Deep neural networks (DNNs) are implemented in Super‐Parameterized Energy Exascale Earth System Model (SP‐E3SM) to imitate the shortwave and longwave radiative transfer calculations. These DNNs were able to emulate the radiation parameters with an accuracy of 90–95% at a cost of 8–10 times cheaper than the original radiation parameterization. A comparison of time‐averaged radiative fluxes and the prognostic variables manifested qualitative and quantitative similarity between the DNN emulation and the original parameterization. It has also been found that the differences between the DNN emulation and the original parameterization are comparable to the internal variability of the original parameterization. Although the DNNs developed in this investigation emulate the radiation parameters for a specific set of initial conditions, the results justify the need of further research to generalize the use of DNNs for the emulations of full model radiation and other parameterization for seasonal predictions and climate simulations.

Direct numerical simulation of flow past a sphere in a stratified fluid is carried out at a subcritical Reynolds number of 3700 and $Fr=U_{\infty }/ND=1,2$ and 3 to understand the dynamics of moderately stratified flows with $Fr=O(1)$. Here, $U_{\infty }$ is the free stream velocity, $N$ is the background buoyancy frequency and $D$ is the sphere diameter. The unstratified flow past the sphere consists of a separated shear layer that transitions to turbulence, a recirculation zone and a wake with a mean centreline deficit velocity, $U_{0}$, that decreases with downstream distance as a power law. With increasing stratification, the separated shear layer plunges inward vertically and its roll up is inhibited, the recirculation zone is shortened and the mean wake decays at a slower rate of $U_{0}\propto (x_{1}/D)^{-0.25}$ in the non-equilibrium (NEQ) region. The transition from the near wake where $U_{0}$ has a decay rate similar to the unstratified case to the NEQ regime occurs as an oscillatory modulation by a steady lee wave pattern with a period of $t=2\unicode[STIX]{x03C0}/N$ that leads to accelerated $U_{0}$ between $Nt=\unicode[STIX]{x03C0}$ and approximately $Nt=2\unicode[STIX]{x03C0}$. Far downstream, the wake is dominated by coherent horizontal motions. The acceleration of $U_{0}$ by the lee wave and the lower turbulence production in the NEQ regime, thereby less loss to turbulence, prolongs the lifetime of the wake relative to its unstratified counterpart. The intensity, temporal spectra and structure of turbulent fluctuations in the wake are assessed. Buoyancy induces significant anisotropy among the velocity components and between their vertical and horizontal profiles. Consequently, the near wake ($x_{1}/D<10$) exhibits significant differences in turbulence profiles relative to its unstratified counterpart. Spectra of vertical velocity show a discrete peak in the near wake that is maintained further downstream. The turbulent kinetic energy (TKE) balance is computed and contributions from pressure transport and buoyancy are found to become increasingly important as stratification increases. The findings of this investigation will be helpful in designing accurate initial conditions for the temporally evolving model of stratified wakes.

A numerical formulation for incompressible flows with stable stratification is developed using the framework of variational multiscale methods. In the proposed formulation, both density and temperature stratification are handled in a unified manner. The formulation is augmented with weakly-enforced essential boundary conditions and is suitable for applications involving moving domains, such as fluid-structure interaction. The methodology is tested using three numerical examples ranging from flow-physics benchmarks to a simulation of a full-scale offshore wind-turbine rotor spinning inside an atmospheric boundary layer. Good agreement is achieved with experimental and computational results reported by other researchers. The wind-turbine rotor simulation shows that flow stratification has a strong influence on the dynamic rotor thrust and torque loads.

Direct numerical simulations are performed to study the evolution of a towed stratified wake subject to external turbulence in the background. A field of isotropic turbulence is combined with an initial turbulent wake field and the combined wake is simulated in a temporally evolving framework similar to that of Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482). Simulations are performed for external turbulence whose initial level varies between zero and a moderate intensity of up to 7 % relative to the free stream and whose initial integral length scale is of the same order as that of the wake turbulence. A series of simulations are carried out at a Reynolds number of 10 000 and Froude number of 3. Background turbulence, especially at a level of 3 % or above, is found to have substantial quantitative effects in the stratified simulations. Turbulence inside the wake increases due to the entrainment of external turbulence, and the energy transfer through turbulent production from mean to fluctuating velocity also increases, leading to reduced mean velocity. The profiles of normalized mean and turbulence quantities in the stratified wake exhibit little change in the vertical direction but the horizontal spread increases in comparison to the case with undisturbed background. The spatial organization of the internal wave field is disrupted even at the 1 % level of external turbulence. However, key characteristics of stratified wakes such as the formation of coherent pancake vortices and the long lifetime of the mean wake are robust to the presence of fluctuations in the background. A corresponding series of simulations for the unstratified situation is carried out at the same Reynolds number of 10 000 and with similar levels of external turbulence. The change of mean and turbulence statistics is found to be weaker in the unstratified cases compared with the corresponding stratified cases and also weaker relative to that found by Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482) at a similar level of external turbulence relative to the free stream and similar integral length scale. Theoretical arguments and additional simulations are provided to show that the level of external turbulence relative to wake turbulence (dissimilar between the present investigation and Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482)) is a key governing parameter in both stratified and unstratified backgrounds.

Vortex dynamics in the flow past a sphere in a linearly stratified environment is investigated numerically. Simulations are carried out for a flow with Reynolds number of Re = 3700 and for several Froude numbers ranging from the unstratified case with Fr = ∞ to a highly stratified wake with Fr = 0.025. Isosurface of Q criterion is used to elucidate stratification effects on vortical structures near the sphere and in the wake. Vortical structures in the unstratified case are tube-like and show no preference in their orientation. Moderate stratification alters the orientation of vortical structures to streamwise preference but does not change their tube-like form. In strongly stratified cases with Fr ≤ 0.5, there is strong suppression in vertical motion so that isotropically oriented vortex tubes of approximately circular cross section are replaced by flattened vortex tubes that are horizontally oriented. At Fr = 0.025, pancake eddies and surfboard-like inclined structures emerge in the near wake and have a regular streamwise spacing that is associated with the frequency of vortex shedding from the sphere. Enstrophy variance budget is used to analyze the vortical structure dynamics. Increasing stratification generally decreases enstrophy variance for Fr ≥ O(1) cases. The flow enters a new regime in strongly stratified cases with Fr ≤ 0.25: increasing the stratification increases enstrophy variance, especially near the body. Stratification distorts the cross-sectional distribution of enstrophy variance from a circular isotropic shape in the unstratified wake into different shapes, depending on Fr and distance from the sphere, that include (1) elliptical distribution, (2) twin peaks suggestive of two-dimensional vortex shedding, and (3) triple-layer distribution where a relatively low enstrophy layer is sandwiched between the upper and the lower layers with high enstrophy. In the near wake, vortex stretching by fluctuating and mean strain are both responsible for enhancing vorticity. Increasing stratification (decreasing Fr) to O(1) values tends to suppress vortex stretching. Upon further reduction of Fr below 0.25, the vortex stretching takes large values near the sphere and, consequently, enstrophy variance in the near wake increases. The increase in vortex stretching is associated with unsteady, intermittent shedding of the boundary layer from the sides of the sphere in highly stratified wakes with Fr < 0.25.

The primary focus of this study is to contrast the influence of the mean velocity profile with that of the initial turbulence on the subsequent evolution of velocity and density fluctuations in a stratified wake. Direct numerical simulation is used to simulate the following cases: (a) a self-propelled momentumless turbulent wake, case SP50 with a canonical mean velocity profile, (b) a patch of turbulence, case TP1 with the same initial energy spectrum as (a), and (c) a patch of turbulence, case TP2 with a different initial energy spectrum with higher small-scale content. The evolution of the fluctuations is found to be strongly dependent on the initial energy spectrum, e.g., in case TP2, the kinetic energy is substantially smaller, and the late-wake vortices are less organized. The effect of the mean velocity field is negligible for mean kinetic energy (MKE) of the order 10% of the total kinetic energy and the evolution in this case is similar to a turbulent patch with the same initial energy spectrum. Increasing the MKE to 50% shows significant difference from the turbulent patch with the same initial energy spectrum during the initial stages of the evolution, but at later stages the evolution of turbulence statistics is similar. Both the turbulent patch and the momentumless wake show layering and formation of pancake eddies owing to buoyancy. Another objective of the paper is to compare the spatially evolving wake with the temporally evolving approximation when the initial near-wake condition of the temporal approximation is chosen to match the inflow of the spatially evolving model. The mean and turbulent flow statistics are found to agree well between the spatial and temporal computational models under these conditions.

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The heat transfer behaviour of convection-driven dynamos in a rotating plane layer between two parallel plates, heated from the bottom and cooled from the top, is investigated. At a fixed rotation rate (Ekman number, $E=10^{-6}$ ) and fluid properties (thermal and magnetic Prandtl numbers, $Pr=Pr_m=1$ ), both dynamo convection (DC) and non-magnetic rotating convection (RC) simulations are performed to demarcate the effect of magnetic field on heat transport at different thermal forcings (Rayleigh number, $Ra=3.83\times 10^{9}\text {--}3.83\times 10^{10}$ ). In this range, our turbulence resolving simulations demonstrate the existence of an optimum thermal forcing, at which heat transfer between the plates in DC exhibits maximum enhancement, as compared with the heat transport in the RC simulations. Unlike any global force balance reported in the literature, the present simulations reveal an increase in the Lorentz force in the thermal boundary layer, due to stretching of magnetic field lines by the vortices near the walls with a no-slip boundary condition. This increase in Lorentz force mitigates turbulence suppression due to the Coriolis force, resulting in enhanced turbulence and heat transfer.