## What is/are Linearly Stratified?

Linearly Stratified - Further, we have proposed a modification in the key nondimensional parameters [Rayleigh number Ra^{'} (signifying buoyancy) and Sherwood number Sh^{'} (signifying mass flux)] and droplet lifetime τ_{c}^{'}, based on the hypothesis of linearly stratified droplet surroundings (with revised concentration difference ΔC^{'}), taking into account the geometry of the confinements.^{[1]}Gravity currents produced from a full-depth lock release propagating at the base of a linearly stratified ambient are investigated by means of newly conducted three-dimensional high-resolution simulations in conjunction with corresponding two-dimensional simulations and laboratory experiments.

^{[2]}We consider small, physically consistent perturbations of a linearly stratified fluid that would result from a localized mixing near a particular depth.

^{[3]}The static linearly stratified state, which is an equilibrium of the unforced system, is not an equilibrium for any non-zero forcing amplitude.

^{[4]}Horizontal warm buoyant jets injecting into a linearly stratified ambience are common in lakes, estuaries, and oceans.

^{[5]}Flows past two spheres immersed in a horizontally moving, linearly stratified fluid are investigated at a moderate Reynolds number of 300.

^{[6]}The system instruments a vertical buoyant jet discharging in a linearly stratified environment.

^{[7]}Experimental results are obtained by towing a horizontal cylinder in a horizontal direction perpendicular to its axes, at a constant speed in a linearly stratified fluid made of salty water.

^{[8]}Coupled triads (two sets of resonant triads with one member in common) can arise in linearly stratified fluids.

^{[9]}We use analog experiments on relatively dense mono- and bi-disperse particle-freshwater and particle-saltwater jets injected into a linearly stratified saltwater layer to revisit, characterize and understand how transitions among Buoyant Plume (BP), Total Collapse (TC) and Partial Collapse (PC) multiphase jet regimes in a traditional source strength (−Ri0) - particle concentration (ϕ0) parameter space are modified by particle inertial effects expressed through a Stokes number (St) and particle buoyancy effects expressed through a Sedimentation number (Σ).

^{[10]}Selective withdrawal is commonly implemented in nonlinearly stratified ambient, which typically has stratified ambient conditions, for purposes of controlling quality.

^{[11]}A numerical model has been constructed and the investigation of the dynamics of a cylindrical localized region of turbulent disturbances in a longitudinal horizontally homogeneous shear flow of a linearly stratified fluid has been carried out.

^{[12]}The transient natural convection boundary-layer flow adjacent to a vertical plate heated with a time-dependent heat flux in an initially linearly stratified ambient fluid with Prandtl number (Pr) smaller than one was studied.

^{[13]}Experiments were conducted to investigate the response of outflow temperature to influencing factors in a nonlinearly stratified fluid with the particle image velocimetry (PIV) technique.

^{[14]}When a fountain is injected into a linearly stratified fluid, its behavior will be governed by the stratification of the ambient fluid, represented by the dimensionless temperature stratification parameter (s), in addition to the Reynolds number (Re) and the Froude number (Fr).

^{[15]}With an experimentally motivated ansatz that the downstream horizontal velocity and buoyancy structure is either i) entirely linearly stratified ii) consists of a well-mixed uniform lower region overlain by a linearly stratified region, we can relate the upstream conditions to the downstream conditions as a function of source Froude number, downstream gradient Richardson number, and a shape factor φ.

^{[16]}Numerical simulation of two coalescing turbulent forced plumes in linearly stratified fluids.

^{[17]}Laboratory studies considering the settling of a sphere in a linearly stratified fluid confirmed that stratification may dramatically enhance the drag on the body, but failed to identify the generic physical mechanism responsible for this increase.

^{[18]}Direct numerical simulations are used to characterize wind-shear effects on entrainment in a barotropic convective boundary layer (CBL) that grows into a linearly stratified atmosphere.

^{[19]}Two zero-order bulk models (ZOMs) are developed for the velocity, buoyancy, and moisture of a cloud-free barotropic convective boundary layer (CBL) that grows into a linearly stratified atm.

^{[20]}When a torus oscillates horizontally in a linearly stratified fluid, the wave rays form a double cone, one upward and one downward, with two focal points where the wave amplitude has a maximum due to wave focusing.

^{[21]}

## linearly stratified fluid

We consider small, physically consistent perturbations of a linearly stratified fluid that would result from a localized mixing near a particular depth.^{[1]}Flows past two spheres immersed in a horizontally moving, linearly stratified fluid are investigated at a moderate Reynolds number of 300.

^{[2]}Experimental results are obtained by towing a horizontal cylinder in a horizontal direction perpendicular to its axes, at a constant speed in a linearly stratified fluid made of salty water.

^{[3]}Coupled triads (two sets of resonant triads with one member in common) can arise in linearly stratified fluids.

^{[4]}A numerical model has been constructed and the investigation of the dynamics of a cylindrical localized region of turbulent disturbances in a longitudinal horizontally homogeneous shear flow of a linearly stratified fluid has been carried out.

^{[5]}Experiments were conducted to investigate the response of outflow temperature to influencing factors in a nonlinearly stratified fluid with the particle image velocimetry (PIV) technique.

^{[6]}When a fountain is injected into a linearly stratified fluid, its behavior will be governed by the stratification of the ambient fluid, represented by the dimensionless temperature stratification parameter (s), in addition to the Reynolds number (Re) and the Froude number (Fr).

^{[7]}Numerical simulation of two coalescing turbulent forced plumes in linearly stratified fluids.

^{[8]}Laboratory studies considering the settling of a sphere in a linearly stratified fluid confirmed that stratification may dramatically enhance the drag on the body, but failed to identify the generic physical mechanism responsible for this increase.

^{[9]}When a torus oscillates horizontally in a linearly stratified fluid, the wave rays form a double cone, one upward and one downward, with two focal points where the wave amplitude has a maximum due to wave focusing.

^{[10]}

## linearly stratified ambient

Gravity currents produced from a full-depth lock release propagating at the base of a linearly stratified ambient are investigated by means of newly conducted three-dimensional high-resolution simulations in conjunction with corresponding two-dimensional simulations and laboratory experiments.^{[1]}Selective withdrawal is commonly implemented in nonlinearly stratified ambient, which typically has stratified ambient conditions, for purposes of controlling quality.

^{[2]}The transient natural convection boundary-layer flow adjacent to a vertical plate heated with a time-dependent heat flux in an initially linearly stratified ambient fluid with Prandtl number (Pr) smaller than one was studied.

^{[3]}