The parametric instability of a plane internal gravity wave is considered. When the two-dimensional equations of vorticity and mass conservation are linearized in the disturbance quantities, partial differential equations with periodic coefficients result. Substitution of a perturbation of the form dictated by Floquet theory into these equations yields compatibility conditions which, when evaluated numerically, give the curves of neutral stability and constant disturbance growth rate. These results reveal that, for an internal wave of even infinitesimal amplitude, disturbance waves can begin to grow in amplitude. Moreover, these parametric instabilities are shown to reduce to the classical case of the nonlinear resonant interaction in the limit of vanishingly small basic-state amplitude. The fact that these unstable disturbances can exist for an internal wave of any amplitude suggests that this phenomenon may be an important mechanism for extracting energy from an internal gravity wave.

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We report observations of isolated lenses of constant-temperature water embedded in the permanent thermocline in the Sargasso Sea. These features are observed to have vertical extents of •<220 m, horizontal dimensions of •<65 km, and residence depths near 700 m. A dynamic model is constructed which permits a balance among the pressure gradient, Coriolis, and cyclostrophic forces and maintains the lens against gravitational collapse. A result is that anticyclonic rim velocities approaching 20 cm s -• are permitted and that these eddies have finite radii of the order of 50 km, at which their thicknesses fall to zero.

Meridional motion driven by kinematic viscosity v and thermal diffusivity k within a warm‐core ring is examined. An analytic quasi‐geostrophic model is constructed that shows that the vertical mixing of heat or momentum is ineffective in driving secondary motion. Single‐celled meridional flows will occur within the ring whenever the Prandtl number Pr = vh/κh is not equal to 1. When Pr is greater than 1, the flow is up in the ring core, while Pr less than 1 causes downward motion at ring center. A numerical primitive equation model leads to qualitatively identical results but shows that the secondary flow is not long‐lived when Pr is less than 1, decaying within 2 months, while in the Pr greater than 1 case the flows are still vigorous at the end of the experiment (90 days).

[1] We address the problem of obtaining ocean surface velocities from sequences of thermal (AVHRR) space-borne images by inverting the heat conservation equation (including sources of surface heat fluxes and vertical entrainment). We demonstrate the utility of the technique by deriving surface velocities from (1) The motion of a synthetic surface tracer in a numerical model and (2) a sequence of five actual AVHRR images from 1 day. Typical formulations of this tracer inversion problem yield too few equations at each pixel, which is often remedied by imposing additional constraints (e.g., horizontal divergence, vorticity, and energy). In contrast, we propose an alternate strategy to convert the underdetermined equation set to an overdetermined one. We divide the image scene into many subarrays and define velocities and sources within each subarray using bilinear expressions in terms of the corner points (called knots). In turn, all velocities and sources on the knots can be determined by seeking an optimum solution to these linear equations over the large scale, which we call the Global Optimal Solution (GOS). We test the accuracy of the GOS by contaminating the model output with up to 10% white noise but find that filtering the data with a Gaussian convolution filter yields velocities nearly indistinguishable from those without the added noise. We compare the GOS velocity fields with those from the numerical model and from the Maximum Cross Correlation (MCC) technique. A histogram of the difference between GOS and numerical model velocities is narrower and more peaked than the similar comparison with MCC, irrespective of the time interval (Dt = 2 or 4 h) between images. The calculation of the root mean square error difference between the GOS (and MCC) results and the model velocities indicates that the GOS/model error is only half that of the MCC/model error irrespective of the time interval (Dt = 2 or 4 h) between images. Finally, the application of the technique to a sequence of five NOAA AVHRR images yields a velocity field, which we compare with that from a Coastal Ocean Dynamics Radar (CODAR) array. We find that the GOS velocities generally agree more closely with those from the CODAR than they do with those from the MCC. Specifically, the root mean square error obtained by differencing GOS and CODAR velocities is smaller than that from the similar calculation with MCC velocities. The magnitude of the complex correlation between GOS and CODAR is larger than that between MCC and CODAR. The phase of the complex correlation indicates that both MCC and GOS on average yield velocity vectors biased in the clockwise direction relative to the CODAR vectors for the period examined.Citation: Chen, W., R. P. Mied, and C. Y. Shen (2008), Near-surface ocean velocity from infrared images: Global Optimal Solution to an inverse model,