A Numerical Model of Convection Driven by a Surface Stress and Non-Uniform Horizontal Heating

Beardsley, Robert C.; Festa, John F.

doi:10.1175/1520-0485(1972)002<0444:anmocd>2.0.co;2

Cited by 44 publications

(48 citation statements)

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“…As in Beardsley and Festa (1972), the power law that relates /max to Ra converges slowly to the desired value which for our case is 1/6 and not 1/5. The transition from proportionality (for very small Rayleigh The description above is examined in the next section where we show that to a large extent, wT, = T is a very good approximation to (5.2b) over most of the domain, with the exception of the northern jet where the Ty, term is important.…”

Section: No Mixingmentioning

confidence: 62%

“…It now seems reasonable that the motion will be in the boundary layers surrounding the cell. The previous arguments in this section neglect a fundamental difference between our system and that of Roberts-and for that matter other works like Beardsley and Festa (1972), and Sommerville (1967). In those works the surface temperature is specified, so the l.h.s.…”

Section: No Mixingmentioning

confidence: 96%

“…Still, for free slip conditions, Stommel's (1962) treatment hints that maybe the nonlinearity in the density equation is enough, since his pipe solution is highly asymmetric, but his 'momentum' relation is linear. Also, Beardsley and Festa (1972) conclude that the advection of vorticity by the flow field is only about 5% of the other terms for their numerical experiments with a Rayleigh number of order 10'.…”

Section: Introductionmentioning

confidence: 92%

“…Other works followed, like that of Beardsley and Festa (1972), who applied a linear temperature along the bottom of an otherwise rigid and insulating rectangular box filled with fluid. The authors used the same dynamical system as Sommerville, with the addition of horizontal diffusion for both the temperature and vorticity equations, and investigated the various parameters associated with the solution of the coupled set.…”

Section: Thesis Supervisormentioning

confidence: 99%

“…The aspect ratio A is equal to one throughout this chapter. The same value was also used in other works, like Beardsley and Festa (1972). It is usually absorbed in the Rayleigh number, and its only influence will be through the operator on the right hand side of (5.2a), having small effects on the flow field.…”

Section: Forcingmentioning

confidence: 99%

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Thermally driven circulation

Nelken¹

1987

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Several problems connected by the theme of thermal forcing are addressed herein. The main topic is the stratification and flow field resulting from imposing a specified heat flux on a fluid that is otherwise confined to a rigid insulating basin. In addition to the traditional eddy viscosity and diffusivity, turbulent processes are also included by a convective overturning adjustment at locations where the local density field is unstable.Two classes of problems are treated. The first is the large scale meridional pattern of a fluid in an annulus. The detailed treatment is carried out in two steps. In the beginning (chapter 2) it is assumed that the fluid is very diffusive, hence, to first approximation no flow field is present. It is found that the convective overturning adjustment changes the character of the stratification in all the regions that are cooled from the top, resulting in a temperature field that is nearly depth independent in the northernmost latitudes. The response to a seasonal cycle in the forcing, and the differences between averaging the results from the end of each season compared to driving the fluid by a mean forcing are analyzed. In particular, the resulting sea surface temperature is warmer in the former procedure. This observation is important in models where the heat flux is sensitive to the gradient of air to sea surface temperatures.The analysis of the problem continues in chapter 5 where the contribution of the flow field is included in the same configuration. The dimensionless parameter controlling the circulation is now the Rayleigh number, which is a measure of the relative importance of gravitational and viscous forces. The effects of the convective overturning adjustment is investigated at different Rayleigh numbers. It is shown that not only is the stratification now always stable, but also that the vigorous vertical mixing reduces the effective Rayleigh number; thereby the flow field is more moderate, the thermocline deepens, and the horizontal surface temperature gradients are weaker. The interior of the fluid is colder compared to cases without convective overturning, and, because the amount of heat in the system is assumed to be fixed, the surface temperature is warmer.The fluid is not only forced by a mean heat flux, or a seasonally varying one, but its behavior under permanent winter and summer conditions is also investigated. A steady state for the experiments where the net heat flux does not vanish is defined as that state where the flow field and temperature structure are not changing with time except for an almost uniform temperature decrease or increase everywhere. It is found that when winter conditions prevail the circulation is very strong, while it is rather weak for continuous summer forcing. In contrast to those results, if a yearly cycle is imposed, the circulation tends to reach a minimum in the winter time and a maximum in the summer. This suggests that, depending on the Rayleigh number, there is a phase leg of several months between the response of ...

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Section: No Mixingmentioning

confidence: 62%

Section: No Mixingmentioning

confidence: 96%