Julia C. Mullarney

Convection driven by differential heating at a horizontal boundary

We report laboratory and numerical experiments with the convective circulation that develops in a long channel driven by heating and cooling through opposite halves of the horizontal base. The problem is similar to that posed by Stommel ( Proc. Natl Acad. Sci . vol. 48, 1962, p. 766) and Rossby ( Deep-Sea Res. vol. 12, 1965, p. 9; Tellus vol. 50, 1998, p. 242), where flow forced by a linear temperature variation along the ocean surface or the base of a tank presented a demonstration of the smallness of sinking regions in the meridional overturning circulation of the oceans. In contrast to the previous experiments, we use small aspect ratio, larger Rayleigh numbers, piecewise uniform boundary conditions and an imposed input heat flux. The flow is characterized by a vigorous overturning circulation cell filling the box length and depth. A stable thermocline forms above the cooled base and is advected over the heated part of the base, where it is eroded from below by small-scale three-dimensional convection, forming a ‘convective mixed layer’. At the endwall, the convective mixing is overshadowed by a narrow but turbulent plume rising through the full depth of the box. The return flow along the top of the box is turbulent with large slowly migrating eddies, and occupies approximately a third of the total depth. Theoretical scaling laws give temperature differences, thermocline thickness and velocities that are in good agreement with the experimental data and two-dimensional numerical solutions. The measured and computed density structure is largely similar to the thermocline and abyssal stratification in the oceans.

A theoretical model for horizontal convection at high Rayleigh number

We present a simple flow model and solution to describe ‘horizontal convection’ driven by a gradient of temperature or heat flux along one horizontal boundary of a rectangular box. Following laboratory observations of the steady-state convection, the model is based on a localized vertical turbulent plume from a line or point source that is located anywhere within the area of the box and that maintains a stably stratified interior. In contrast to the ‘filling box’ process, the convective circulation involves vertical diffusion in the interior and a stabilizing buoyancy flux distributed over the horizontal boundary. The stabilizing flux forces the density distribution to reach a steady state. The model predictions compare well with previous laboratory data and numerical solutions. In the case of a point source for the plume (the case which best mimics the localized sinking in the large-scale ocean overturning) the thermal boundary layer is much thicker than that given by the two-dimensional boundary layer scaling of H. T. Rossby (T ellus, vol. 50, 1965, p. 242).

Resonant modulation of the flow in a tidal channel

[1] The coupling between a quarter-wave resonance in a coastal bay and a Helmholtz mode in an adjacent cove (connected to the bay through a narrow channel) is investigated by comparing field measurements to analytical and numerical model predictions. Pressure and velocity spectra from locations throughout the bay reveal an oscillation with a period of approximately 1 hour, consistent with a quarter-wave seiche mode. The associated sea surface displacements throughout the bay are small (less than 5 cm RMS, i.e., only 10% of the tidal elevation). Velocities within the channel are significantly modulated in the 1-hour band, with amplitudes up to 40% of the peak tidal current. The analytical model shows that the modulation of the channel flow results from the interaction between the quarter-wave mode in the main basin and a Helmholtz resonance in the cove, also with a period near 1 hour. The amplitude and phase of the 1-hour oscillation varies through the tidal cycle because of the change in Helmholtz frequency with tidal elevation. Good quantitative agreement between the data and the model predictions is obtained if a drag coefficient approximately 3-4 times larger than the classical value of 3 x 10 -3 is used in the channel and cove.

Gravity currents from a dam-break in a rotating channel

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