Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHindered energy cascade in highly helical isotropic turbulence
111
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The conventional approach to the turbulent energy cascade, based on Richardson-Kolmogorov phenomenology, ignores the topology of emerging vortices, which is related to the helicity of the turbulent flow. It is generally believed that helicity can play a significant role in turbulent systems, e.g., supporting the generation of large-scale magnetic fields, but its impact on the energy cascade to small scales has never been observed. We suggest for the first time a generalized phenomenology for isotropic turbulence with an arbitrary spectral distribution of the helicity. We discuss various scenarios of direct turbulent cascades with new helicity effect, which can be interpreted as a hindering of the spectral energy transfer. Therefore the energy is accumulated and redistributed so that the efficiency of non-linear interactions will be sufficient to provide a constant energy flux. We confirm our phenomenology by high Reynolds number numerical simulations based on a shell model of helical turbulence. The energy in our model is injected at a certain large scale only, whereas the source of helicity is distributed over all scales. In particular, we found that the helical bottleneck effect can appear in the inertial interval of the energy spectrum.
rate research
Read More
In this work, the scaling statistics of the dissipation along Lagrangian trajectories are investigated by using fluid tracer particles obtained from a high resolution direct numerical simulation with $Re_{lambda}=400$. Both the energy dissipation rate $epsilon$ and the local time averaged $epsilon_{tau}$ agree rather well with the lognormal distribution hypothesis. Several statistics are then examined. It is found that the autocorrelation function $rho(tau)$ of $ln(epsilon(t))$ and variance $sigma^2(tau)$ of $ln(epsilon_{tau}(t))$ obey a log-law with scaling exponent $beta=beta=0.30$ compatible with the intermittency parameter $mu=0.30$. The $q$th-order moment of $epsilon_{tau}$ has a clear power-law on the inertial range $10<tau/tau_{eta}<100$. The measured scaling exponent $K_L(q)$ agrees remarkably with $q-zeta_L(2q)$ where $zeta_L(2q)$ is the scaling exponent estimated using the Hilbert methodology. All these results suggest that the dissipation along Lagrangian trajectories could be modelled by a multiplicative cascade.
We investigate non-equilibrium turbulence where the non-dimensionalised dissipation coefficient $C_{varepsilon}$ scales as $C_{varepsilon} sim Re_{M}^{m}/Re_{ell}^{n}$ with $mapprox 1 approx n$ ($Re_M$ and $Re_{ell}$ are global/inlet and local Reynolds numbers respectively) by measuring the downstream evolution of the scale-by-scale energy transfer, dissipation, advection, production and transport in the lee of a square-mesh grid and compare with a region of equilibrium turbulence (i.e. where $C_{varepsilon}approx mathrm{constant}$). These are the main terms of the inhomogeneous, anisotropic version of the von K{a}rm{a}n-Howarth-Monin equation. It is shown in the grid-generated turbulence studied here that, even in the presence of non-negligible turbulence production and transport, production and transport are large-scale phenomena that do not contribute to the scale-by-scale balance for scales smaller than about a third of the integral-length scale, $ell$, and therefore do not affect the energy transfer to the small-scales. In both the non-equilibrium and the equilibrium decay regions, the peak of the scale-by-scale energy transfer scales as $(overline{u^2})^{3/2}/ell$ ($overline{u^2}$ is the variance of the longitudinal fluctuating velocity). In the non-equilibrium case this scaling implies an imbalance between the energy transfer to the small scales and the dissipation. This imbalance is reflected on the small-scale advection which becomes larger in proportion to the maximum energy transfer as the turbulence decays whereas it stays proportionally constant in the further downstream equilibrium region where $C_{varepsilon} approx mathrm{constant}$ even though $Re_{ell}$ is lower.
The 4/5-law of turbulence, which characterizes the energy cascade from large to small-sized eddies at high Reynolds numbers in classical fluids, is verified experimentally in a superfluid 4He wind tunnel, operated down to 1.56 K and up to R_lambda ~ 1640. The result is corroborated by high-resolution simulations of Landau-Tiszas two-fluid model down to 1.15 K, corresponding to a residual normal fluid concentration below 3 % but with a lower Reynolds number of order R_lambda ~ 100. Although the Karman-Howarth equation (including a viscous term) is not valid emph{a priori} in a superfluid, it is found that it provides an empirical description of the deviation from the ideal 4/5-law at small scales and allows us to identify an effective viscosity for the superfluid, whose value matches the kinematic viscosity of the normal fluid regardless of its concentration.
Small scale characteristics of turbulence such as velocity gradients and vorticity fluctuate rapidly in magnitude and oscillate in sign. Much work exists on the characterization of magnitude variations, but far less on sign oscillations. While averages performed on large scales tend to zero because of the oscillatory character, those performed on increasingly smaller scales will vary with the averaging scale in some characteristic way. This characteristic variation at high Reynolds numbers is captured by the so-called cancellation exponent, which measures how local averages tend to cancel out as the averaging scale increases, in space or time. Past experimental work suggests that the exponents in turbulence depend on whether one considers quantities in full three-dimensional space or uses their one- or two-dimensional cuts. We compute cancellation exponents of vorticity and longitudinal as well as transverse velocity gradients in isotropic turbulence at Taylor-scale Reynolds number up to 1300 on $8192^3$ grids. The 2D cuts yield the same exponents as those for full 3D, while the 1D cuts yield smaller numbers, suggesting that the results in higher dimensions are more reliable. We make the case that the presence of vortical filaments in isotropic turbulence leads to this conclusion. This effect is particularly conspicuous in magnetohydrodynamic turbulence, where an increased degree of spatial coherence develops along the imposed magnetic field.
The low wavenumber expansion of the energy spectrum takes the well known form: $ E(k,t) = E_2(t) k^2 + E_4(t) k^4 + ... $, where the coefficients are weighted integrals against the correlation function $C(r,t)$. We show that expressing $E(k,t)$ in terms of the longitudinal correlation function $f(r,t)$ immediately yields $E_2(t)=0$ by cancellation. We verify that the same result is obtained using the correlation function $C(r,t)$, provided only that $f(r,t)$ falls off faster than $r^{-3}$ at large values of $r$. As power-law forms are widely studied for the purpose of establishing bounds, we consider the family of model correlations $f(r,t)=alpha_n(t)r^{-n}$, for positive integer $n$, at large values of the separation $r$. We find that for the special case $n=3$, the relationship connecting $f(r,t)$ and $C(r,t)$ becomes indeterminate, and (exceptionally) $E_2 eq 0$, but that this solution is unphysical in that the viscous term in the K{a}rm{a}n-Howarth equation vanishes. Lastly, we show that $E_4(t)$ is independent of time, without needing to assume the exponential decrease of correlation functions at large distances.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
