Stabilizing Buoyancy Flux Research Articles

Evolution of the Velocity Structure in the Diurnal Warm Layer

AbstractThe daily formation of near-surface ocean stratification caused by penetrating solar radiation modifies heat fluxes through the air–sea interface, turbulence dissipation in the mixed layer, and the vertical profile of lateral transport. The transport is altered because momentum from wind is trapped in a thin near-surface layer, the diurnal warm layer. We investigate the dynamics of this layer, with particular attention to the vertical shear of horizontal velocity. We first develop a quantitative link between the near-surface shear components that relates the crosswind component to the inertial turning of the along-wind component. Three days of high-resolution velocity observations confirm this relation. Clear colocation of shear and stratification with Richardson numbers near 0.25 indicate marginal instability. Idealized numerical modeling is then invoked to extrapolate below the observed wind speeds. This modeling, together with a simple energetic scaling analysis, provides a rule of thumb that the diurnal shear evolves differently above and below a 2 m s−1 wind speed, with limited sensitivity of this threshold to latitude and mean net surface heat flux. Only above this wind speed is the energy input sufficient to overcome the stabilizing buoyancy flux and thereby induce marginal instability. The differing shear regimes explain differences in the timing and magnitude of diurnal sea surface temperature anomalies.

Stratified Ekman layers evolving under a finite-time stabilizing buoyancy flux

Stratified flow in nocturnal boundary layers is studied using direct numerical simulation (DNS) of the Ekman layer, a model problem that is useful to understand atmospheric boundary-layer (ABL) turbulence. A stabilizing buoyancy flux is applied for a finite time to a neutral Ekman layer. Based on previous studies and the simulations conducted here, the choice of $L_{\mathit{cri}}^{+}=Lu_{\ast }/\unicode[STIX]{x1D708}\approx 700$ ($L$ is the Obukhov length scale and $u_{\ast }$ is the friction velocity) provides a cooling flux that is sufficiently strong to cause the initial collapse of turbulence. The turbulent kinetic energy decays over a time scale of $4.06L/u_{\ast }$ during the collapse. The simulations suggest that imposing $L_{\mathit{cri}}^{+}\approx 700$ on the neutral Ekman layer results in turbulence collapse during the initial transient, independent of Reynolds number, $Re_{\ast }$. However, the long-time state of the flow, i.e. turbulent with spatial intermittency or non-turbulent, is found to depend on the initial value of $Re_{\ast }$ since the cooling flux and resultant stratification increase with $Re_{\ast }$ for a given $L^{+}$. The lower-$Re_{\ast }$ cases have sustained turbulence with shear and stratification profiles that evolve in a manner such that the gradient Richardson number, $Ri_{g}$, in the near-surface layer, including the low-level jet, remains subcritical. The highest $Re_{\ast }$ case has supercritical $Ri_{g}$ in the low-level jet and turbulence does not recover. A theoretical discussion is performed to infer that the bulk Richardson number, $Ri_{b}$, is more suitable than $L^{+}$ to determine the fate of stratified Ekman layers at late time. DNS results support the implications of $Ri_{b}$ for the effect of initial $Re_{\ast }$ and $L^{+}$ on the flow.

Scaling Surface Mixing/Mixed Layer Depth under Stabilizing Buoyancy Flux

AbstractThis study concerns the combined effects of Earth’s rotation and stabilizing surface buoyancy flux upon the wind-induced turbulent mixing in the surface layer. Two different length scales, the Garwood scale and Zilitinkevich scale, have been proposed for the stabilized mixing layer depth under Earth’s rotation. Here, this study analyzes observed mixed layer depth plus surface momentum and buoyancy fluxes obtained from Argo floats and satellites, finding that the Zilitinkevich scale is more suited for observed mixed layer depths than the Garwood scale. Large-eddy simulations (LESs) reproduce this observed feature, except under a weak stabilizing flux where the mixed layer depth could not be identified with the buoyancy threshold method (because of insufficient buoyancy difference across the mixed layer base). LESs, however, show that the mixed layer depth if defined with buoyancy ratio relative to its surface value follows the Zilitinkevich scale even under such a weak stabilizing flux. LESs also show that the mixing layer depth is in good agreement with the Zilitinkevich scale. These findings will contribute to better understanding of the response of stabilized mixing/mixed layer depth to surface forcings and hence better estimation/prediction of several processes related to stabilized mixing/mixed layer depth such as air–sea interaction, subduction of surface mixed layer water, and spring blooming of phytoplankton biomass.

Direct numerical simulations of turbulent Ekman layers with increasing static stability: modifications to the bulk structure and second-order statistics

AbstractDirect numerical simulations of stably stratified Ekman layers are conducted to study the effect of increasing static stability on turbulence dynamics and modelling in wall-bounded flows at three moderate Reynolds numbers. The flow field is analysed by examining the mean profiles of wind speed, potential temperature and momentum flux, as well as streamwise velocity and temperature spectra. The maximum stabilizing buoyancy flux that a flow can sustain while remaining fully turbulent is found to depend on the Reynolds number. The flows with the highest Reynolds number display a relatively well-developed inertial range and logarithmic layer, and are found to bear similarities to much higher-Reynolds-number flows like the ones encountered in the atmospheric boundary layer. In particular, the near-wall mean profiles follow the Monin–Obukhov similarity theory. However, several flow features, such as the critical Richardson number and the stress–strain alignment, are found to maintain significant dependence on the Reynolds number. The budgets of turbulence kinetic energy (TKE), vertical velocity variance, momentum and buoyancy fluxes, and temperature variance are analysed. The results indicate that the effect of stability on turbulence is first directly manifested in the vertical velocity variance budget, and results in damping of vertical motions. This then leads to a reduction in the downward transport of horizontal momentum components towards the surface, and consequently to a decrease in the shear production term in the TKE budget: changes in the vertical profile of TKE shear production with increasing Richardson number are significant and have a larger impact on TKE than direct buoyancy destruction. The reduction in vertical velocity variance also results in significant drops in the production terms in the momentum flux, buoyancy flux and temperature variance budgets. Various assumptions and parameters related to low-order turbulence closures are investigated. The results suggest that the vertical velocity variance is a more appropriate parameter than the full TKE on which to base eddy-diffusivity and viscosity models.

Horizontal convection dynamics: insights from transient adjustment

AbstractThe dynamics of horizontal convection are revealed by examining transient adjustment toward thermal equilibrium. We restrict attention to high Rayleigh numbers (of $O(1{0}^{12} )$) and a Prandtl number ${\sim }5$ that characterize many practical applications, and consider responses to small changes in the thermal boundary conditions, using laboratory experiments, three-dimensional direct numerical simulations (DNS) and simple theoretical models. The experiments and the mechanical energy budget from the DNS demonstrate that unsteady forcing can produce flow dramatically more active than horizontal convection under steady forcing. The physical mechanisms at work are indicated by the time scales of approach to the new equilibrium, and we show that these can range over two orders of magnitude depending on the imposed change in boundary conditions. Changes that lead to a net destabilizing buoyancy flux give rapid adjustments: for applied heat flux conditions the whole of the circulation is controlled by conduction through the stable portion of the boundary layer, whereas for applied temperature difference the circulation is controlled by small-scale convection within the unstable part of the boundary layer. The experiments, DNS and models are in close agreement and show that the time scale under applied temperatures is as small as 0.01 vertical diffusion time scales, a factor of four smaller than for imposed flux. Both cases give adjustments too rapid for diffusion in the interior to play a significant role, at least through 99 % of the adjustment, and we conclude that diffusion through the full depth is not significant in setting the equilibrium state. Boundary changes leading to a net stabilizing buoyancy flux give a very different response, causing the convection to quickly form a shallow circulation cell, followed eventually by a return to full-depth overturning through a combination of penetrative convection and conduction. The time scale again varies by orders of magnitude, depending on the boundary conditions and the location of the imposed boundary perturbation.

The sensitivity of convection from a horizontal boundary to the distribution of heating

Results of experimental and numerical studies are presented for a class of horizontal thermal convection in a long box forced at one horizontal boundary by two regions of destabilizing buoyancy flux separated by a region of stabilizing buoyancy flux. The steady-state circulation with zero net heat input is examined. The circulation generally involves two plumes, one at each end of the box, which drive overturning throughout the domain. The flow is classified into three regimes according to the pattern of interior circulation and depending on the relative heat input applied to the two destabilizing regions. Unequal heat inputs can double the interior stratification above that created by symmetric flow with two identical plumes, and when the heat inputs differ by more than 10%, the interior stratification is set by the stronger plume. The arrangement of boundary forcing broadly parallels the distribution of the zonally averaged surface cooling and heating in the Northern and Southern Hemispheres, and the results suggest that ocean overturning circulations may be sensitive to interhemispheric differences in the buoyancy inputs.

Formation of a Diurnal Thermocline in the Ocean Mixed Layer Simulated by LES

Abstract The formation of a diurnal thermocline in the ocean mixed layer under a stabilizing buoyancy flux was simulated successfully by large-eddy simulation, reproducing various features consistent with observation. The analysis of the simulation result revealed that the formation of a diurnal thermocline passes through two different phases: the formation of a thermocline (formation stage) and increasing thickness of the thermocline thereafter (growth stage). Turbulent kinetic energy (TKE) flux dominates TKE production within the mixed layer, but turbulence maintained by shear production at the thermocline causes stratification below the mixed layer. In addition, once the thermocline is formed, both the gradient and flux Richardson numbers maintain constant values at the thermocline. It was also found that a diurnal thermocline cannot be formed in the absence of both wave breaking and Langmuir circulation. Furthermore, the effects of stratification on turbulence were investigated based on the time series of various physical variables of turbulence at the diurnal thermocline and within the mixed layer, and the mechanism for diurnal thermocline formation is discussed.

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 (Tellus, vol. 50, 1965, p. 242).

Convective instability mechanism for a binary mixture heated from above

It is shown that the intensification of a stabilizing buoyancy flux directed from the surface to the bulk of a binary mixture (e.g., salt water) may give rise to convective instability.

Dynamics of Diurnal Thermocline Formation in the Oceanic Mixed Layer

Abstract Diurnal thermocline formation in the oceanic mixed layer under a stabilizing buoyancy flux is studied by numerical simulation of a turbulence model in which the interaction between turbulence structure and density stratification is taken into consideration, and the mechanism for its formation is clarified based on the results. From the simulations, the flux of turbulent kinetic energy is a dominant source of turbulence in the upper mixed layer and plays an indispensable role for the formation of a diurnal thermocline; below the diurnal thermocline, turbulence is maintained by shear production, which causes the growth of diurnal thermocline thickness. The flux Richardson number at the diurnal thermocline maintains a constant value (about unity), regardless of the shear stress and buoyancy flux at the sea surface, and the diurnal thermocline depth grows more slowly than predicted by the Monin-Obukhov length scale. The model results are compared with the observational data, and the assumptions intro...

Onset of stratification in a mixed layer subjected to a stabilizing buoyancy flux

The formation of a thermocline in a water column, in which shear-free turbulence is generated both at the surface and bottom, and a stabilizing buoyancy flux is imposed at the surface, is studied using a laboratory experiment and a numerical model with the aim of understanding the formation of a tidal front in coastal seas. The results show that the formation of a thermocline, which always occurs in the absence of bottom mixing, is inhibited and the water column maintains a vertically mixed state, when bottom mixing becomes sufficiently strong. It is found from both experimental and numerical results that the criterion for the formation of a thermocline is determined by the balance between the rate of work that is necessary to maintain a mixed state against the formation of stratification by the buoyancy flux and the turbulent kinetic energy flux from the bottom supplied to the depth of thermocline formation. The depth of the thermocline, when it is formed, is found to decrease with bottom mixing.

A numerical model for the onset of stratification in shear-free turbulence

Abstract The formation of a thermocline in a water column, where shear-free turbulence is generated from both the surface and the bottom, and a stabilizing buoyancy flux is imposed on the surface, was studied using a numerical model with the aim of understanding the formation of a tidal front in the coastal area. The time evolutions of the distributions of density and turbulent kinetic energy calculated from the model shows that the emergence of a thermocline depends on the conditions determined by the buoyancy flux at the surface Q, the eddy diffusivities maintained at the bottom and at the surface Kb and Ks and the height of the water column H. The criterion for the formation of a thermocline was predicted as Rdelta4 ∼ constant for large δ (δ > 0.5), but the dependence on δ decreases as δ tends to 0, where R = H 4 Q/K 3 b , δ = 1 − D 0/H is the depth of a thermocline in the absence of bottom mixing. The depth of a thermocline was found to decrease as the bottom mixing increases for a given value of D 0....

A numerical study on the formation of a thermocline in shear-free turbulence

The formation of a thermocline generated by the interaction between a stabilizing buoyancy flux and shear-free turbulence was studied using a numerical model. The time evolutions of the vertical distributions of the buoyancy and turbulent kinetic energy were calculated and were used to evaluate the depth of the thermocline and the time required for its formation. The numerical results are compared with the results of previous laboratory experiments. The mechanisms responsible for the formation of the thermocline are discussed in view of the numerical results.

Turbulent mixing in a rotating, stratified fluid

Abstract An experimental study was carried out to investigate the effect of rotation on turbulent mixing in a stratified fluid when the turbulence in the mixed layer is generated by an oscillating grid. Two types of experiments were carried out: one of them is concerned with the deepening of the upper mixed layer in a stable, two-fluid system, and the other deals with the interaction between a stabilizing buoyancy flux and turbulence. In the first type of experiments, it was found that rotation suppresses entrainment at larger Rossby numbers. As the Rossby number becomes smaller (Ro 0.1), the entrainment rate increases with rotation—the onset of this phenomenon, however, was found to coincide with the appearance of coherent vortices within the mixed layer. The radiation of energy from the mixed layer to the lower non-turbulent layer was found to occur and the magnitude of the energy flux was found to be increased with the rotational frequency. It was also observed that vortices are generated, rather abrup...

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

Abstract 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 ( q 0 ) across the interface and through the turbulent layers (of depth D ) becomes steady and constant in magnitude in the vertical direction, only when q 0 ≅ 1.5 u 3 D , 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, Ri = ΔbD u 2 , 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.

Formation of thermoclines in zero-mean-shear turbulence subjected to a stabilizing buoyancy flux

Laboratory experiments in which a stabilizing buoyancy flux is imposed on zero-mean-shear turbulence generated by an oscillating grid are discussed. The buoyancy flux is imposed at the top of a water column either as a constant heat flux or by the continuous addition of fresh water at the top of a salt solution. Two types of experiments were carried out. In the first, the oscillating grid was positioned near the buoyancy input plane at the top of the water column to represent an input of turbulence kinetic energy near the surface. In this case a mixed layer was formed which extended from the surface down to a finite depth, and was bounded below by a stable thermocline. The mixed-layer depth remained constant in time but, contrary to earlier suggestions, was not found to be proportional to the Monin-Obukhov length. Instead the depth of the mixed layer was found to depend on the rate of decay of the turbulent kinetic energy with depth through the mixed layer. A second set of experiments was carried out with the grid positioned well below the surface to represent turbulence produced by bottom stirring. At low values of the buoyancy flux the fluid column remained well mixed, but once the buoyancy flux exceeded a critical value a stable stratification built up near the surface. Under certain conditions, a steady stratification was produced in which the diffusive flux balanced the turbulent flux in the mixed layer below. At larger values of the buoyancy flux, the diffusive flux is not large enough to remove the buoyancy from the surface and a ‘runaway’ stratification develops. The criterion for the formation of surface stratification is also found to depend on the rate of decay of the turbulent kinetic energy with depth, and the implications of this work for the formation of fronts produced by tidal stirring are discussed.

Turbulent mixing with stabilizing surface buoyancy flux

A laboratory experiment is studied with turbulence in salt water produced by an oscillating grid. A stabilizing buoyancy flux leads to a mixed layer depth that is proportional to the properly defined Monin–Obukhov length scale.