The Entrainment Rate for Buoyant Plumes in a Crossflow

We consider large-eddy simulations (LES) of buoyant plumes from a circular source with initial buoyancy flux F ₀ released into a stratified environment with constant buoyancy frequency N and a uniform crossflow with velocity U. We make a systematic comparison of the LES results with the mathematical theory of plumes in a crossflow. We pay particular attention to the limits [(U)\tilde] << 1{\tilde{U}\ll1} and [(U)\tilde] >> 1{\tilde{U}\gg 1}, where [(U)\tilde]=U/(F₀ N)^1/4{\tilde{U}=U/(F_0 N)^{1/4}}, for which analytical results are possible. For [(U)\tilde] >> 1{\tilde{U}\gg 1}, the LES results show good agreement with the well-known two-thirds law for the rise in height of the plume. Sufficiently far above the source, the centreline vertical velocity of the LES plumes is consistent with the analytical z ^−1/3 and z ^−1/2 scalings for respectively [(U)\tilde] << 1{\tilde{U}\ll 1} and [(U)\tilde] >> 1{\tilde{U}\gg 1}. In the general case, where the entrainment is assumed to be the sum of the contributions from the horizontal and vertical velocity components, we find that the discrepancy between the LES data and numerical solutions of the plume equations is largest for [(U)\tilde]=O(1){\tilde{U}=O(1)}. We propose a modified additive entrainment assumption in which the contributions from the horizontal and vertical velocity components are not equally weighted. We test this against observations of the plume generated by the Buncefield fire in the U.K. in December 2005 and find that the results compare favourably. We also show that the oscillations of the plume as it settles down to its final rise height may be attenuated by the radiation of gravity waves. For [(U)\tilde] << 1{\tilde{U}\ll 1} the oscillations decay rapidly due to the transport of energy away from the plume by gravity waves. For ${\tilde{U}>rsim 1}${\tilde{U}>rsim 1} the gravity waves travel in the same direction and at the same speed as the flow. In this case, the oscillations of the plume do not decay greatly by radiation of gravity waves.     

Penetrative convection in rapidly rotating flows: preliminary results from numerical simulation

Turbulent convection forced by a surface heat flux into a stably stratified region is a feature of both the atmospheric and oceanic planetary boundary layers. Of particular interest is the interface between the convective layer and the stable stratification, where the entrainment of fluid into the convective layer by penetrating plumes may lead to a reverse buoyancy flux, and an enhancement of the stable stratification. Whereas in the atmosphere the influence of rotation on this penetrative convection is negligible, oceanic convection may be subjected to lower Rossby numbers and hence greater rotational influence. To isolate the effects of rotation, we present three numerical solutions for turbulent penetrative convection, characterised by different rotation rates, with all other parameters being held constant. Our results indicate that at lower Rossby numbers the lateral scale of the plumes is reduced, whereas the vertical vorticity of the plumes is much enhanced. Vertical transports of buoyancy and kinetic energy across the convective layer are reduced, leading to less efficient penetration at the interface with the stratified layer, and hence less reverse buoyancy flux in this region.     

The role of molecular diffusion in the deepening of the mixed layer

Turbulent mixing across heat-stratified density interfaces was studied in the laboratory using oscillating-grid generated turbulence. The aim was to study the transition between the entrainment regimes dominated by interfacial wave-breaking and molecular diffusion, and to study the characteristics of the latter. It was observed that, above a critical Richardson number Ri_c, which depends on the Peclet number Pe, the mixing due to wave breaking disappears and that Ri_c Pe⁻ⁿ, where the mean value of the exponent n is approximately . Above Ri_c, the entrainment is molecular-diffusion dominated and takes place through a sequence of events: the buoyancy gradient of the initially sharp density interface is weakened by molecular diffusion until the mixed-layer eddies can engulf a portion of the interfacial layer wherefore the interface sharpens again. Thus, the entrainment events are recurrent with a rate-controlling diffusion stage between them. An entrainment law of the form E Ri⁻²Pe⁻², where E is the entrainment coefficient and Ri is the Richardson number, is suggested for the diffusion-dominated entrainment regime.     

Experiments on steady buoyancy transfer through turbulent fluid layers separated by density interfaces

A laboratory experiment was performed to investigate mixing across a density interface which separates two turbulent fluid layers and coexists with a stabilizing buoyancy flux. It was found that the buoyancy flux (q₀) across the interface and through the turbulent layers (of depth D) becomes steady and constant in magnitude in the vertical direction, only when , where u is the horizontal r.m.s. velocity at the base of the mixed layers. The results suggest that mixing across the density interface is controlled by a dynamically important buoyancy gradient induced in the turbulent layers and that parameters such as the bulk Richardson number, , where Δb is the interfacial buoyancy jump, are of secondary importance. Measurements are used to infer the mixing mechanism at the interface, the mixing efficiency of stratified fluids and the entrainment law. Some geophysical applications of the results are also discussed.     

Instabilities of the tidally induced bottom boundary layer in the rotating frame and their mixing effect

To investigate the stability of the bottom boundary layer induced by tidal flow (oscillating flow) in a rotating frame, numerical experiments have been carried out with a two-dimensional non-hydrostatic model. Under homogeneous conditions three types of instability are found depending on the temporal Rossby number Ro_t, the ratio of the inertial and tidal periods. When Ro_t < 0.9 (subinertial range), the Ekman type I instability occurs because the effect of rotation is dominant though the flow becomes more stable than the steady Ekman flow with increasing Ro_t. When Ro_t > 1.1 (superinertial range), the Stokes layer instability is excited as in the absence of rotation. When 0.9 < Ro_t < 1.1 (near-inertial range), the Ekman type I or type II instability appears as in the steady Ekman layer. Being much thickened (100 m), the boundary layer becomes unstable even if tidal flow is weak (5 cm/s). The large vertical scale enhances the contribution of the Coriolis effect to destabilization, so that the type II instability tends to appear when Ro_t > 1.0. However, when Ro_t < 1.0, the type I instability rather than the type II instability appears because the downward phase change of tidal flow acts to suppress the latter. To evaluate the mixing effect of these instabilities, some experiments have been executed under a weak stratification peculiar to polar oceans (the buoyancy frequency N²  10⁻⁶ s⁻²). Strong mixing occurs in the subinertial and near-inertial ranges such that tracer is well mixed in the boundary layer and an apparent diffusivity there is evaluated at 150–300 cm²/s. This suggests that effective mixing due to these instabilities may play an important role in determining the properties of dense shelf water in the polar regions.     

The temporal evolution of a geostrophic flow in a rotating stratified basin

A laboratory study in a rotating stratified basin examines the instability and long time evolution of the geostrophic double gyre introduced by the baroclinic adjustment to an initial basin-scale step height discontinuity in the density interface of a two-layer fluid. The dimensionless parameters that are important in determining the observed response are the Burger number S=R/R₀ (where R is the baroclinic Rossby radius of deformation and R₀ is the basin radius) and the initial forcing amplitude (H₁ is the upper layer depth). Experimental observations and a numerical approach, using contour dynamics, are used to identify the mechanisms that result in the dominance of nonlinear behaviour in the long time evolution, τ>2⁻¹ (where τ is time scaled by the inertial period T_I=2π/f). When the influence of rotation is moderate (0.25≤S≤1), the instability mechanism is associated with the finite amplitude potential vorticity (PV) perturbation introduced when the double gyre is established. On the other hand, when the influence of rotation is strong (S≤0.1), baroclinic instability contributes to the nonlinear behaviour. Regardless of the mechanism, nonlinearity acts to transfer energy from the geostrophic double gyre to smaller scales associated with an eddy field. In the lower layer, Ekman damping is pronounced, resulting in the dissipation of the eddy field after only 40T_I. In the upper layer, where dissipative effects are weak, the eddy field evolves until it reaches a symmetric distribution of potential vorticity within the domain consisting of cyclonic and anticyclonic eddy pairs, after approximately 100T_I. The functional dependence of the characteristic eddy lengthscale L_E on S is consistent with previous laboratory studies on continuously forced geostrophic turbulence. The cyclonic and anticyclonic eddy pairs are maintained until viscous effects eventually dissipate all motion in the upper layer after approximately 800T_I. The outcomes of this study are considered in terms of their contribution to the understanding of the energy pathways and transport processes associated with basin-scale motions in large stratified lakes.     

The lower symmetric regime and its transition to waves in rotating annulus convection

Measurements of the temperature and zonal velocity fields which develop in a rotating annulus of fluid with an upper surface, differentially heated from the inner to outer cylinder, are described for the lower symmetric regime (small radial temperature differences). The temperature field is essentially conductive for moderate to large rotation rates, Ω (>1.0 sec⁻¹). The zonal velocity field is poorly approximated by the thermal wind equation.Measurements of the transition to waves from the lower symmetric regime at very large rotation rates are presented for positive and negative radial temperature differences. They suggest that the centrifugal buoyancy force and the free surface curvature may be important factors for the lower symmetric-wave transition at large Ω. By varying the stratification of the fluid over a range of 10³ independently of the radial temperature difference, Δr_wT, it is conclusively shown that several theories are correct in predicting that the lower symmetric transition is independent of the stratification at small Δr_wT > 0 for large enough Ω.     

On gradient transport turbulence models for stably stratified shear flow

The gradient transport model for stably stratified horizontal shear flow in which eddy diffusivity and viscosity are assumed to depend on the gradient Richardson number, Ri, is augmented with terms representing a finite adjustment time of the exchange coefficients. Barenblatt et al. (J. Fluid Mech., 253: 341–358, 1993) showed that using such a model, initial value problems for the formation of a stepwise structure of the buoyancy distribution are well posed. The model proposed is analysed taking into account the interaction between buoyancy and velocity fields. A condition for the formation of steps is derived from a linear stability analysis. Numerical computations show that a realistic stepwise finestructure develops, provided linear instability is allowed on a finite interval of Ri only.     

A one-dimensional model for the parameterization of deep convection in the ocean

A one-dimensional penetrative plume model has been constructed to parameterize the process of deep convection in ocean general circulation models (OGCMs). This research is motivated by the need for OGCMs to better model the production of deep and intermediate water masses. The parameterization scheme takes the temperature and salinity profiles of OGCM grid boxes and simulates the subgrid-scale effects of convection using a one-dimensional parcel model. The model moves water parcels from the surface layer down to their level of neutral buoyancy, simulating the effect of convective plumes. While in transit, the plumes exchange water with the surrounding environment; however, the bulk of the plume water mass is deposited at e level of neutral buoyancy. Weak upwelling around the plumes is included to maintain an overall mass balance. The process continues until the negative buoyant energy of the one-dimensional vertical column is minimized. The parameterized plume entrainment rate, which plays a central role in the parameterization, is calculated using modified equations based on the physics of entraining buoyant plumes. This scheme differs from the convective adjustment techniques currently used in OGCMs, because the parcels penetrate downward with the appropriate degree of mixing until they reach their level of neutral stability.     

The limitations on stress parameterization imposed by intermittency in turbulent flow

The indirect dissipation technique is used to estimate 1-min averages of friction velocity u _*in the surface layer over the tropical ocean. These estimates are compared to estimates of u _*obtained using a drag coefficient and the relative difference between the two is examined in relation to stability and averaging time. Plumes and downdrafts are found to be responsible for an anomalous behavior of the drag coefficient estimates. Certain factors relating to plume properties, derived using conditional sampling as described in Khalsa (1980), are shown to be related to the variance between the two estimates of friction velocity. An investigation into the effects of increasing the averaging time reveals that plume spacing, which is dependent on stability, and the mean wind speed determine the minimum time for smoothing the influence of plumes and downdrafts.Department of Atmospheric Sciences contribution number 513.     

Wind-tunnel Modelling of Dispersion from a Scalar Area Source in Urban-Like Roughness

A wind-tunnel study was conducted to investigate ventilation of scalars from urban-like geometries at neighbourhood scale by exploring two different geometries a uniform height roughness and a non-uniform height roughness, both with an equal plan and frontal density of λ _p = λ _f = 25%. In both configurations a sub-unit of the idealized urban surface was coated with a thin layer of naphthalene to represent area sources. The naphthalene sublimation method was used to measure directly total area-averaged transport of scalars out of the complex geometries. At the same time, naphthalene vapour concentrations controlled by the turbulent fluxes were detected using a fast Flame Ionisation Detection (FID) technique. This paper describes the novel use of a naphthalene coated surface as an area source in dispersion studies. Particular emphasis was also given to testing whether the concentration measurements were independent of Reynolds number. For low wind speeds, transfer from the naphthalene surface is determined by a combination of forced and natural convection. Compared with a propane point source release, a 25% higher free stream velocity was needed for the naphthalene area source to yield Reynolds-number-independent concentration fields. Ventilation transfer coefficients w _T /U derived from the naphthalene sublimation method showed that, whilst there was enhanced vertical momentum exchange due to obstacle height variability, advection was reduced and dispersion from the source area was not enhanced. Thus, the height variability of a canopy is an important parameter when generalising urban dispersion. Fine resolution concentration measurements in the canopy showed the effect of height variability on dispersion at street scale. Rapid vertical transport in the wake of individual high-rise obstacles was found to generate elevated point-like sources. A Gaussian plume model was used to analyse differences in the downstream plumes. Intensified lateral and vertical plume spread and plume dilution with height was found for the non-uniform height roughness.     

On the effects of rotation on fluid motions in cylindrical containers of various shapes and topological characteristics

Previous theoretical and laboratory studies of mechanically driven fluids in general rotation relative to an inertial frame have shown that there is a special class of flows for which the (Eulerian) flow field u(r, t) relative to the rotating frame of reference is unaffected by gyroscopic (Coriolis) forces, and therefore remains the same for all values of the rotation vector Ω. (Here t denotes time and r the position of a general point R in a reference frame attached to the rotating apparatus.) Such flows occur when (a) Ω is independent of time t; (b) u(r, t) is independent of the coordinate z (say) parallel to Ω, (c) the fluid has constant density and is therefore ‘barotropic’ (i.e. no density variations on horizontal surfaces) and (d) the topology of the cross-section of the (cylindrical) container, in planes z = constant, is such that the bounding surfaces can support the concomitant field of (kinematic) pressure P₁ satisfying P₁ + 2 Ω × U = 0 Condition (d) is equivalent to the requirement that any fluid sources or siks within the system be multipole in character, but not monopole. In the present study the ‘baroclinic’ case is treated, where buoyancy forces due to the action of gravity (and centripetal forces) on horizontal density variations have to be taken into account. These include investigations of flows due entirely to buoyancy forces, such as thermal convection in fluids in rotating cylindrical containers of various shapes and topological characteristics subject to horizontal temperature gradients. The implications for the impressed temperature field of the mathematical requirements that the fields of kinematic pressure P₁ and density (where denotes the mean density) be everywhere single-valued are guiding such investigations and facilitating the interpretation of their findings. The investigations include laboratory studies, reported elsewhere, of convection in a rotating fluid annulus with a circular cross-section blocked by a radial barrier, where it is found inter alia that advective heat transfer is virtually independent of |Ω| over a wide range of conditions. They also include (as yet unpublished) studies of thermal convection in rotating systems with topologically triply connected cross-sections which can be rendered doubly or simply connected by the insertation of suitable barriers.     

Transfer processes in a simulated urban street canyon

The transfer processes within and above a simulated urban street canyon were investigated in a generic manner. Computational fluid dynamics (CFD) was used to aid understanding and to produce some simple operational parameterisations. In this study we addressed specifically the commonly met situation where buoyancy effects arising from elevated surface temperatures are not important, i.e. when mechanical forces outweigh buoyancy forces. In a geophysical context this requires that some suitably defined Richardson number is small. From an engineering perspective this is interpreted as the important case when heat transfer within and above urban street canyons is by forced convection. Surprisingly, this particular scenario (for which the heat transfer coefficient between buildings and the flow is largest), has been less well studied than the situation where buoyancy effects are important. The CFD technique was compared against wind-tunnel experiments to provide model evaluation. The height-to-width ratio of the canyon was varied through the range 0.5–5 and the flow was normal to the canyon axis. By setting the canyon’s facets to have the same or different temperatures or to have a partial temperature distribution, simulations were carried out to investigate: (a) the influence of geometry on the flow and mixing within the canyon and (b) the exchange processes within the canyon and across the canyon top interface. Results showed that the vortex-type circulation and turbulence developed within the canyon produced a temperature distribution that was, essentially, spatially uniform (apart from a relatively thin near-wall thermal boundary layer) This allowed the temperatures within the street canyon to be specified by just one value T _can , the canyon temperature. The variation of T _can with wind speed, surface temperatures and geometry was extensively studied. Finally, the exchange velocity u _E across the interface between the canyon and the flow above was calculated based on a heat flux balance within the canyon and between the canyon and the flow above. Results showed that u _E was approximately 1% of a characteristic wind velocity above the street canyon. The problem of radiative exchange is not addressed but it can, of course, be introduced analytically, or computationally, when necessary.     

Approximation formulas for the microphysical properties of saline droplets

Microphysical theory has proven essential for explaining sea spray's role in transferring heat and moisture across the air–sea interface. But large-scale models of air–sea interaction, among other applications, cannot afford full microphysical modules for computing spray droplet evolution and, thus, how rapidly these droplets exchange heat and moisture with their environment. Fortunately, because the temperature and radius of saline droplets evolve almost exponentially when properly scaled, it is possible to approximate a droplet's evolution with just four microphysical endpoints: its equilibrium temperature, T_eq; the e-folding time to reach that temperature, τ_T; its equilibrium radius, r_eq; and the e-folding time to reach that radius, τ_r.Starting with microphysical theory, this paper derives quick approximation formulas for these microphysical quantities. These approximations are capable of treating saline droplets with initial radii between 0.5 and 500 μm that evolve under the following ambient conditions: initial droplet temperatures and air temperatures between 0 and 40 °C, ambient relative humidities between 75% and 99.5%, and initial droplet salinities between 1 and 40 psu.Estimating T_eq, τ_T, and τ_r requires only one-step calculations; finding r_eq is done recursively using Newton's method. The approximations for T_eq and τ_T are quite good when compared to similar quantities derived from a full microphysical model; T_eq is accurate to within 0.02 °C, and τ_T is typically accurate to within 5%. The estimate for equilibrium radius r_eq is also usually within 5% of the radius simulated with the full microphysical model. Finally, the estimate of radius e-folding time τ_r is accurate to within about 10% for typical oceanic conditions.     

Measurements of spray at an air-water interface

The spray content in the surface boundary layer above an air—water interface was determined by a series of measurements at various feteches and wind speeds in a laboratory facility. The droplet flux density N(z) can be described in terms of the scaling flux density N_* and von Karman constant K throguh the equation, N(z)/N_* = −(1/K) ln(z/z_0d) where z is height above the mean water level and z_0d is the droplet boundary layer thickness. N_* is given by a unique relationship in terms of the roughness Reynolds number u_*σ/ν where σ is the root-mean-square surface displacement. Spray inception occurred for u_* 0.3. The dominant mode of spray generation in the present and most other laboratory tests, as well as in available field data, appears to be bubble bursting.     

Dissipative effects on inertial flows over a sill

A systematic investigation of the effects of various parametrizations of dissipation, e.g. quadratic and linear frictional drag, harmonic lateral viscosity, and harmonic lateral diffusion on inertial flow over a sill and possible hydraulic control is presented. Rotation effects are ignored and the geometry is assumed to vary only slowly with downstream distance so that the flow may be considered one-dimensional. Results are given both for a single-active layer and for two-active layers with a rigid lid.If the parametrization is only a function of the dependent variables and not of their spatial derivatives, then it may be possible to hydraulically control the flow. A general expression is derived for the possible control point and the two gradients there, which are functions of the slope and possibly of flow rate. Specific energy is irreversibly removed from the flow and non-controlled as well as controlled flows can exhibit significant asymmetry in fluid depth over a sill. The upstream specific energy, and hence depth of the lower layer, of the controlled flow is greater than for an ideal fluid. Frictional effects modify the behaviour of long gravity waves, such that they are dispersive and damped with time. The system will only exhibit hydraulic control if these effects are small.For a viscous single layer of fluid, the gradient in surface elevation is always uniquely defined, so classically defined hydraulic control, as such, cannot exist. However, for values of non-dimensional lateral eddy viscosity coefficient, , where q is the flow rate, there is a narrow band of specific energies centred around that for the control solution in an ideal fluid, E_crit, for which the surface elevation, h is very asymmetric over the sill; the solutions resemble the inviscid, hydraulically controlled solutions. Outside this range, either the fluid depth tends to zero, or the surface elevation is almost uniform over the sill. A ‘control’-type solution exists which has the conjugate values of the inviscid equation up- and downstream of the sill, where the gradient in fluid depth, and hence the viscous term, is zero. For larger values of A_M, the band of specific energies is much wider, and the upstream specific energy of the ‘control’-type solution is much lower than that for an inviscid fluid. Long gravity waves are dispersive and damped with time. There is a short-wave cut-off, k² > h/(4A_M²), above which waves are stationary in the flow. Longer waves, k² h/(4A_M²), are critical if , as for an ideal fluid. If these waves can propagate significant distances, then any observed asymmetry in h will be due to inertial and not to viscous effects. The behaviour of unidirectional, two-layer flow is similar. The governing equation for viscous, two-layer exchange flow is singular, and typically excludes the ‘control’-type solutions found for unidirectional flows.Establishing the existence and behaviour of steady inertial flows in the presence of lateral diffusion between layers is more difficult. It significantly alters the single-layer solutions once the non-dimensional coefficient A_H is large, i.e. . The flow rate may become zero on the downslope as all the fluid diffuses into the inert, infinitely deep, overlaying layer. The fluid depth is maintained by reverse flow from downstream. In this case, the depth of the active layer tends to zero downstream for all values of specific energy. For two-layer flow, both unidirectional and exchange, the governing equation is such that the lower-layer flow rate and interfacial height return to their upstream values.Motivation for the study is provided by the increasingly fine spatial resolution achievable in large-scale numerical models of the ocean general circulation, and the question of whether they are capable of simulating some form of hydraulic control. Application to modelling oceanic flows over a sill is discussed.     

The reflection and diffraction of internal waves from the junction of a slit and a half-space, with application to submarine canyons

We consider the three-dimensional reflection and diffraction properties of internal waves in a continuously stratified rotating fluid which are incident on the junction of a vertical slit and a half-space. This geometry is a model for submarine canyons on continental slopes in the ocean, where various physical phenomena embodying reflection and diffraction effects have been observed. Three types of incident wave are considered: (1) Kelvin waves in the slit (canyon); (2) Kelvin waves on the slope; and (3) plane internal waves incident from the half-space (ocean). These are scattered into Kelvin and Poincaré waves in the slit, a Kelvin wave on the slope and Poincaré waves in the half-space. Most of the discussion is centered around case (1). Various properties of the wave field are calculated for ranges of the parameters c/cot θ, γα and ƒ/ω where cot θ is the topographic slope, c is the internal wave ray slope, α is the canyon half-width, γ is the down-slope wave-number, ƒ is the Coriolis parameter and ω is the wave frequency. Analytical results are obtained for small γα and some approximate results for larger values of γα. The results show that significant wave trapping may occur in oceanic situations, and that submarine canyons may act as source regions for internal Kelvin waves on the continental slope.     

Localized stirring in a field of salt-fingers

In a series of laboratory experiments, a partially mixed patch was produced in thick linear concentration gradients favorable to salt-finger convection. Salt-fingers, which give rise to an up-gradient flux of buoyancy, can reduce and invert the density gradient in the initial imposed patch. This leads to overturning convection within the patch if (a) the ratio of ambient T and S gradients, R_ρ=αT_z/βS_z, is near one; (b) the initial imposed turbulence results in a nearly well-mixed patch; and (c) the patch thickness is large enough that convective eddies are able to transport T and S faster than salt-fingers. Once overturning occurs, subsequent turbulent entrainment can lead to growth of the patch thickness. Experimental results for one-dimensional patches (layers) agree well with the theoretical prediction. This thickening is in contrast to the collapse that a partially mixed three-dimensional patch would experience due to lateral intrusion in a wide tank.     

The transport of CO2-induced warming into the ocean: an analysis of simulations by the OSU coupled atmosphere-ocean general circulation model

The OSU global coupled atmosphere-ocean general circulation model has been used to investigate a 2xCO₂-induced climate change. A previous analysis of the simulated 2xCO₂–1xCO₂ temperature differences showed that the CO₂-induced warming penetrated into the ocean and thereby caused a delay in the equilibration of the climate system with an estimatede-folding time of 50–75 years. The objective of the present study is to determine by what pathways and through which physical processes the simulated ocean general circulation produces the penetration of the CO₂-induced warming into the ocean.A global-mean oceanic heat budget analysis shows that the ocean gains heat at a rate of 3 W/m² due to the CO₂ doubling, and that this heat penetrates downward into the ocean predominantly through the reduction in the convective overturning. A zonal-mean oceanic heat budget analysis shows that the surface warming increases from the tropics toward the midlatitudes of both hemispheres and gradually penetrated into the deeper ocean, with a greater penetration in the subtropics and midlatitudes than in the equatorial region. The zonal-mean heat budget analysis also shows that the CO₂-induced warming of the ocean occurs predominantly through the down-ward transport of heat, with the meridional heat flux being only of secondary importance. In the tropics the penetration of the CO₂-induced heating is minimized by the upwelling of cold water. In the subtropics the heating is transported down-ward more readily by the downwelling existing there. In the high latitudes the suppressed convection plays the dominant role in the downward penetration of the CO₂-induced heating. The latter result should be considered as tentative, however, as the ocean component of the coupled model employed a prescribed surface salinity field and did not include the mechanism of brine rejection when sea water freezes into sea ice.     

Turbulence decay in stratified and homogeneous marine layers

A spectral approach is applied to shear-induced turbulence in stratified layers. A system of spectral equations for stationary balance of turbulent energy and temperature variances was deduced in the vicinity of the local shear scale L_U = (ε/U_Z³)^1/2. At wavenumbers between the inertial-convective (k^−5/3) and wak turbulence (k⁻³) subranges, additional narrow spectral intervals—‘production’ subranges—may appear (E k⁻¹, E_T k⁻²). The upper boundary of these subranges is determined as L_U, and the lower boundaries as L_R (ε/U_ZN²)^1/2(χ/T_Z²). It is shown that the scale L_U is a unique spectral scale that is uniform up to a constant value for every hydrophysical field. It appears that the spectral scale L_U is equivalent to the Thorpe scale L_Th for the active turbulence model. Therefore, if turbulent patches are generated in a background of permanent mean shear, a linear relation between temperature and mass diffusivities exists. In spectral terms, the fossil turbulence model corresponds to the regime of the Boldgiano-Obukhov buoyancy subrange (E k^−11/5, E_T k^−7/5). During decay the buoyancy subrange is expanded to lower and higher wavenumbers. At lower wavenumbers the buoyancy subrange is bounded by L_** = 3(χ^1/2/N^1/2T_Z), which is equivalent to the Thorpe scale L_Th. In such a transition regime only, when the viscous dissipation rate is removed from the set of main turbulence parameters, the Thorpe scale does not correlate with the buoyancy scale L_N ε^1/2/N^3/2 and fossil turbulence is realized. Oceanic turbulence measurements in the equatorial Pacific near Baker Island confirm the main ideas of the active and fossil turbulence models.