Observations and Modelling of Fronts and Frontogenesis

More documents

Recommendations

Info

continuously stratified case (with distributions of stress divergence and heating constrained to match those of the original layer 1), the equations analogous to (1) and (3) Ut + vuy + wu - fv (rX(z) 7e(Z))/hl, (Al) fu Py/PO' (A2) Pz -gp, (A3) vy+wzO (A4) Pt + VPy + WPz [-aQ(z)/c + (i Pl)e(z)]/hl. (A5) Here u, v, w, p, and p are functions of y, z, and t. The advective terms wu and WPz must be retained because of the vertical dependence of u and p. Layer 3 still obeys the equations (2) with i 3. For reference, we note the identities, (B)y (y)B zBhy (B)t (t)B zB't (A6) where is any dependent variable in the composite layer, h = h1 + h2 is the depth of the composite layer, and subscript B means evaluation at z = -h(y,t), the base of the composite layer. gives, Integrating the hydrostatic equation (2c) vertically P3 PB - gp3(z + h). (A7) Then the use of (20) yields the thermal wind relation, POf(UB - u3) = [(Py)B P3yI - B(P3 PBThy (A8) 87
In a manner exactly analogous to that leading to (16), making careful use of (A6), an equation for the ageostrophic velocities may be obtained: g(pofY1(p3 pB)[(h3v3) vBh3TjI + (f u3y)(vB - v3) g(p0f)[(p3 PB) We] y This may be rewritten as re(z) [ Q + (PB p)w(z)Jy) g(pf)((p3 PB)(h3v3)yy + [(P3 PB)e]y g(pfY1-(p3 pB)vBh3 (f U3y)(V - v3) - (poh1)(rX(z) Te(z) (A9) [- Q + (PB - p)w(z)]y). (AlO) Then (AlO) may be integrated across the interval (y2 6'Y2 + 6), in which the transition layer between the two homogeneous parts of the composite layer meet the surface of layer 3, and the width 26 of this region allowed to approach zero. If we assume that h3 is twice differentiable at y2(t), none of the terms on the right hand side of (AlO) will be singular in the limit as 5 0, so their integral across this region will vanish in that limit. Since layer 1 consists primarily of fluid that has been entrained from layer 2, the variation in PB is very small. If it is neglected altogether, the left hand side of (AlO) may be integrated exactly across the transition region. The result is (23c).
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 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 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: APPENDIX A: DYNAMICAL DERIVATION OF
Page 103 and 104: smoothness. The large vorticities t
show all

Observations and Modelling of Fronts and Frontogenesis

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?