Salt-finger convection provides a key mixing process in geophysical and astrophysical fluid flows. Because of its small characteristic spatial scale and slow diffusive time scale, this process must be parameterized in geophysical and astrophysical models, where relations linking background gradients to fluxes are required. To obtain such relations, most authors study the dependence of temperature and salinity fluxes on fixed background gradients. Using the reduced model derived by Xie et al. [“A reduced model for salt-finger convection in the small diffusivity ratio limit,” Fluids 2(1), 6 (2017)] for salt-finger convection in the limit of small diffusivity and large density ratios, this paper considers the conjugate problem where the fluxes are fixed, but the mean gradients are permitted to adjust in response. In small domains, the fixed-flux condition leads to stable single-mode solutions, which are not achievable with fixed-gradient conditions. In large domains, with statistically steady saturated states, the relations between mean fluxes and mean gradients are identical for both sets of conditions. The fixed-flux condition provides a new perspective for understanding the resulting statistically steady states by identifying two distinct regimes with the same dissipation rate. We find that the statistically steady dynamics select the state with the smaller Rayleigh ratio Ra subject to the constraint Ra > 1, ensuring that the background state is linearly unstable. The fixed-flux formulation results in a more potent restoring mechanism toward the statistically steady state, with a smaller variance, skewness, and characteristic time scale than in the fixed-gradient setup. This distinctive feature can be used as a diagnostic to determine whether in situ salt-finger convection is flux-driven or gradient-driven.
Acoustic and electromagnetics to artificial intelligence (AETA) is a system used to predict seismic events through monitoring of electromagnetic and geoacoustic signals. It is widely deployed in the Sichuan–Yunnan region (22° N–34° N, 98° E–107° E) of China. Generally, the electromagnetic signals of AETA stations near the epicenter have abnormal disturbances before an earthquake. When a significant decrease or increase in the signal is observed, it is difficult to quantify this change using only visual observation and confirm that it is related to an upcoming large earthquake. Considering that the AETA data comprise a typical time series, current work has analyzed the anomalism of AETA electromagnetic signals using the long short-term memory (LSTM) autoencoder method to prove that the electromagnetic anomaly of the AETA station can be regarded as an earthquake precursor. The results show that there are 2–4% anomalous points and some outliers exceeding 0.7 (after normalization) in the AETA stations within 200 km of the epicenter of the Jiuzaigou earthquake (M. 7.0) and the Yibin earthquake (M. 6.0) half a month before the earthquakes. Therefore, the AETA electromagnetic disturbance signal can be used as an earthquake precursor and for further earthquake prediction.
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