Observations and Modelling of Fronts and Frontogenesis

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temperature differences of surrounding thermistors are not far from the noise level of the calibrations, so these estimates have limited value as measurements of internal wave energy. They are however consistent with the assumption that the difference in the 70 m and 15 m spectral levels in the 0.1-1 cpkm band is due to internal waves, and that the variance in the 15 m spectrum in this band is due to other processes. Below 0.1 cpkm, where the break in slope in the 15 m spectrum occurs, the internal wave energy appears to fall off. This apparently fortuitous correspondence gives the 70 m spectrum a nearly uniform slope (Figure 11.10). Figure 11.12 displays ensemble averaged spectra of horizontal temperature gradients at 15, 23, 31, 50, and 70 m, as well as ensemble averaged coherence from cross-spectra between the 15 m record and the others, all band averaged to 5 bands per decade. There is significant vertical coherence in the 0.1-1 cpkm band over most of the surface layer. Where the internal wave variance raises the spectral levels above the 15 m values, coherence is rapidly destroyed. This occurs at successively shorter wavelengths as the vertical separation decreases, presumably since only short wavelength internal waves may exist on infrequent shallow patches of vertical gradient. 20
11.5 Geostrophic turbulence We have interpreted the low wavenumber plateau in the 15 m horizontal temperature gradient spectrum (Figure 11.8) as the signature of the mesoscale eddy field and a probable baroclinic production range, and the high wavenumber plateau as a surface boundary layer production range. At wavenumbers above 0.1 cpkm, internal waves consistently account for the difference between the 70 m and .15 m spectra (Figures 11.10 and 11.11). It remains to identify the source of the additional temperature variance in the 0.1-1 cpkm wavenuniber band. In this band, the temperature gradient spectrum has 95%-significant vertical coherence and is very nearly proportional to k1- (Figures 11.8 and 11.9). Charney (1971) predicted a k3 subrange in the potential energy spectrum above a baroclinic production range. If the potential energy spectrum has the same slope as the temperature spectrum in the 0.1-1 cpkm band, the observations will be consistent with this prediction, since the temperature spectrum (Figure 11.10) is proportional to times the temperature gradient spectrum. Charney (1971) discovered a formal analogy that holds under certain conditions between the spectral energy evolution equations associated with the two-dimensional Navier-Stokes equations and the quasigeostrophic potential 21
Page 1 and 2: AN ABSTRACT OF THE THESIS OF Roger
Page 3 and 4: Observations and Modelling of Front
Page 5 and 6: To my parents, Hans and Nancy Samel
Page 7 and 8: This research was supported by ONR
Page 9 and 10: TABLE OF CONTENTS I. INTRODUCTION 1
Page 11 and 12: Figure LIST OF FIGURES (continued)
Page 13 and 14: OBSERVATIONS AND MODELLING OF FRONT
Page 15 and 16: II. TOWED THERMISTOR CHAIN OBSERVAT
Page 17 and 18: oriented multiple surface fronts up
Page 19 and 20: gravity waves. A maximum of 21 and
Page 21 and 22: small, since the large-scale temper
Page 23 and 24: front at about 18.5 °C. There is f
Page 25 and 26: given in the stable cases (downward
Page 27 and 28: temperatures for January and Februa
Page 29 and 30: dominates the spectrum. At these wa
Page 31: typically iO-2iO3 °c m1-), and sin
Page 35 and 36: energy of each of the longitudinal
Page 37 and 38: varying N and a flow isolated from
Page 39 and 40: adiabatic meridional displacements
Page 41 and 42: z0 34 32 V v 30 a -J 28 26 a) - 2b$
Page 43 and 44: U0 V L 0 L V 20 E 16 V 12 p ; t *,
Page 45 and 46: 30 E 50 -c a- I, 0 70 90 300 360 37
Page 47 and 48: 10 10° 10-2 1 0 -3.0 -2.0 -1.0 0.0
Page 49 and 50: 1 o 1 102 101 - 0 LU 00 x I.- - -1
Page 51 and 52: E (I) a. z 106 1 o5 102 101 100 1O
Page 53 and 54: Table 11.1 Tow start and finish pos
Page 55 and 56: Table 11.3 Climatological sea surfa
Page 57 and 58: Paulson, C. A., R. J. Baumann, L. M
Page 59 and 60: 111.1 Introduction In this chapter
Page 61 and 62: interior layers, on the horizontal
Page 63 and 64: polynomials in z.) The vertical mom
Page 65 and 66: hit + (hivi) = We, (8a) h2t + (h2v2
Page 67 and 68: Equations (la) and (2a) are dynamic
Page 69 and 70: subdivided into subdomains with dif
Page 71 and 72: mixed layer. As is the case with (2
Page 73 and 74: constant pressure c = 4.1x103 J K1-
Page 75 and 76: When (28) have been solved for the
Page 77 and 78: occur with the initial conditions w
Page 79 and 80: analytically. Let Al2 and A23 be th
Page 81 and 82: Shortly after t = 8.1, the mixed la
Page 83 and 84:
that around the offshore front, exc
Page 85 and 86:
the reduced equations numerically.
Page 87 and 88:
(1) The upwelled horizontal profile
Page 89 and 90:
Figure 111.1 Model geometry. zO z z
Page 91 and 92:
* j 0. -20. >\ - -40. 0 > .0 0. 40.
Page 93 and 94:
4) 20. 10. 0. 20. 1 0. 0. 0 y/X 0.
Page 95 and 96:
BIBLIOGRAPHY Batchelor, G. K. , 195
Page 97 and 98:
Rhines, P. B., 1979: Geostrophic Tu
Page 99 and 100:
APPENDIX A: DYNAMICAL DERIVATION OF
Page 101 and 102:
In a manner exactly analogous to th
Page 103 and 104:
smoothness. The large vorticities t
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