Nov 20, 1984 - current systems flowing far above the earth and by the dynamo interaction of ocean .... sourceless geomagnetic induction. The electric field â¢' is.
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 89, NO. C6, PAGES 10,519-10,528,NOVEMBER 20, 1984
On the ElectromagneticFields Induced by OceanicInternal Waves ALAN D. CHAVE
Instituteof Geophysics andPlanetaryPhysics, Scripps Institutionof Oceanography, University of Californiaat SanDiego Model spectrafor the electricand magneticfields inducedby oceanicinternal wavesare obtained by combining Green function solutions to the two electromagneticmodal equationswith the Garrett-Munk kinematicdescriptionof the internal wave field. The poloidal magneticmode is dominant at frequenciesabove 3f, where f is the local Coriolis frequency,and self and mutual inductionare not importantover this range. The toroidalmagneticmode is increasinglyimportant at frequenciesbelow 3f and is sensitiveto the conductivitystructurebelow the seafloorfor nearinertialfrequencies.The mooredelectricfield is shownto be largelya measureof the localvelocity field at high frequencies.The verticalelectricfield is sensitiveto the horizontalvelocityfield, while the horizontal electricfield primarily reflectsthe vertical velocity field and is quite small at the seaearth and sea-airinterfaces.The magneticfield is a measureof the spatiallyaveragedvelocityfield and is dominated by the poloidal magnetic mode. Electromagneticboundary effects reduce the horizontal magneticspectrumby decadesat the seafloorand sea surface. At the seafloorand sea surface,internalwave-inducedmagneticfieldsare within an order of magnitudeof their externally inducedcounterparts,while in the ocean'sinterior, internalwavesare probablythe largestsource of magneticsignalsin the period range one day to one hour. The internal wave-inducedelectric field is not measurableexceptin the verticalcomponent.
vided by the kinematic spectral description of Garrett and
INTRODUCTION
Munk [1972, 1975, see also Munk, 1981]; this developNatural electromagneticfields in the oceansare induced by both external ionospheric and magnetosphericelectric current systems flowing far above the earth and by the dynamo interaction of ocean currents with the earth's magnetic field. The gross spatial and temporal morphology of the former are fairly well characterized at the
ment has inspired and guided much of the experimental effort of the last decade.
The Garrett-Munk
model util-
izes linear theory and experimental data to predict displacement and velocity spectra of internal waves in both moored and towed configurations. Recent theoretical work has concentrated on the dynamics of internal waves earth's surface [e.g., Nishida, 1978], and external elec- and attempts to explain the universality in shape and tromagnetic induction fields are frequently used in geo- amplitude of the observations. This research is reviewed physical exploration, chiefly through the magnetotelluric by Munk [1981], Levine[1983], and Olbers[1983]. In this paper, theoretical spectraof the electromagnetic method. By contrast, ocean-inducedelectromagneticfields are less well understood, primarily due to a paucity of fields and their gradients generated by ambient internal actual observationsand the complexity of the ocean veloc- waves are obtained by combining the poloidal and toroidal magnetic modal form of the field equations given by ity field. Studies of motional electromagnetic induction in the Chave [1983], which accountsfor the influenceof selfoceansare numerous, although the phenomenaexamined and mutual induction on the electromagneticfields, with are confinedprincipallyto the barotropictides [e.g., Lar- an eigenfunction expansion of the water velocity field and sen, 1968; Chave, 1983] and surfacegravitywaves [e.g., the Garrett-Munk variance spectrum. Both moored and Weaver, 1965; Larsen, 1971]. In a recent study, Chave towed sensors are considered. The spectral levels are and Filloux [1984] showedthat the seafloorelectromag- shown to be quite high in the interior of the ocean, netic power spectrumcould be separatedinto nearly equal dwarfing any external contribution except during intense parts of ionospheric and oceanic origin over the period geomagneticstorms,but boundaryeffectsreducethe specrange 1 day to 1 hour and suggesteda combination of a tra by orders of magnitude at the seafloorand sea surface, barotropic long wave and an internal wave mechanism to a phenomenonnot noted by Petersenand Poehis[1982]. explain the result. Since internal waves are a ubiquitous Magnetic gradientspectraare found to be near the limit of feature of the oceans, a more detailed look at their elec- detection for moored instruments but are substantial in a tromagneticeffects is required to assesstheir role in the towed sensor near the ocean's surface. These results indideep ocean electromagnetic environment. Previous cate that internal wave contamination, along with surface attempts to compute internal wave-induced electromag- gravity wave contributions, may be a source of noise in netic fieldsincludePodney[1975] and Petersen and Poehis aeromagneticsurveying.
[1982], and the magneticfield gradientsproducedby intense, shallow water internal wave packets were
HYDRODYNAMIC
THEORY
observedby PodneyandSager[1979]. It is essential that the model for internal waves be con-
A unified picture of oceanic internal waves was proCopyright 1984 by the American GeophysicalUnion.
sistent with the Garrett-Munk description to which the electromagneticspectrawill be tied; the linear form of the
Paper Number 4C0893.
hydrodynamicequationsused by Garrettand Munk [1972]
0148-0227 / 84/ 004C-0893505.00
will be followed. The f plane equations under the Bous10,519
10,520
ellAVE: EM FIELDSDUE TO INTERNALWAVES
sinesq approximation with the horizontal component of rotation, bottom topography, and wave current interactions neglected are
8t u -- f v ------8xP/Po
Otv + fu ----OyP/po &t• + N:< = -&zP/Po
(1)
where u, u, and w are the east, north, and vertical fluid velocity components,p is the pressure,P0 is the mean fluid density, • is the particle displacement, f is the Coriolis parameter, and N is the buoyancy or BruntV/fis/fl// frequency. Together with the incompressibility condition, these constitute a suitable set of equationsfor
wherethe boundary conditions on• aremetby the and the number of terms M is a free parameter. Appropriate choices for the basis functions include local types using spline functions or nonlocal types using orthogonal functions such as sinusoids;the former have better convergencepropertiesbut are usually more difficult to handle. For this problem, an appropriate choice is the set of eigenfunctions for the constant N case,
{sin (j'rrz/H)}. Substitutionof (6) into (5) yieldsa quadraticform to be minimized in the usual way with respect to the expansion
coefficients aj. The resultcan be expressedas the algebraic eigenvalue problem
X:Ax = Bx
small-scale waves at moderate latitudes.
A singleequationin • may be obtainedfrom (1) and the incompressibilitycondition by eliminating u, u, w, and p, and vertical normal mode solutions are sought in the form
• (x,y, z) = • (z)ei(¾•-•t)
(2)
where•' = ,/k + ½.•is thehorizontal wavenumberand•o is the angular frequency. The resulting eigenmodeequation for the displacementis
Oz2• + m:(z)-o•: o•2.._f2 k2• =0
, aM]r is
the eigenvector, and A and B are M x M matrices with elements
A• =J•m dz Oz• (Z)Oz• (z) B•j =[J•H dz (N:(z )-o•:)Oi (z )Oj (z)]/(o•:-f:) If the basisset is orthogonal,then A is diagonaland posi-
(3) tive definite, while B is symmetric but is positive definite
Together with the usual boundary conditionsof vanishing displacementat the seafloor (z =-H) and sea surface (z = 0), (3) constitutes a Sturm-Liouville eigenvalue problem. The desired velocity components are obtained from (1)'
u= ife)O v = (oe-if)Oz
