Observations and Modelling of Fronts and Frontogenesis

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The energy input from wind stirring is taken as proportional to the cube of the friction velocity u*, with mo an empirical proportionality constant of order one. For simplicity, we neglect shear- driven deepening. Negative entrainment velocities and detrainnient are not allowed, so the expression for We we = max ( (2m0p0u*3 - gh1aQ/c)[g(p1 - p1)h1], 0 ). (5) Since water being entrained into the mixed layer from the interior must be accelerated to the velocity of the mixed layer, an entrainment stress 1e arises. This stress is the flux of momentum deficit into the mixed layer, Te p0(u1 uI)we. (6) In keeping with the assumption that geostrophic velocities are large relative to ageostrophic velocities, the ageostrophic momentum deficit flux is neglected. The small horizontal scales to be considered (see Section III.2c) justify the rigid lid approximation, so the layer depths satisfy, h1+h2+h3=H, (7) where H is the constant total fluid depth. Integration of the continuity equations (ld) and (2d), with the requirements that normal velocity be continuous at layer interfaces and vertical velocity vanish at the top and bottom boundaries, yields prognostic equations for the layer depths, 52
hit + (hivi) = We, (8a) h2t + (h2v2) We, (8b) h3t + (h3v3)y 0. (8c) If layer 2 vanishes in a region, so that layer 3 comes in contact with the mixed layer, the entrainment velocity must be subtracted from the layer 3 depth evolution equation. In this case the layer depth evolution equations are, hit + (hlvl)y We, (9a) h3t + (h3v3)y We. (9b) Note that the base of the mixed layer is not a material surface; fluid may pass (upward) through it. De Szoeke (1981) gives a careful discussion of the form of these equations. Addition of (8a-c) and integration from the coastal boundary, where normal velocities must vanish, yields the condition of no net offshore mass flux, h1v1 + h2v2 + h3v3 = 0. (10) This holds as well if h2 is equal to zero. When layer 3 is isolated from the mixed layer, potential vorticity in layer 3 is conserved following the motion, that is, where 3t + v3P3y = 0, (ila) P3 = (f u3y)/h3 (llb) is the potential vorticity in layer 3. This may be verified by direct differentiation and the use of (2a) and (8c). It 53
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
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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 and 32: 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: polynomials in z.) The vertical mom
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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