Numerical Simulations of Melt-Driven Double-Diffusive Fluxes in a Turbulent Boundary Layer beneath an Ice Shelf

The transport of heat and salt through turbulent ice shelf-ocean boundary layers is a large source of uncertainty within ocean models of ice shelf cavities. This study uses small-scale, high resolution, 3D numerical simulations to model an idealised boundary layer beneath a melting ice shelf to investigate the influence of ambient turbulence on double-diffusive convection (i.e. convection driven by the difference in diffusivities between salinity and temperature). Isotropic turbulence is forced throughout the simulations and the temperature and salinity are initialised with homogeneous values similar to observations. The initial temperature and the strength of forced turbulence are varied as controlling parameters within an oceanographically relevant parameter space. Two contrasting regimes are identified. In one regime double-diffusive convection dominates, and in the other convection is inhibited by the forced turbulence. The convective regime occurs for high temperatures and low turbulence levels, where it is long-lived and affects the flow, melt rate and melt pattern. A criterion for identifying convection in terms of the temperature and salinity profiles, and the turbulent dissipation rate, is proposed. This criterion may be applied to observations and theoretical models to quantify the effect of double-diffusive convection on ice shelf melt rates.

Turbulent viscosity and magnetic Prandtl number from simulations of isotropically forced turbulence

Context. Turbulent diffusion of large-scale flows and magnetic fields plays a major role in many astrophysical systems, such as stellar convection zones and accretion discs. Aims. Our goal is to compute turbulent viscosity and magnetic diffusivity which are relevant for diffusing large-scale flows and magnetic fields, respectively. We also aim to compute their ratio, which is the turbulent magnetic Prandtl number, Pmt, for isotropically forced homogeneous turbulence. Methods. We used simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow. Turbulent viscosity was computed either from the resulting Reynolds stress or from the decay rate of the large-scale flow. Turbulent magnetic diffusivity was computed using the test-field method for a microphysical magnetic Prandtl number of unity. The scale dependence of the coefficients was studied by varying the wavenumber of the imposed sinusoidal shear and test fields. Results. We find that turbulent viscosity and magnetic diffusivity are in general of the same order of magnitude. Furthermore, the turbulent viscosity depends on the fluid Reynolds number (Re) and scale separation ratio of turbulence. The scale dependence of the turbulent viscosity is found to be well approximated by a Lorentzian. These results are similar to those obtained earlier for the turbulent magnetic diffusivity. The results for the turbulent transport coefficients appear to converge at sufficiently high values of Re and the scale separation ratio. However, a weak trend is found even at the largest values of Re, suggesting that the turbulence is not in the fully developed regime. The turbulent magnetic Prandtl number converges to a value that is slightly below unity for large Re. For small Re we find values between 0.5 and 0.6 but the data are insufficient to draw conclusions regarding asymptotics. We demonstrate that our results are independent of the correlation time of the forcing function. Conclusions. The turbulent magnetic diffusivity is, in general, consistently higher than the turbulent viscosity, which is in qualitative agreement with analytic theories. However, the actual value of Pmt found from the simulations (≈0.9−0.95) at large Re and large scale separation ratio is higher than any of the analytic predictions (0.4−0.8).

THEORETICAL STUDY OF THE SUPPLY ADDITIONAL AIR PARAMETERS FOR FORCED TURBULENCE OF THE CHARGE

The article touches upon the problem of the power unit’s operation, which has been modernized in order to increase its technical, economic and environmental indicators. Namely, it addresses the main issues of quantitative and qualitative mixture formation, the correct location of the fittings for supplying additional air is selected, the effect of additional air on the physical processes occurring in the cylinder of the power unit during its operation is determined. In addition, it considers the theoretical aspects of the dynamics of additional air introduced at the end of the filling and at the beginning of compression in the cylinder of the power unit. All of the above must be done so that the measures taken to improve the technical, economic and environmental indicators of the power unit do not contradict the conditions and requirements that were originally laid down by the manufacturer when developing this power unit. Firstly, today it is quite difficult to achieve this, the reason for this is the fact that the power units each time become more powerful in order to meet all the requirements that arise in the context of fierce competition between different manufacturers, and secondly - a high degree of unification of the constituent parts of automotive - tractor equipment and other transport technological machines and equipment that are equipped with ICE. Based on this, any refinement, even the slightest, leads to significant changes in all the main output parameters of the nodes and assemblies of the machine. In addition, it is necessary, whenever possible, to take into account all types of modernization that have been done by other researchers to improve the abovementioned parameters of the power unit.

Dimensional analysis of two-dimensional turbulence

We study the scaling properties of two-dimensional turbulence using dimensional analysis. In particular, we consider the energy spectrum both at large and small scales and in the “inertial ranges” for the cases of freely decaying and forced turbulence. We also investigate the properties of an “energy condensate” at large scales in spatially finite systems. Finally, an analysis of a possible inverse cascade in freely decaying turbulence is presented.

Laboratory experiments on the temporal decay of homogeneous anisotropic turbulence

We experimentally investigate the temporal decay of homogeneous anisotropic turbulence, monitoring the evolution of velocity fluctuations, dissipation and turbulent length scales over time. We employ an apparatus in which two facing random jet arrays of water pumps generate turbulence with negligible mean flow and shear over a volume that is much larger than the initial characteristic turbulent large scale of the flow. The Reynolds number based on the Taylor microscale for forced turbulence is $Re_{\unicode[STIX]{x1D706}}\approx 580$ and the axial-to-radial ratio of the root mean square velocity fluctuations is $1.22$. Two velocity components are measured by particle image velocimetry at the symmetry plane of the water tank. Measurements are taken for both ‘stationary’ forced turbulence and natural decaying turbulence. For decaying turbulence, power-law fits to the decay of turbulent kinetic energy reveal two regions over time; in the near-field region ($t/t_{L}<10$, $t_{L}$ is the integral time scale of the forced turbulence) a decay exponent $m\approx -2.3$ is found whereas for the far-field region ($t/t_{L}>10$) the value of the decay exponent was found to be affected by turbulence saturation. The near-field exhibits features of non-equilibrium turbulence with constant $L/\unicode[STIX]{x1D706}$ and varying $C_{\unicode[STIX]{x1D716}}$ (dissipation constant). We found a decay exponent $m\approx -1.4$ for the unsaturated regime and $m\approx -1.8$ for the saturated regime, in good agreement with previous numerical and experimental studies. We also observe a fast evolution towards isotropy at small scales, whereas anisotropy at large scales remains in the flow over more than $100t_{L}$. Direct estimates of dissipation are obtained and the decay exponent agrees well with the prediction $m_{\unicode[STIX]{x1D716}}=m-1$ throughout the decay process.

Electrokinetically Forced Turbulence in Microfluidic Flow

While laminar flow heat transfer and mixing in microfluidic geometries has been investigated experimentally, as has the effect of geometry-induced turbulence in microfluidic flow (it is well documented that turbulence increases convective heat transfer in macrofluidic flow), little literature exists investigating the effect of electrokinetically-induced turbulence on heat transfer at the micro scale. Using recently observed experimental data, this work employed computational fluid dynamics coupled with electromagnetic simulations to determine if electrokinetically-forced, low-Reynolds number turbulence could be observed in a rectangular microchannel with using Newtonian fluids. Analysis of the results was done via comparison to the experimental criteria defined for turbulent flow. This work shows that, even with a simplified simulation setup, computational fluid dynamics (CFD) software can produce results comparable to experimental observations of low-Reynolds turbulence in microchannels using Newtonian fluids. In addition to comparing simulated velocities and turbulent energies to experimental data this work also presents initial data on the effects of electrokinetic forcing on microfluidic flow based on entropy generation rates.