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J. C. McWilliams and P. R. Gent

Abstract

Several sets of model equations are presented which represent coupled processes in the tropical atmosphere and ocean. The distribution of ocean surface temperature generates large-scale convective motions in the atmosphere. These winds in turn drive ocean currents which advect ocean temperatures. Under most parametric circumstances, the model solutions have the character of moderately damped oscillations of several year period. This period is characteristic of either ocean particle advection across the zonal extent of the basin or potential energy release associated with the ocean temperature distribution. Less stable model solutions can also occur—limit cycle oscillations, alternative mean climatic balances for fixed parameters—but these are not typical of the parameters selected for application to the tropical Pacific. Simulations of possible El Niño sequences are discussed; in general the responses seem weaker than observed.

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Sue Ellen Haupt, James C. McWilliams, and Joseph J. Tribbia

Abstract

Modons in shear flow are computed as equilibrium solutions of the equivalent barotropic vorticity equation using a numerical Newton–Kantorovich iterative technique with double Fourier spectral expansion. The model is given a first guess of an exact prototype modon with a small shear flow imposed, then iterated to an equilibrium solution. Continuation (small-step extrapolation of the shear amplitude) is used to produce examples of modons embedded in moderate amplitude background shear flows. It is found that in the presence of symmetric shear, the modon is strengthened relative to the prototype. The best-fit phase speed for this case is significantly greater than the Doppler-shifted speed. Nonsymmetric shear strengthens the poles selectively: positive shear strengthens the low while weakening the high. The diagnosed functional relationship between the streamfunction in the traveling reference frame and the vorticity appears linear for all types of shear studied. The modons in symmetric shear are stable within time integrations, at least for small to moderate shear amplitude. Antisymmetric shear appears to trigger a tilting instability of the stationary state; yet coherence of the modon is maintained. This study strengthens the plausibility of using modons as a model of coherent structures in geophysical flow.

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C-H. Moeng, J. C. McWilliams, R. Rotunno, P. P. Sullivan, and J. Weil

Abstract

The performance of a two-dimensional (2D) numerical model in representing three-dimensional (3D) planetary boundary layer (PBL) convection is investigated by comparing the 2D model solution to that of a 3D large- eddy simulation. The free convective PBL has no external forcing that would lead to any realizable 2D motion, and hence the 2D model represents a parameterization (not a simulation) of such a convective system. The present solutions show that the fluxes of conserved scalars, such as the potential temperature, are somewhat constrained and hence are not very sensitive to the model dimensionality. Turbulent kinetic energy (TKE), surface friction velocity, and velocity variances are sensitive to the subgrid-scale eddy viscosity and thermal diffusivity in the 2D model; these statistics result mostly from model-generated hypothetical 2D plumes that can be tuned to behave similarly to their 3D counterparts. These 2D plumes are comparable in scale with the PBL height due to the capping inversion. In the presence of shear, orienting the 2D model perpendicular to the mean shear is essential to generate a reasonable momentum flux profile, and hence mean wind profile and wind- related statistics such as the TKE and velocity variances.

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Peter P. Sullivan, James C. McWilliams, Jeffrey C. Weil, Edward G. Patton, and Harindra J. S. Fernando

Abstract

Turbulent flow in a weakly convective marine atmospheric boundary layer (MABL) driven by geostrophic winds U g = 10 m s−1 and heterogeneous sea surface temperature (SST) is examined using fine-mesh large-eddy simulation (LES). The imposed SST heterogeneity is a single-sided warm or cold front with temperature jumps Δθ = (2, −1.5) K varying over a horizontal distance between [0.1, −6] km characteristic of an upper-ocean mesoscale or submesoscale regime. A Fourier-fringe technique is implemented in the LES to overcome the assumptions of horizontally homogeneous periodic flow. Grid meshes of 2.2 × 109 points with fine-resolution (horizontal, vertical) spacing (δx = δy, δz) = (4.4, 2) m are used. Geostrophic winds blowing across SST isotherms generate secondary circulations that vary with the sign of the front. Warm fronts feature overshoots in the temperature field, nonlinear temperature and momentum fluxes, a local maximum in the vertical velocity variance, and an extended spatial evolution of the boundary layer with increasing distance from the SST front. Cold fronts collapse the incoming turbulence but leave behind residual motions above the boundary layer. In the case of a warm front, the internal boundary layer grows with downstream distance conveying the surface changes aloft and downwind. SST fronts modify entrainment fluxes and generate persistent horizontal advection at large distances from the front.

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