Observations and Modelling of Fronts and Frontogenesis

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y 51/2 and io1/2, respectively. The distance between the two fronts is roughly l.5Al2 or 3X23 in each case. Upper layer characteristics for Case 1 are displayed in Figure III.5a. The fronts move along these characteristics with very little change in form. The velocity v1(y,t) is just the inverse slope of the characteristics in Figure III.5a. The increase in offshore velocity near the coast associated with the upwelling event at t 8.1 is visible as a decrease in slope of the characteristics. As the front propagates offshore, the spreading of characteristics on its inshore side illustrates the divergence in the mixed layer. The characteristics may be interpreted as the y-components of particle paths. The x-components must be obtained by time- integrating the geostrophic velocities. The characteristics in layer 2 are shown in Fig III.5b. They bend slightly as the front passes over them and the local divergence momentarily alters the layer 2 velocity near the front. They are drawn toward y with increasing rapidity as they approach The characteristics in layer 3 are shown in Figure III.5c. They show a nearly uniform convergence toward the coastal boundary. 111.4 Summary We have formulated analytically a semigeostrophic model for thermocline upwelling at a coastal boundary and solved 72
the reduced equations numerically. The model combines a two-layer stratified interior with a mixed layer capable of handling strong horizontal gradients. This combination allows the modelling of the process of upwelling and entrainment into the surface layer of deep, dense interior fluid that is initially isolated from the surface layer by an intermediate layer of less-dense fluid. We employ two principal analytical simplifications: all flow variables are uniform in the alongshore direction, and semigeostrophic dynamics apply. Though these are idealizations, the equations retain the essential dynamics of wind-driven upwelling. The reduction to one horizontal dimension allows the efficient resolution of a wide range of scales (100 m - 25 km) that are crucial to the proper understanding of upwelling dynamics. The semigeostrophic approximation filters out inertio-gravity waves. The resulting equations are numerically stable with no lateral friction, so that the horizontal scales result solely from the dynamics of the model. We solve the reduced equations numerically. The flow is driven by an alongshore wind stress and surface heating. A modified Ekman balance forces surface layer fluid offshore, causing a surface divergence and upwelling of isopycnals near the coastal boundary. The horizontal scale of this 73
Page 1 and 2:
AN ABSTRACT OF THE THESIS OF Roger
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Observations and Modelling of Front
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To my parents, Hans and Nancy Samel
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This research was supported by ONR
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TABLE OF CONTENTS I. INTRODUCTION 1
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Figure LIST OF FIGURES (continued)
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OBSERVATIONS AND MODELLING OF FRONT
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II. TOWED THERMISTOR CHAIN OBSERVAT
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oriented multiple surface fronts up
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gravity waves. A maximum of 21 and
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small, since the large-scale temper
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front at about 18.5 °C. There is f
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given in the stable cases (downward
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temperatures for January and Februa
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dominates the spectrum. At these wa
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typically iO-2iO3 °c m1-), and sin
Page 33 and 34: 11.5 Geostrophic turbulence We have
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: that around the offshore front, exc
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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