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LAWRENCE A. HUGHES

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LAWRENCE A. HUGHES

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A. Lawrence Rotch

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Lawrence A. Hughes

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A. Lawrence Rotch

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Lawrence A. Mysax

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A theory of barotropic, nondivergent, zonally propagating waves on an equatorial beta-plant with topography is presented. The bottom contours are assumed to be parallel to the equator, so that the depth profile H is a function only of y, the northward coordinate. Solutions for trapped waves are derived for the following depth profiles: 1) a single-step escarpment, 2) a flat continental shelf, 3) a semi-infinite sloping beach. and 4) an exponentially varying continental shelf/slope region that monotonically increases to a constant depth far from the shoreline. For each wave solution presented. numerical examples of typical periods and phase speeds are also given. The eigenfrequencies ωn for the waves trapped on a sloping beach with depth profile H=H 0y take a particularly simple form: ωn=−βH 0/|α|(2n+3), where n=0,1,2,..., and β=2ΩE/RE and R are the earth's angular speed of rotation and radius, respectively). A number of qualitative results are also derived. For example, a WKB-type argument is used to show that equatorial trapping will always occur over any monotonic depth profile that straddles the equator. Also, it is proved that the phase of an equatorial topographic wave propagates westward or eastward according to whether the equilibrium potential vorticity βy/H(y) is a monotonic increasing or decreasing function of y.

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Lawrence A. Mysak

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The theory of barotropic nondivergent waves trapped on an exponential shelf lying on an equatorial β-plane is presented. The bottom contours are parallel to the equator so that phase propagation is either eastward or westward. according to the following general rule: when the shelf region is entirely in the Northern (Southern) Hemisphere the shallow water is to the right (left) of the direction of the phase velocity. When both the shelf and deep sea regions are located in the same hemisphere (case 1), the results concerning the dispersion curves and eigenfunctions are qualitatively similar to those obtained by Buch-wald and Adams (1968) for shelf waves on a mid-latitude exponential shelf on an f-plane. However, when the shelf region is on one side of the equator and the deep sea region extends across the equator (case 2), the dispersion curves and eigenfunctions are quite different. In case 2 the dispersion curve for each trapped mode has a long-wave cutoff. However, the cutoff for each mode generally does not preclude the existence of a zero group velocity at an intermediate wavelength. a phenomenon which always occurs in case 1. In case 2 the range of oscillation for each eigenfunction is generally much larger than that of the corresponding eigenfunction in case 1. Finally, when the shelf region straddles the equator (case 3), both westward and eastward propagating modes may exist. Further, one set of these modes has a long-wave cutoff (e.g., if the coast is in the Southern Hemisphere with deep water to the north, the westward propagating modes have a long-wave cutoff). In case 3 the oscillations of each eigenfunction tend to be concentrated near the shelf edge.

The theory is applied to the Gulf of Guinea. where a 0.07 cycle per day (cpd) oscillation in the sea surface temperature has been observed to propagate westward along the Ghaina-lyory coast. It is shown that this signal may be due to the presence of a fundamental mode shelf wave of the type discussed in this paper.

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Lawrence A. Hughes

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Data from a number of reconnaissance flights into large Pacific tropical cyclones are combined to obtain a generalized pattern of winds at low level (about 1000 feet) under both stationary and non-stationary conditions. With these winds, a number of dependent computations are made including relative trajectories, divergence, vertical motion, rainfall, energy, and relative vorticity.

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Lawrence A. Hughes

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Lawrence A. Mysak

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A new mechanism is proposed for the generation of the annual-period baroclinic Rossby waves which have been observed in the central North Pacific by Kang and Magaard. It is shown that annual north-south fluctuations in the eastern boundary current off Vancouver Island can efficiently generate first baroclinic mode Rossby waves throughout the central North Pacific. In particular, to the southwest of Vancouver Island the direction, wavelength and speed of phase propagation associated with the far field (asymptotic) wave solution agree favorably with observations. Also, along and fixed latitude contained within the observed latitude band (30–40°N), the amplitudes of the vertical displacement at 300 m and surface horizontal current speed both monotonically increase to the west, in agreement with the observed trends for these quantities. However, the existence of this monotonicity in the solution appears to be quite sensitive to the north-south spatial structure of the fluctuating coastal current. For example, the oscillations of a point source (delta function) current excite a wave field with a fairly uniform amplitude across most of the observation region.

Within the context of a reduced gravity, quasi-geostrophic model, the theory presented here is quite general. For example, baroclinic waves of other than annual period could be investigated, and the radiation pattern due to a number of coastal sources could be determined.

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