Gas bubbles form an acoustically important part of the sea’s constituents, as they are involved in the creation, scattering, and destruction of sound.Animals and plants, many of which contain a gas enclosure of some kind, are also important.The acoustical properties of both are reviewed here.13
4.2.1 Properties of air bubbles in water 4.2.1.1 Properties of air under pressure
The (adiabatic) sound speed in air can be calculated as a function of temperatureT as:
cairðTÞ ¼ ½airRairYðTÞ 1=2 ð4:36Þ
13For a discussion of the influence of solid suspensions, see Chapter 5.Suspensions can usually be ignored in the open sea, but are sometimes important in coastal waters, especially near river outlets.
4.2 Properties of bubbles and marine life 149 Sec.4.2]
Figure 4.16. Seawater attenuation coefficientvs.frequency calculated using Equations (4.26) to (4.33).Upper graph: sensitivity to temperature and acidity; lower graph: curves for different oceans with parameters from Table 4.2.
where the specific heat ratio of air is airðCPÞair
ðCVÞair¼1:4011; ð4:37Þ
Rair is the gas constant of air, equal to 287 J kg1K1; and Y is the absolute Table 4.2. Seawater parameters used for evaluation of attenuation
curves plotted in Figure 4.16 (adapted from Ainslie and McColm, 1998).
Ka S T/C z/km
Arctic Ocean 1.58 30 1.5 0.0
Atlantic Ocean 1.00 35 4.0 1.0
Baltic Sea 0.79 8 4.0 0.0
Pacific Ocean 0.50 34 4.0 1.0
Red Sea 1.58 40 22.0 0.2
aThe parameterKis defined in Section 4.1.3.4.
Figure 4.17. Fractional sensitivitysðfÞof seawater attenuation (Equation 4.35) to temperature (T), salinity (S), acidity (parameterized throughK), and depthðzÞ.The attenuation coefficient aðfÞis calculated using Equations (4.26) to (4.33).
temperature.The ideal gas law gives the equilibrium air density under pressure airðzÞ ¼STPYSTP
PSTP
PairðzÞ
YðzÞ ; ð4:38Þ
whereSTPis the density of air at standard temperature and pressure (STP), equal to 1.29 kg m3.
The rate at which heat can be transported in a gas bubble is controlled by the thermal diffusivityof the gas.The higher the diffusivity, the more quickly heat can be dissipated and the more acoustical energy is lost to heat when the bubble pulsates.It is defined by Morfey (2001)14as
Dair Kair
airðCPÞair; ð4:39Þ whereðCPÞair is the specific heat capacity of air, equal to 1.005 J g1K1 (Leacock, 2003); andKair is the thermal conductivity of air, equal to 0.0249 W m1K1 at a temperature of 10C.For other temperatures it can be calculated using (Pierce, 1989, p.513)
KairðTÞ ¼K0 YðTÞ Y0
3=2
Y0þYAexpðYB=Y0Þ
YðTÞ þYAexp½YB=YðTÞ ; ð4:40Þ whereY0,YA, andYB are constant temperatures, given by
Y0¼300:0 K; ð4:41Þ
YA¼245:4 K; ð4:42Þ
and
YB¼27:6 K: ð4:43Þ
The remaining constant, K0, is the value of Kair at temperature Y0, equal to 2.624102W m1K1.The value of Dair at 10C and atmospheric pressure is about 20 mm2/s.
4.2.1.2 Properties of water that affect the behavior of a pulsating bubble
The pressure inside a submerged gas bubble exceeds hydrostatic pressure by an amount that depends on thesurface tensionof water.The attractive force between water molecules results in a tension at the surface of the bubble.The surface tension can be defined as the force acting tangentially to the (air–water) interface, per unit length of that interface.For clean water it is equal to 0.072 N/m.The surface tension of slightly dirty bubbles is lower (a value of 0.036 N/m is quoted by Thorpe, 1982), whereas for bubbles in salt water it is slightly higher.
4.2 Properties of bubbles and marine life 151 Sec.4.2]
14Alternative definitions are sometimes encountered.Weston (1967) uses specific heat at constant volume instead of at constant pressure, and Stephens and Bate (1966, p.765) omits the specific heat factor altogether.
4.2.1.3 Properties of bubbly water
A presentation of the acoustical properties of bubbly water (such as sound speed and attenuation of the air–water mixture) is deferred to Chapter 5.
4.2.2 Properties of marine life 4.2.2.1 Basic physiological properties 4.2.2.1.1 Zooplankton
Greenlaw and Johnson (1982) give expressions for the volume V of individual euphausiids, decapods, and copepods, as a function of their lengthL.For example, the average for all euphausiids is
V¼ ð5:75103mm3Þ L 1 mm
3:10
; ð4:44Þ
and for a species of decapod (Sergestes similis) V¼ ð3:74103mm3Þ L
1 mm
3:00
: ð4:45Þ
For arthropods, Stanton et al.(1987) provide expressions relating animal length L and volume V to their weight.Combining them gives the following relationship between length and volume
V ¼7:7 mm3þ ð4:06104mm3Þ L 1 mm
2:295
: ð4:46Þ
4.2.2.1.2 Fish
The single most important physiological property of fish, from an acoustical point of view, is the presence or absence of a gas-filled bladder.It is known that entire families of fish, such as gadoids and clupeoids, possess such a bladder.The effect of the gas- filled enclosure is to enhance the scattering properties of the fish, with a particularly dramatic effect close to the resonance frequency of the enclosure.
Two types of bladdered fish can be distinguished.Some, known asphysostomes, are equipped with a connecting tube between the bladder and the gut, enabling the exchange of air between these two organs.Others, called physoclists, have a com- pletely closed bladder.According to MacLennan and Simmonds (1992), all gadoids (e.g., cod or haddock) are physoclists, and all clupeoids (e.g., herring) are physo- stomes.Other classes of fish, such as mackerel, have no bladder at all.Appendix C contains a list of species, compiled from various sources, with information for each species concerning the presence or absence of a bladder, and the type of bladder if present.For a valuable and comprehensive Internet resource describing the taxonomy and physiology of fish generally, seefishbase(Froese and Pauly, 2007).15
15The bladder is absent in the gadoidsMelanonusandSqualogadus(Froese and Pauly, 2007).
Assuming a fish has a bladder, the volume and surface area of the bladder can be estimated from the lengthL of the fish by means of the equations (Haslett, 1962)
Vbladder3:40104L3 ð4:47Þ
and Weston (1995)
Sbladder0:0291L2: ð4:48Þ
The volume of the whole fish is approximately (Haslett, 1962)
Vfish0:0083L3: ð4:49Þ
An estimate of the surface area of the fish can be made by a simple geometrical scaling of the form16
SfishSbladder Vfish Vbladder
2=3
¼0:238L2: ð4:50Þ
4.2.2.1.3 Marine mammals
Typical values of mass m and length L are given for selected species of marine mammal in Table 4.3. The ratiom=L3is also included, providing information relating to the aspect ratio of the animal.A prolate spheroid of volumeVand lengthLhas a breadth-to-length aspect ratioX given by (see Table 4.4)
X¼ ffiffiffiffiffiffiffiffiffi
6V L3 r
: ð4:51Þ
The final column of Table 4.3 shows this aspect ratioX, estimated for each species by replacing the volumeV with that of the animalm=.The value ofXvaries between 0.11 (usingm=L37 kg/m3, for the franciscana dolphin and sperm whale) and 0.26 (m=L337 kg/m3, for the northern sea lion, walrus, and elephant seal).
4.2.2.2 Acoustical properties 4.2.2.2.1 Fish flesh
The response of a fish bladder to sound is similar to that of an air bubble, but influenced in a non-trivial way by the surrounding fish flesh.The sound speed and density of fish flesh exceed those of seawater by a few percent, as summarized in Table 4.5.
The elasticity of fish flesh is determined by the (complex) shear modulus.The real part determines the pressurePeexerted by the bladder wall on the gas contents (Andreeva, 1964)
Pe¼ 4
3aReðÞ: ð4:52Þ
The imaginary part ofdetermines losses due to vibration of the flesh.The value of is subject to considerable uncertainty but a typical value, attributed by Love (1978) to 4.2 Properties of bubbles and marine life 153 Sec.4.2]
16Use of Equation (4.50) implies an assumption that the bladder and fish are of similar shape.
Table 4.3. Mass, length, and aspect ratio of selected sea mammals (based on Pabstet al., 1999).
Speciesa Mass Length m L3/ Aspect
m/kg L/m kg m3 ratiob X Northern fur seal (female) (Callorhinus ursinus) 30 1.4 10.9 0.14
Franciscana dolphin (Pontoporia blainvillei) 32 1.7 6.5 0.11
Sea otter (Enhydra lutris) 45 1.5 13.3 0.16
Harbor seal (Phoca vitulina) 140 1.9 20.4 0.19
Amazonian manatee (Trichechus inunguis) 450 3.0 16.7 0.18 Bottlenose dolphin (Tursiops truncatus) 650 4.0 10.2 0.14
Northern sea lion (Eumetopias jubatus) 1,100 3.2 33.6 0.25
Walrus (Odobenus rosmarus) 1200 3.2 36.6 0.26
Elephant seal (Mirounga leonina, Mirounga angustirostris) 5000 5.0 40.0 0.27 Steller’s sea cow (Hydrodamalis gigas)c 10000 7.0 29.2 0.23 Sperm whale (male) (Physeter macrocephalus) 45000 18.5 7.1 0.11
Right whale (Lissodelphis borealis, Eubalaena glacialis) 90000 17.7 16.2 0.17
aThumbnail images Garth Mix, GMIX Designs.Reprinted with permission.
bOf an equivalent prolate spheroid with the same length and mass (see Equation 4.51).
cExtinct species.
#
Andreeva (1964), is
¼ ð300þ90iÞ kPa; ð4:53Þ consistent with a value ofPeclose to 300 kPa.Weston (1995) suggests a smaller value forPein the range 50 kPa to 100 kPa, based on the measurements of Love (1978) and Løvik and Hovem (1979).
An alternative model introduced by Love (1978) treats fish flesh as a viscous fluid medium described by a viscosity parameter, defined as
¼43 Sþ B: ð4:54Þ
Neroet al.(2004) suggest for fish flesh a value of
¼50 Pa s: ð4:55Þ
4.2 Properties of bubbles and marine life 155 Sec.4.2]
Table 4.4. Volume and surface area of ellipsoids with semi-axesabc.
Shape Volume Surface area Ellipticity
General ellipsoid, Expressable in terms of an
semi-axesa,b, andc 43abc elliptic integral N/A
(Weisstein, www) Prolate spheroid,a
semi-major axisa, 43ab2 2 b2þabarcsine e
1b2 a2
1=2
semi-minor axesb, ellipticitye Oblate spheroid,b
semi-major axesa, 43a2c 2 a2þc2
2eloge1þe 1e
1c2 a2
1=2
semi-minor axisc, ellipticitye
Sphere, radiusa 43a3 4a2 0
aA prolate spheroid has one major axis and two minor ones, like an airship.
bAn oblate spheroid has two major axes and one minor one, like a flying saucer.
Table 4.5. Acoustical properties of fish flesh.
Species Sound speed Density ratio Reference
ratio c=cw =w
Cod (Gadus morhua) 1.050 1.040 Clay and Horne (1994)
Unspecified fish with swimbladder 1.033 1.023 Love (1978)
4.2.2.2.2 Whale tissue
The acoustical properties of whale tissue, as reported by Miller and Potter (2001) and Jaffeet al.(2007), are summarized in Table 4.6.
4.2.2.2.3 Zooplankton
The density and sound speed of krill (euphausiid) flesh are correlated with animal length.Chu and Wiebe (2005) give the following correlation equations, valid for krill lengthLexceeding 25 mm (i.e.,LL^>0:025):
ckrill
cw ¼1:009þ0:50LL^ ð4:56Þ
krill
w ¼1:002þ0:54LL:^ ð4:57Þ
A summary of the acoustical properties of euphausiids is given in Table 4.7 and for other zooplankton in Table 4.8 (see also Laveryet al., 2007).
4.2.2.3 Population estimates
4.2.2.3.1 Fish in the North Sea: population density and case study
An order of magnitude estimate of the average areic17mass of all marine fauna is about 10 g/m2 in both deep and shallow water.It is difficult to improve on this estimate except for well-studied locations.Despite this uncertainty, the effects can be large and should therefore be considered.Population estimates for the North Sea are provided as an example although, at the time of writing, the data on which the estimates are based are already 20 years out of date.
The total North Sea biomass is estimated (Sparholt, 1990; Yang, 1982) to be
Table 4.6. Acoustical properties of whale tissue.Attenuation measurements are standardized for ease of comparison by dividing them by frequency and presenting in units of dB/(m kHz).The actual measurement frequencies are 100 kHz (Miller and Potter, 2001) and 10 MHz (Jaffeet al., 2007).
Species Tissue type c=m s1 =kg m3
f
dB m1 Reference kHz1
Atlantic northern Skin 1700 1200 Miller and Potter (2001)
right whale Blubber 1600 900 0.09 Miller and Potter (2001)
(Eubalaena glacialis)
Florida manatee Connective 1680–1710 1030–1150 0.3–0.6 Jaffeet al.(2007) (Trichechus manatus tissue
latirostris) Blubber 1520–1530 960–1060 0.5–0.8 Jaffeet al.(2007) Muscle 1600–1630 1020–1070 0.3–0.5 Jaffeet al.(2007)
17Following Taylor (1995), the adjectives ‘‘areic’’ and ‘‘volumic’’ are used, respectively, to mean ‘‘per unit area’’ and ‘‘per unit volume’’.
about 10 Tg (1 teragram is equal to 1012 grams, or 1 million metric tons).Assuming for the North Sea a total surface area of 575 000 km2 and volume 42 300 km3, the average areic and volumic biomass densities for the North Sea are 17 g/m2and 0.24 g/
m3, respectively.Data by individual species appear in Table 4.9.Additional informa- tion about North Sea fish can be found in Knijnet al.(1993).Also worth mentioning are the argentines (Argentina spp.), pelagic physostomes of length about 13 cm, common in the Norwegian Deep.The estimated biomass of argentines in the Nor- wegian Deep is 0.4 Tg (Yang, 1982).
The geographical distribution of two important North Sea species is shown in Figure 4.18, including an indication of the variation with season (summervs.winter) and fish size (adults vs.juveniles).The data show that, during the 1980s, herring were common in both summer and winter throughout the North Sea except in the 4.2 Properties of bubbles and marine life 157 Sec.4.2]
Table 4.7. Acoustical properties of euphausiids (from Simmonds and MacLennan, 2005).
Species Sound speed ratio Density ratio
c=cw =w
Euphausia pacifica 1.005–1.015 1.035–1.040
Euphausia superba 1.0280.002 1.021–1.040
Thysanoessa raschii 1.010 1.027
Thysanoessaspp. 1.025 1.026–1.044
Meganyctiphanes norvegica 1.035 1.029–1.048
Table 4.8. Values of zooplankton density and sound speed ratios (from Clay and Medwin, 1998, Table 9.5 and Simmonds and MacLennan, 2005, p. 277).
Class Sound speed ratio Density ratio
c=cw =w
Amphipods 1.000–1.009 1.055–1.088
Cladocerans 1.011–1.017
Copepods 1.006–1.012 1.023–1.049
Decapods 0.997–1.006
Mysids 1.075
Cephalopods 1.007 1.003
Cod eggs 1.017–1.026 0.979–0.992
various periods between 1977 and 1992.
Species B/Tg Reference L50/ma Estimated Description
(Knijn North Sea et al., population/
1993) millions
Sandeel 1.82 Sparholt (1990)b (0.20) 26 700 Demersal (no bladder)
(Ammodytesspp.)
Herring 1.33 Sparholt (1990) 0.24 11 300 Pelagic (physostome)
(Clupea harengus)
Norway pout 1.20 Sparholt (1990) 0.13 64 100 Pelagic (physoclist) (Trisopterus esmarkii)
Dab (Limanda limanda) 0.74 Yang (1982)c 0.12 50 300 Demersal (bladder absent in adults)
Grey gurnard 0.64 Yang (1982) 0.19 11 000 Demersal
(Eutrigla gurnardus)
Plaice 0.55 ICES (1994)d 0.33 1800 Demersal flatfish
(Pleuronectes platessa) (bladder absent in
adults)
Haddock 0.50 ICES (1994) 0.30 2200 Pelagic (physoclist)
(Melanogrammus aeglefinus)
Starry ray (Raja radiata) 0.45 Yang (1982) 0.47 500 Demersal
Mackerel 0.44 Sparholt (1990) (0.30) 1900 Pelagic (no bladder)
(Scomber scombrus)
Whiting 0.40 ICES (1994) 0.20 5900 Pelagic (physoclist)
(Merlangius merlangus)
Cod (Gadus morhua) 0.35 ICES (1994) 0.70 100 Pelagic (physoclist) Saithe (Pollachius vireus) 0.30 ICES (1994) (0.45) 400 Pelagic (physoclist) Silvery pout 0.25 Yang (1982) (0.06) 135 800 Pelagic (physostome) (Gadiculus argenteus)
Long rough dab 0.23 Yang (1982) 0.17 5500 Demersal flatfish
(Hippoglossoides (bladder absent in
platessoides) adults)
Horse mackerel 0.22 Yang (1982) 0.24 1900 Pelagic (no bladder)
(Trachurus trachurus)
Sprat (Sprattus sprattus) 0.20 Sparholt (1990) 0.10 23 500 Pelagic (physostome)
aThe lengthL50 is the fish length ‘‘at which 50 % of the individuals sampled in that length class are sexually maturing/
mature’’
(Knijnet al., 1993) (values in brackets are estimates).
bThree-year average (1983–1985).
cTwo-year average (1977–1978).
northernmost region, and that most were juveniles (withL<L50).By comparison, Norway pout were present mainly in the north and northwest, with a population that was more evenly balanced between adults and juveniles.
4.2.2.3.2 Marine mammals
A biogeographical database, including information from marine mammal sightings, is available from the Ocean Biogeographic Information System (obis, www).The abundance of different species varies enormously.Global population estimates from Bowen and Siniff (1999) for various periods in the 1980s and 1990s include
— for pinnipeds, between 12 000 000 crabeater seals18 or 6 000 000 harp seals to fewer than 500 Mediterranean monk seals;
— for cetacea, between 2 000 000 sperm whales or 2 000 000 spinner dolphins19to 500 Indus river dolphins and fewer than 1000 northern right whales;
— for sirenians, between 100 000 dugongs or 100 000 sea otters to just 2500 Florida manatees.