RYURAKU vs ViscousJoukowski

RYURAKU is an interactive educational simulation app for experiencing fluid dynamics phenomena firsthand. The 6th installment in the SUUGAKU / BUTURAKU / DENRAKU / HARAKU / NETURAKU series. The theme is "flow." Discover the wonders of fluid physics and the depth of physical laws through 10 hands-on simulations. [10 Simulations] 1. Streamline Visualization Visualize potential flow around a cylindrical obstacle in a uniform stream using particles. Drag the obstacle to move it and observe how the flow field changes in real time. 2. Bernoulli's Principle Visualize flow inside a Venturi tube. Watch how flow speed increases and pressure drops as the pipe narrows, with real-time pressure gauges. Intuitively understand the continuity equation A1v1 = A2v2. 3. Vortex Simulate point vortex creation and mutual induction. Tap to add a counterclockwise vortex, long press for clockwise. Observe complex vortex motion patterns. 4. Reynolds Number Visualize laminar-turbulent transition in pipe flow. Adjust flow speed, viscosity, and pipe diameter to manipulate the Reynolds number and experience the dramatic change at Re ≈ 2300. 5. Lift Force Visualize flow around an airfoil and the mechanisms behind lift and drag generation. Change the angle of attack or camber to see how the lift coefficient varies, with force vectors displayed in real time. 6. Kármán Vortex Street Visualize alternating vortex shedding behind a cylinder. Strouhal and Reynolds numbers are displayed in real time, helping you understand the relationship between shedding frequency, flow speed, and cylinder diameter. 7. Boundary Layer Visualize boundary layer development over a flat plate. Observe how viscous effects slow the fluid near the wall. Experience the transition from laminar (Blasius solution) to turbulent flow at the critical Reynolds number Re_x ≈ 5×10^5. 8. Magnus Effect Visualize the asymmetric flow and lift force around a spinning cylinder. Understand the physics behind curveballs in baseball, banana kicks in soccer, and slice shots in golf. 9. Darcy's Law [NEW] Visualize slow flow through a porous medium such as sand or rock. Adjust permeability, pressure gradient, and porosity to experience the law q = (k/μ)·∇P that governs groundwater, oil reservoirs, filters, and soil seepage. 10. Surface Wave [NEW] Visualize free-surface gravity waves. As the depth-to-wavelength ratio changes, particle orbits transition smoothly from circles (deep water) to flattened ellipses (shallow water). Directly observe the Airy dispersion relation ω^2 = gk·tanh(kh). [Features] - Real-time parameter adjustment for all simulations - Live physics formulas and numerical values - Japanese / English support - Dark mode / Light mode - Clean, intuitive UI [Monetization & Ads] - This app is free to download and use - No in-app purchases, no subscriptions, no paid unlocks - A banner ad (Google AdMob) is shown at the bottom of the screen - On iOS, personalized ads are only delivered after the user grants App Tracking Transparency (ATT) permission [Recommended for] - Students studying fluid dynamics in physics class - Anyone who wants to intuitively understand the behavior of flow - Teachers looking for interactive teaching materials - Anyone interested in aeronautical engineering or fluid mechanics

Are you interested in fluid dynamics? Viscous Joukowski simulates the flow around a Joukowski airfoil by solving the two-dimensional incompressible Navier–Stokes equations directly on your device. For teachers, students, and curious aerodynamicists, it provides an interactive way to explore how viscosity changes lift, drag, pressure, boundary layers, separation, and wake formation. Watch vorticity, speed, pressure, and streamlines evolve around the airfoil. Change the angle of attack, thickness, and camber by dragging directly on the flow field, or use precision controls. Adjust the Reynolds number to explore steady flow, separated wakes, starting vortices, and vortex shedding. Surface-pressure curves and aerodynamic-force estimates update as the simulation develops. The app also includes the classical analytical Joukowski potential-flow solution. Overlay it on the computed viscous pressure distribution to see where the ideal textbook model agrees with—or departs from—the Navier–Stokes result. In the potential solution, circulation is selected using the Kutta condition; in the viscous simulation, circulation and the wake develop dynamically from the no-slip flow. All calculations run locally using Apple MLX and GPU-accelerated Fourier methods. No server, account, or cloud computation is required.