Although various numerical experiments have been carried out to investigate the cascade of internal tide energy associated with parametric subharmonic instability (PSI), most of them assume idealized oceanic situations, ignoring the existence of background relative vorticity (ζ). Here we show, for the first time, that the existence of ζ can significantly modify the behavior of PSI by changing the local effective Coriolis frequency ( ). A set of numerical experiments for 25.4°N show that the PSI efficiency significantly increases at the position where positive ζ shifts f_eff close to the M₁ critical frequency (ω = ω_M1). Furthermore, numerical experiments for 31°N, poleward of the M₁ critical latitude, show that significant PSI energy transfer is possible when negative ζ is low enough. The presented results provide important implications for understanding the spatial distribution of diapycnal mixing in the ocean where background geostrophic currents prevail.

Background: To evaluate the strain ratio (SR) combined with molecular pathological and serum markers for the diagnosis of breast masses. Methods: SR and 7-point scale elasticity scores were used with real-time tissue elastography and 2-dimensional color-Doppler ultrasound (US) to diagnose breast lesions in 311 hospitalized patients. Immunohistochemical staining and enzyme-linked immunosorbent assays (ELISAs) were used to examine pathological and serum tumor markers and their correlations with SR findings. Results: SR had a higher diagnostic value compared to the 7-point scale elasticity score, displaying an obvious low-to-high distribution from benign to malignant lesions with an optimal cutoff point at 3.88, which yielded an area under the curve (AUC) of 0.896 with 89.1% sensitivity, 85.6% specificity, and positive and negative predictive values of 91.0% and 82.8%, respectively. The differences of SR values between small (≤1.5 cm), large (>3 cm) (P=0.010), and moderate (>1.5 cm and ≤3 cm) sizes (P=0.038) in distinguishing benign from malignant breast masses were statistically significant, with SR being most specific and sensitive for diagnosing small lesions. Expression of 3 molecular pathological indicators (p75NTR, p63, and CK5/6), and 5 serum mastocarcinoma markers (uPA, PAI-I, CA27-29, CEA, and CA15-3) showed statistical significance (P<0.05) in distinguishing between benign and malignant breast lesions. Furthermore, SR combined with CA15-3 and CK5/6 positivity showed 94.2% sensitivity and 89.2% specificity as combined markers for triple-negative (TN) breast cancer, whereas SR combined with D2-40 and CK19 were good diagnostic markers for breast cancer lymph node metastasis. Conclusions: SR, together with a molecular and serological marker, may serve as an additional tool for the diagnosis of small breast cancer tumors.