Numerical Study Of Double-Diffusive Convection Driven By Horizontal Thermohaline Gradients

Thermohaline intrusion is very likely to occur in the earth's oceans when temperature and salinity are both gradient distributed.This kind of phenomena are ubiquitous in the ocean,and have an important impact on the horizontal transport of heat and salinity in the ocean.One of the important mechanism of thermohaline intrusion is the double-diffusion convection process,which is a special kind of buoyancy driven flow,due to the distinct molecular diffusion rates of temperature and salinity.In this paper,we studied the phenomenon of thermohaline intrusion driven by horizontal temperature and salinity gradient,especially the effect of double diffusion mechanism.The paper focus on the typical flow structure and how heat and salinity's horizontal transport vary with the flow control parameters.The model used in this paper is the flow of the fluid between two vertical and parallel plates in the gravitational field.The velocity on the plate satisfies the nonslip boundary condition,and the temperature and salinity remain constant,so there are given temperature and salinity differences between the two plates.Periodic boundary conditions are used in parallel plate direction,and the gravity direction is parallel to the plate.Since the physical parameters of the fluid are consistent with oceanic water,the flow control parameters only include the dimensionless salinity difference,defined by the salinity Rayleigh number RaS,and the density ratio ?,which describes the relative intensity of the temperature difference,defined by the ratio of the density difference caused by temperature difference to part caused by the salinity difference.Firstly,the linear stability analysis is carried out based on the derived linear stability equation of the model.Set the density ratio ? = 1,the salinity Prandtl number PrS= 700,and analyze the effects of the critical salinity Rayleigh number and vertical wave number.The analysis shows that critical salinity Rayleigh number and the critical vertical wave number increase with the increase of the spanwise wave number.The range of instable wave number in both spanwise and vertical directions increases with the increase of salinity Rayleigh number.The analysis on the influence of salinity Prandtl number in stability shows that the critical salinity Rayleigh number decreases with the increase of salinity Prandtl number,while the critical vertical wave number mostly remains unchanged.The critical salinity Rayleigh number is calculated for different salinity Prandtl number.Calculations of the two-dimensional flow fields with different Rayleigh number and salinity Prandtl number shows there are two different kinds of flow patterns.Secondly,two-dimensional direct numerical simulation was carried out for the doublediffusion convection model in this paper to systematically study the flow field morphology and horizontal transport characteristics of temperature and salt under the conditions of different salinity and temperature Rayleigh number and salinity Prandtl number when density ratio was equal to 1.And the flow characteristics were explored when density ratio was not equal to1.When the density ratio is equal to 1,there are three different kinds modes of time evolution:the stable mode accompanied by oscillation with rapid decay,the periodic mode accompanied by the rapid oscillation,and the instantaneous growth mode.At the same time,there are also two different forms in spatial structure: the stratified flow state with obvious salinity stratification and the shear flow state with uniform salinity distribution.Compared and analyzed profile of the salinity,temperature and velocity distribution in flow field when the density ratio is equal to 1,found that when the salinity gradient intensity is larger,salinity diffusion rate does not affect salinity distribution,and when salinity diffusion rate is a given value,salinity boundary is tend to be thinner when temperature and salinity gradient intensity is smaller.Temperature diffusion is inhibited when salinity diffusion rate is relatively large.And the intensity of salinity gradient does not affect the temperature distribution when the salinity diffusivity is set to be a given value.When the density ratio is not equal to 1,unstable flows can be developed only when the density ratio is in a very narrow small range near 1.The flow field with density ratio equal to 1 was statistically analyzed,and the horizontal temperature and salinity transfer efficiency in the flow field were characterized by temperature and salinity Nussel number.The power-law relationship between horizontal salinity transfer efficiency and flow control parameters,salinity Prandtl number,temperature and salinity Rayleigh number was preliminarily found.Reducing temperature and salinity gradient,or increasing salinity diffusivity are beneficial to promoting salinity mixing.At higher salinity transport intensity,the velocity along the thermohaline gradient is unexpectedly smaller.