed at points (1) (2) and (3) and these positions are plotted on Fig. 3. Near position (2) the 16°C isotherm descends nearly 60 m. (b) SeaSoar sections of temperature (°C) and chlorophylla (mg m -a) fluorescence (24.7.83) showing the internal displacement of the thermocline. The positions of points '1' and '2' are shown in the upper left of Fig. 6. The shading represents clorophyll values between 1 and 2 mg m -a. Values at the surface are typically 0.3-0.4 mg m-3 except where the maximum reaches the surface in the region of shelf-break cooling near the 200 m contour. correspond to the arrival of the internal tidal signal at thermistor chain mooring 069 (see Fig. 2) and current meter mooring 065 (47°37.5'N, 06°22.5'W). These latter measurements were made in 1982 but correspond to the same time of year with a similar development of the thermocline. In fitting a line to the points in Fig. 6 it is important to remember that the waves will be advected by the barotropic tidal currents. Whilst these appears to be a considerable variability between individual points, they can be broadly represented by a single best fit curve. This corresponds to a phase speed of 70 cm s -1 superimposed on an oscillating tidal current with the same on-shelf maximum amplitude ( 7 0 c m s-l), this latter value being in agreement with tidal currents derived from current meters and numerical models (PINGREE, MARDELL, HOLLIGAN and GRIFFITHS, 1982). This intercept on the time axis indicates that the waves propagate on-shelf about 3 hr after high water Plymouth or about 1 hr after maximum offshelf streaming, suggesting they are generated during off-shelf tidal streaming. 2.3. Following an internal wave packet Three of the internal wave packets were clearly identified by the ship's radar and a special study was made following a single wave group, Fig. 7. The surface signatures of these internal




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Time(H.) FIG. 6. Travel graphs for the internal wave trains encountered on the course shown in the upper left. The curved line represents a speed of 70 cm s-' with a superimposed tidal oscillation also of maxknum amplitude of 70cm s-'. Results from the thermistor chain record (see Fig. 2) and a current meter record taken at the same time are indicated by a triangle. Time zero is the time of high water at Plymouth. The observations are centred around spring tides (24.7.8328.7.83). waves could also be seen visually. Parallel "walls of white water" (breaking surface waves) separated by about "- 1 km and stretching for several miles indicated the presence of the internal waves. The wave group progressed in a direction 350°N and moved on-shelf 28.6 km in a tidal period. A surface drifting buoy indicated a southerly flow o f about "" 5 cm s -1 so that phase speed o f the internal wave could be as high as 69 cm s -1. Tidal advection is clearly evident in Fig. 7 and the deviation from the straight line is consistent with the M2 tidal currents derived from a numerical model (semi-major axis 33 cm s -1, ratio o f minor to major axis 60% and orientation 034°N). The tidal advection is less apparent here than in Fig. 4 since the tidal streams are weaker in this region, the wave is propagating obliquely to the m a j o r axis o f the tidal streams and the observations were made about 3 days after spring tides. Repeated C.T.D. and chlorophyll a fluorescence profiles through the internal waves were obtained by steaming up wind (the wind was from the North with a speed o f about 10 m s -1) and allowing the waves to propagate past the ship. The results are shown in Fig. 8 and the horizontal scale for the waves was obtained by measuring their separation by ship's radar. During the total period o f the observations the separation of the first two leading waves increased from

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FIG. 7. Propagation speed of the leading wave of a gzoup of internal waves travelling ~ 350 ° N from the shelf-break [see Fig. 4(c)]. The inset shows the ship's track and the radar signature of the waves at about 1530hr G.M.T. on 29.7.83. Tidal advection on the propagation speed is clearly evident.

1.1 km to 1.8 kin. The first two waves can also be seen in the echo-sounder trace shown in Fig. 4(c) where the solitary nature of the waves is again apparent. The ratio of the maximum amplitude, no, to the depth of the thermocline, hi, is of order a = no~hi "" 1 for the leading wave and the maximum wave slope exceeds 1 in lO.

3. DISCUSSION Taken as a whole the results show that high frequency internal wave trains are generated at the shelf-break during off-shelf tidal streaming and propagate on-shelf as off-shelf tidal streaming slackens. Thus a description in terms of lee waves would appear appropriate (HAURY, BRISCOE and ORR, 1979). When account is taken for tidal advection the phase speed for typical summer (July) density structure is about 70cm s-1 giving a wavelength between successive disturbances of about 30kin. Approximating the thermocline as a sudden density step, ~p (equivalent to about 5°C, salinity effects on density were small, generally less than 20% of that due to temperature) with mixed layers hi = 3 0 m and h2 = 135m above and below gives a phase speed c for linear long internal waves on a sharp density interface as:

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hours FIG. 8. Vertical sections of (a) temperature (*C) and (b) Chlorophyll a (mgm -3) through the internal waves shown in Fig. 4(c) (and followed in Fig. 7) and obtained as the waves travelled past the R.V. Frederick Russell. This is clearly less than that estimated from the measurements and demonstrates the importance o f ffmite amplitude on the propagation speed o f the internal waves trains. Following WHITHAM (1974) the amplitude, n, of an internal solitary wave travelling in the x direction against time can be written in the form: n = - - n o sech 2 L-l(x -- Ut)


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The phase speed U dependson the maximum amplitude no and the ratio r = hl/h2, of the upper, h l, and lower layers, h2. These relationships which are derived from the Korteweg and de Vries equation (KORTEWEG and DE VRIES, 1895) assume a = n o [ h l ~ 1, r < 1 and that the Boussinesq and rigid lid approximations are valid (OSBORNE and BURCH, 1980).

Solitary internal waves in the Celtic Sea


Whilst the observed waves were not propagating without change of form it is instructive to estimate their phase speed and horizontal length scale near the solitary wave limit of the more general cnoidal waveform. Using (3) and taking hi ,c 30m, r "" 0.22 and no[hi ~ 0.8 gives U ~ 66 cm s -1 close to that observed even though a cannot be considered as small. From (4) the corresponding length L is ~ 90 m showing that the amplitude should fall to half its maximum value in a distance of 0.88L "~ 80m. This is about 55% of that actually observed and this discrepancy is thought to be partially due to the tendency for the ship to remain relatively longer in those parts of the wave (i.e. the troughs) where the currents are flowing faster in the direction of wave propagation. Since a is not small, hx/h-~h2/L is not small and (4) is not strictly applicable. Some of the internal wave trains encountered did not appear to fit the simple lee wave model. For example, points 4 and 16 on Fig. 6 appear too far on-shelf and it may be that some of the waves may have been created by the linear tidal sand ridges that are a conspicuous feature of the near shelf-break bathymetry of the Celtic Sea. Tidal generated internal waves may be generated by specific topographic features at the shelf break and so a tight distance-time relationship would not be expected from a number of localised sources producing waves which may propagate along the shelf-break as well as on-shelf. Further studies are planned to identify the major sources for intemal waves along the Celtic Sea shelf-break. It is of interest to consider what distribution of points might occur in Fig. 6. if the internal waves generated near the shelf-break arrived on the shelf at random states of tide. On the shelf, advection by the barotropic tidal currents could cause concentrations and rarefactions in the distributions. If it is assumed that the phase speed of the internal waves along the ship's track and approximately normal to the shelf-break is 70cm s-1 and that the maximum amplitude of the oscillating barotropic currents is of similar magnitude in this direction then 1/3 of the plotted points would on average tend to lie outside the bounded region, indicated in Fig. 6 by dotted lines. If the internal waves were propagating from several different sources along the shelf-break then the expected scatter would increase with more points falling outside the bounded region. Near the shelf-break of the Celtic Sea the seasonal thermocline broadens and shelf-break cooling with its associated increase of surface chlorophyll a occurs where the surface isotherms outcrop at the sea surface. Mixing by internal tides is one candidate that might cause the observed shelf-break cooling and release of nutrients (PINGREE, MARDELL, HOLLIGAN, GRIFFITHS and SMITHERS, 1982). Whilst the SeaSoar sections show many apparent inversions of temperature associated with the internal tidal displacements they can mostly be discredited and result from the towed recorder intersecting the trough of a deeply penetrating internal wave. C.T.D. profiles at timed stations have on the other hand shown what are considered to be genuine inversions. These inversions are generally on scales of < 5 m though no statistical anlysis has yet been made. An example of a larger inversion on a 10m scale is illustrated in Fig. 9. At this station the inversions were observed in association with a second baroclinic mode, being more conspicuous when the thermocline was compressed. 4. SUMMARY The on-shelf propagation of tidal displacements of the seasonal thermocline has been studied along a 300kin stretch of the Celtic Sea and Armorican shelf-break using the undulating recorder SeaSoar housing a C.T.D. and in situ fluorometer. The peak to trough amplitude of the






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FIG. 9. (a) Vertical profiles of 'T', temperature (°C), 'S', salinity (%0) and 'D', potential density o0 showing instabilities on the seasonal thermocline. This profile corresponds to the ftrst C.T.D. dip indicated in Fig. 4(t)). Co) Corresponding temperature (*C), 'C', Chia fluorescence (mg m -s) and 'A', attenuation (m -t) profiles. tidally generated internal waves can exceed 5 0 m at spring tides. Some o f the internal tidal disturbances can take on the more regular form recently characterised in the Synthetic-Aperture Radar images obtained during the Seasat space mission and can be observed at sea using ship's radar, echo sounder or even visually. Individual internal wave packets appear near the shelfbreak during off-shelf tidal streaming and can be followed for at least a tidal period, propagating at speeds o f about 7 0 c m s -], considerably in excess o f that given by linear theory, resulting in a wavelength o f ~ 3 0 k m between successive internal tidal disturbances. Tidally generated internal waves are thought to promote mixing and the release of nutrients thereby creating a favourable environment for p h y t o p l a n k t o n growth, locally at the shelf-break where they are generated and again well on-shelf where t h e y propagate into the shelf tidal fronts. Acknowledgements-We are indebted to Captain M. Harding for identifying internal waves by ship's radar.

REFERENCES COLL,_NS, D. S., R. T. POLLARD and P. U. SUCHEN (1983). Long SeaSoar C.T.D. sections in the North East Atlantic ocean collected during R.R.S. Discovery Cruise 116. Institute o f Oceanographic Sciences Report No. 148, 75 pp. FASHAM, M. J. R., P. R. PUGH, D. GRIFFITHS and J. E. G. WHEATON (1981). 'Subaquatraka' a submersible fluorometer for detection of chlorophyll. In: Electronics for ocean technology, Proceedings of the Institution of electronic and Radio Engineers, London. pp. 49-58. HAURY, L. R., M. G. BRISCOE and M. M. ORR (1979). Tidally generated internal wave packets in Massachusetts Bay. Nature, 278, 312- 317. HAURY, L. R., P. H. WIEBE, M. H. ORR and M. G. BRISCOE (1983). Tidally generated high-frequency internal wave packets and their effects on plankton in Massachusetts Bay. Journal o f Marine Research, 41, 65-112. KORTEWEG, D. J. and G. DE VRIES (1895). On the change of form of long waves advancing in a rectangulax channel, and on a new type of long stationary wave. PhilosophiealMagazine, 39, 422-443. OSBORNE, A. R. and T. L. BURCH, (1980). Internal Sohtons in the Andaman Sea. Science, 208, 451-460. PINGREE, R. D. and G. T. MARDELL (1981). Slope turbulence, internal waves and phytoplankton growth at the Celtic Sea shelf-break. Philosophical Transitions o f the Royal Society, London, A302, 663-682.

Solitary internal waves in the Celtic Sea


PINGREE, R. D., G. T. MARDELL, P. M. HOLLIGAN, D. K. GRIFFITHS and J. SMITHERS (1982). Celtic Sea and Armorican current structure and the vertical distributions of temperature and chlorophyll. Continental ShelJ~Research, 1, 99-116. WHITHAM, G. B. (1974). Linear and non-linear waves. Wiley, New York, 636 pp. WHITTING, J. M. (1982). A Unified Model for the Evolution of Non-linear Water waves. NRL Memorandum Report 5001, 64 pp. ZABUSKY, N. J. and M. D. KRUSTAL (1965). Interaction of "solitons" in a collisionless plasma and the recurrence on initial states. Physical Review Letters, 15,240-243. ZIEGENBEIN, J. (1969). Short internal waves in the Strait of Gibraltar. Deep Sea Research, 16, 479-487.