Modulational instability of two obliquely interacting waves in presence of a thin pycnocline

Nonlinear evolution equations, correct up to fourth order in wave steepness, are derived for a pair of obliquely interacting wave packets in the presence of a thin pycnocline. These evolution equations are then employed to perform stability analysis of a pair of obliquely interacting uniform wave trains. Figures plotted here reveal that the growth rate of instability decreases with the increase in pycnocline depth and also with the increase in density difference across the pycnocline. When the angle of interaction between the two wave packets is less than certain critical value the growth rate of instability decreases with the increase in angle and beyond this critical value the result is reversed.